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Readers’ Reviews of the Big Fat Genius Guide to LSAT Logic Games

It is the best written, most concise, and most coherent book about the LSAT on the market. It reinforces the concepts taught, and I found it very engaging (which I cannot say about most LSAT books). I received a 173, but more importantly I scored a perfect games section. I tell everyone I can to get this book. — M. P. This book helped me a lot. I used to finish only 3 games, but Brian's method helped me make it through all of them. After reading this book, I took the LSAT in October (for the second time) and got a 175 (which was 9 points higher than my first score). I liked the way this book really broke down the questions by category and guided me through the process of studying. Games was by far my worst section before I began to use the Big Fat Genius Guide, but I got all of the questions in the games section correct on the day of the actual test. I would recommend the book to anyone; it was better than all of the other books I used. — M. M. The Big Fat Genius Guide to the logic games was the best $40 I have ever spent. When I bought the book, I was running out of time on every practice logic games section I did, and on average getting about half of the questions wrong. After reading it and practicing with it, I was finishing on time and averaging one question wrong per game. I took the October LSAT, I answered every single question right, AND I finished an insane 12 minutes ahead of time!!! Thanks to this book, the answers in the logic games just pop out at me. Logic games were the one section I had trouble with before studying from this book, and on the actual test it was my best section! I am in love with this book. — C. J. I cannot express how great a favor Brian Talbot has done for the luckless souls like myself who've gone through Stanley Kaplan courses and come out the other side convinced they were never going to get more than half of the Logic Games questions right. In my wildest dreams I never thought that my strongest section would be the games, but it was, and I scored a 168 on the LSAT. The efficacy and clarity of the method, and the depth to which it is thought through, are nothing short of remarkable. The book teaches a method of solving logic games based on simple principles applied efficiently and quickly. The prose style is friendly and reassuring. This method is utterly different from anything I’d learned before. You can really get a high score on the Logic Games section. Not just a "getting-by score" or a "better than I thought I'd do score," but a high score. For people like me, for whom the Logic Games were the most daunting section, this book is incredibly useful. — M. J. Turn the page for more reader reviews

More Readers’ Reviews of the Big Fat Genius Guide to LSAT Logic Games

This book is simply outstanding. It is clear in its explanations and concise in its methods. With this combination, it offers you a powerful weapon to score well on the games section. I improved 14 points, and I know that this book was key to that success. — J. Z. I was absolutely "stuck" on the logic games section – it was what handicapped me the first time I took the LSAT, when I missed roughly half the logic games questions. I got every other prep book out there, and they only made my problem worse – infinite game types and setups to memorize, etc. By a few weeks before my second LSAT, I was at a point of extreme desperation. This book was akin to divine revelation – it's concise and conversational, and the answer to all logic games hang-ups. Brian Talbot tells you that all logic games are basically THE SAME, and that they can all be solved using one straightforward method. I went from missing half the questions on logic games to missing only three – I improved my LSAT score to a 166, and I honestly owe almost all of that improvement to this book. If you can only buy one, get this one – no BS, it's the best book out there. — L. H. I cannot say enough good things about this book. I studied for almost two months, and my scores jumped more than 15 points! When I took the exam, I was so relaxed that I flew through the questions. I started to worry that I was doing something wrong, but took Brian's advice and relaxed. He said not to stress over the answers, they had to be right, because I knew how to take the exam and beat it. I did. I only missed two questions in the entire section, a personal best! I have recommended this book to everyone I know and will continue to do so! — L. E. The book is exceptional – Brian's manner and conversation-like writing style are a great way to learn a difficult subject (perhaps the most challenging part of the LSAT). He analyzes a selection of games in sequence from easy to (very) difficult and, along the way, teaches you principles and methods that will help you attack games that you have never seen. He explains what you should have achieved at each stopping point and makes suggestions about what to do and what to not do. I found it a comfortable way to learn. If you trust the methods, they will work for you and you will come out of the test knowing you did great. I made quantum leaps in my skill with this book – it worked for me. If I had it to do over again, I'd use this book again. It's worth every cent! — J. R.

THE

BIG FAT GENIUS GUIDE TO LSAT LOGIC GAMES

BY

BRIAN TALBOT

THE BIG FAT GENIUS GUIDE TO LSAT LOGIC GAMES Copyright © 2004 by Brian Talbot. All rights reserved. Cover design copyright © 2004 by Mariya Ishkhanova. Published by Big Fat Genius. WWW.BIGFATGENIUS.COM Big Fat Genius is a trademark of Brian Talbot. This book and its author is not affiliated with the Law School Admissions Council, Inc., who are the creators of the LSAT. LSAC does not review or endorse specific test preparation materials or services, and the reference to LSAT questions within this work does not imply the review or endorsement of LSAC. LSAT is a registered trademark of LSAC. ISBN: 0-9763959-0-8

For their invaluable assistance in making this book what it is, I would like to thank Jeremy Moreno-Gershman and Valeri Williams.

For his support and belief in my ability, I would like to thank my grandfather Hersey Steinwinter

Table of Contents Introduction

1

How to Use This Book

3

Studying Timeline

7

Studying Guide

9

How to Take the LSAT Logic Games Section

21

The Fundamentals

29

Game One

52

"If… then…" Rules and Negations

64

Game Two

76

Game Three

96

The Five Most Important Skills

112

Intermediate Techniques

115

Game Four

120

Game Five

134

Game Six

146

Game Seven

162

Game Eight

176

Advanced Techniques

192

Game Nine

204

Game Ten

220

Game Eleven

234

Game Twelve

246

Timing for the Section

261

Before the Test

266

During the Test

268

Glossary

273

Introduction

1

Introduction My name is Brian Talbot, and I am going to teach you how to answer LSAT logic games questions faster and more accurately than you do now. Before we get started, I'd like to address a couple of basic questions: first, what are LSAT logic games, and second, why should you listen to me? Every LSAT consists of six sections. Two of these are Logical Reasoning – these sections consist of paragraphs followed by single questions, such as "What does the above argument assume?" or "Which of the following best supports the author's conclusion?" Another section is called Reading Comprehension. In this section you will have to read four longer passages (generally four or five paragraphs) and answer questions about the contents of each passage. There is also a section called Analytical Reasoning, where you will be presented with four odd situations, governed by seemingly arbitrary rules, and asked questions about how the situation may or may not be arranged, given the rules. This is the section I, and most LSAT teachers, call logic games. The LSAT also has an Experimental section, which will be the same format as one of the three sections I just described. In the Experimental section the makers of the LSAT test out new questions; you will not be told when you are working on the Experimental section. Finally, at the end of the test, you will be required to write a short Writing Sample. This book is only about the Analytical Reasoning section (which I will call the "logic games" section from now on). If you've never studied for the LSAT before, you may wonder why I devote an entire book to this one section. For the vast majority of people, logic games are the single most difficult aspect of the LSAT. Yet this section can be made the most straightforward section of the test if you follow a series of fairly simple rules. The goal of this book is to teach you those rules. Now to answer the second question: why should you listen to what I have to say about logic games? I took the LSAT in June of 1994. On the first sample LSAT I ever took before I started studying, I got in the upper 150s, which I wasn't happy about. Logic games was the section that held me back. I studied smart and got a 176 on the actual test. I got my law degree from UC Berkeley in 1998, took and passed the California Bar in 1999, and then realized I liked teaching better than the law. In other words, I've been where you are now, I struggled and succeeded, and (except for the deciding not to practice part), I've been where you are going. I've been teaching the LSAT since 1996, originally for a large national test preparation company. In January of 2001, I started Big Fat Genius, a company dedicated to teaching students my system for approaching the LSAT (and GMAT). In the time I've been teaching, I've seen more students than I can count, and I've worked individually with a large number of them. With Big Fat Genius I work almost exclusively as a one-on-one tutor. This has allowed me to study in a very focused way the types of problems students have on LSAT logic games, to work out strategies to deal with the games, and to see how students are able to use these strategies. I create all the lessons for my students, I develop all the techniques, and I get to see first-hand those techniques applied by students. This has allowed me to refine and hone my approach to the test.

2

Introduction

What you have in your hands, then, is the result of seven years of constant improvement in my approach to logic games, and in my teaching. All of these techniques have been tested by me and by students. These techniques are designed not only to be as efficient and accurate as possible, but also to be learnable and apply-able by practically anyone – it does me no good to have a perfect system if no one but me can use it. This book is written with my teaching experiences in mind. I have done my best to make it readable, somewhat enjoyable, clear, and thorough. My students often come to me after going through entire courses with other companies. Thus, I have been able to compare my system to those taught by every major test preparation company – Kaplan, Princeton Review, Test Masters, Power Score. My system is significantly different from each of theirs; it is simpler, easier to learn, easier to apply, and more effective in more LSAT situations. The final proof of the system is up to you. Read this book, apply what it says, and experience the score improvement.

How to Use This Book

3

How to Use This Book Before We Begin There are two things you need to do before you start using this book. First, you need to look at at least a couple of logic games. It will be much easier for you to understand what it is you are supposed to be learning if you have a bit of context. I expect that most of you have at least a little logic games experience – you wouldn't be buying a book just on logic games if you weren't a little bit worried about them, and you wouldn't be worried about them if you hadn't done them before. For those of you who haven't seen an LSAT logic game before, go to www.lsac.org (not .com, which is a yachting club). You can download a sample LSAT there (at the time of this writing, if you put your mouse over the "Downloadable Forms and Documents" button on the left, a new menu will appear; click on "Sample LSAT." Of course, knowing the internet, the page will change ten times this year). Download it (wait – don't download it until you've read the next paragraph). This test is the same test given in October of 1996 (minus the Experimental section); section 3 of the test is logic games. Work through that section; time yourself, but don't stop when your time is up. Timing yourself at this point is just to get a feeling for how long these things take. Now we all know what LSAT logic games are. The other thing you need to do before you start using this book is to make sure that you have access to some LSATs to study from. This book contains twelve logic games, all of which come from actual, previously administered LSATs. But you will need more games to practice on, and you should only practice from real LSATs (if you have a book with logic games in it, but you don't know if they are actual real LSATs, check the beginning of the book where the copyright information is; if the book doesn't attribute its questions to LSAC, it doesn't contain real LSATs). You can order LSATs at www.lsac.org. I recommend ordering at least ten LSATs to study from. You should always try to get the newest LSATs available (the higher the number of the LSAT, the newer it is – December 2003 is 42, for example), because the logic games have changed a bit over the years (that's why in this book I only use games from 1999 and later). LSAC sells a book called The Next Ten Actual, Official LSAT PrepTests which contains ten of the more recent tests (tests 29 through 38), although not the most recent ones. Ordering this book and whatever more recent (higher numbered) LSATs are currently available would give you a good number of tests to work from without forcing you to spend too much money. If you want more exams than that I also recommend 10 More Actual, Official LSAT PrepTests from LSAC. It contains LSATs 19 through 28 in one book, and is fairly economical (note the title is "More actual…"). Don't bother ordering 10 Actual, Official LSAT PrepTests (without the "more"), or any of the Triple Prep books; the tests in these books are old and the games are somewhat outdated. If you don't have access to LSATs to study from (or you don't have enough), order them now, so that they will have arrived by the time you need them. You can still study from this book while you wait for them to arrive, but by the time you finish the chapter called Game Three you need to have some LSATs on hand. Some of you may have access to LSATs that are not numbered; I know that some test prep companies give their students old LSATs but put the test administration date on them rather than the number that LSAC uses. To help you out, I've put a list of the recent LSATs (19 and on) and the date they were administered at the end of this chapter. OK, those are the basics out of the way.

4

How to Use This Book

Using This Book Everyone who uses this book should use it in the same way. It doesn't matter how much LSAT experience you have. Begin at the beginning of the book and go through it word by word, chapter by chapter. Chapters will tell you if you should reread previous chapters, or if you should do work outside the book (and they will give you suggestions on what to do). Some of you who have studied logic games extensively before this may want to skip around in the book, or jump to the more "advanced" techniques given at the end. Don't do this. As I said in the Introduction, the techniques in this book are on the cutting edge of LSAT thought. They are different from anything you are likely to have seen before; even the most basic things I teach, like diagramming games and writing down rules, are very different from the way other companies approach games. You may find that, while you are pretty good at the games now, the fundamental techniques I teach suddenly help you see the games in a whole new way and that you make a large improvement without using any of the "advanced" techniques. In fact, I will argue in the course of the book that the fundamental, "basic" techniques are much more crucial to your score than the "advanced" ones. I give two possible schedules for how to use this book – one for people who have only two weeks to study logic games, one for people who have more than two weeks – in the chapter entitled Studying Timeline. The two-week plan is very rushed, so don't use it if you can avoid it. This book is written a little idiosyncratically. First, I write in a sort of "chatty" style. I like to ask you questions, as if you were really sitting with me studying. I do this for a very good reason. Human beings have been talking for tens of thousands of years. We have only been reading and writing for a couple thousand, and it has only been in the last century that anything like a majority of us have been literate. We have evolved as talkers, not as readers. Thus, we understand things better by talking them out than by reading them. I can't talk to each of you individually, but I can write a book that simulates the way we learn through dialogue. So, when I ask you a question in the text, I expect you to stop reading, think about it, and give your best answer. Then keep on reading and see how your answer compares to mine; if it isn't close, you haven't been understanding what you have been reading, so you might want to go back and reread it. Why do I do this? Because you think better by talking things through; answering questions allows you to activate those dialogue centers of your mind. Plus, it keeps you awake and engaged. Just to review, you should have answered that question ("Why do I do this?") when I asked it. However, the second answer I gave (about keeping you awake) wasn't in the text, so don't worry if you didn't give that as an answer. Second, I like to underline things. If I underline something, it is something I think you need to remember. There are lots of things in this book you should remember, that you will want to remember. I won't underline all of them – the book would be 90% underlined. But I will underline the most crucial concepts, the ones that are most essential to remember. You should be taking notes as you read; write down anything that you consider important. But you must write down and remember the stuff I underline, although you should write it in your own words (that forces you to process it and understand it). If you start getting too lazy or tired to do that, take a break from reading for a while.

How to Use This Book

5

Third, I will occasionally put things in a box. Here is an example of something in a box. Often there will be quite a bit of text in the box, unlike here. This is generally stuff I consider important or interesting, but not necessary for you to read. Sometimes it is an inspiring story, sometimes an interesting example, sometimes a little joke. I think you should read it, but I put it in the box so as not to interrupt the flow of the main text. In a few chapters I will use text in boxes to show alternate ways of answering the questions; in these chapters I will tell you that this is what I am going to do. Fourth, I use boldface in a certain way. I use it for chapter and section titles. I also use it when I refer to chapter titles in the text; so if I mention Game One, or the Advanced Techniques chapter, I'll put them in bold. Finally, when I use a word for the first time in a chapter that is defined in the Glossary, I put that in bold (the first time only, otherwise it just gets obnoxious). So if you see a word in boldface and you don't know what it means, look it up in the Glossary. Fifth, the numbering of the questions in each game might seem a little odd. For example, the first question in Game Three is number 6, but the last question in Game Two is number 12. There is a reason for this. Each of these games comes from a previously administered LSAT, but the games don't all come from the same LSATs. I have preserved the numbering that was used on the actual LSATs. So Game Two and Game Three, for example, were both the second game on their respective LSATs, and so use the same question numbers. One last note. For each game I go through, I reproduce the game, as it was on the actual LSAT, at the beginning of the chapter. Unfortunately, LSAC's policy on licensing LSAT questions prevents me from printing the questions, or their answers, more than once in the book. You may have to flip back to the beginning of the chapter periodically to see what a question or answer says. I do my best to reduce this necessity, but there's no way I can eliminate it (legally). Let me recap: Answer when I ask questions. Take notes as you read, and especially note anything underlined. Stuff in boxes is side commentary. Boldfaced words are chapter or chapter section titles, or vocabulary from the Glossary. Got it? Good.

A Final Note Before You Begin Students generally want to spend the most time studying what scares them the most about a test. For the majority of LSAT students this is the logic games section. But the logic games section is only one quarter of your LSAT score. Spending more time on it than on Logical Reasoning or on Reading Comprehension may not be the best way to improve your LSAT score. How do you know how much time to devote to one section versus another? This involves balancing two considerations. First, how many questions are you missing in each section? You have to double this for Logical Reasoning, because there are two of these sections. Second, how easy will it be to improve your performance? For most people, logic games is easier to improve. This will also change as time goes on; as you get better and better at a section, you reach a point of diminishing returns, where you see less improvement for more time put in.

6

How to Use This Book

For example, a student who misses ten questions total on both Logical Reasoning sections (five per section), and ten questions on logic games, should study logic games more than Logical Reasoning. They are pretty good on Logical Reasoning – missing only five questions per section – so it will be harder (but not impossible) for them to improve that than to improve logic games. Evaluate where you stand in LSAT performance, and what score you want to achieve. Then ask yourself how best to achieve that. Is spending more time on Logical Reasoning going to give you better score gains than spending more time on logic games or Reading Comprehension? Don't focus disproportionately on logic games just because they make you nervous.

LSAT Number to Date Conversion Chart This chart lists the LSATs from 19 to 48 (48 is the most recent released LSAT as of the writing of this book) and gives the dates they were administered. I only list from 19 on because the LSATs from earlier tests are slightly different and not as good to study from. 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

June 1996 October 1996 December 1996 June 1997 October 1997 December 1997 June 1998 September 1998 December 1998 June 1999 October 1999 December 1999 June 2000 October 2000 December 2000 June 2001 October 2001 December 2001 June 2002 October 2002 December 2002 June 2003 October 2003 December 2003 June 2004 October 2004 December 2004 June 2005 October 2005 December 2005

Studying Timeline

7

Studying Timeline Here are two possible timelines for studying LSAT logic games. These are just for logic games, not the whole test. Both are guidelines, intended to give you a general idea of how you might spend your time; you should tailor your studying timeline to your needs and situation.

Short Plan (Approximately Two Weeks) This plan is for people who have only two weeks to study logic games. I highly recommend devoting more than two weeks to studying logic games. If you really feel that you have to take the LSAT now, and you have only two weeks, consider the difference going to a better law school will make in your life. If you consider that difference minimal, or not worth putting off applications for some period of time, go ahead with the test. If not, take a later LSAT. If you have exactly two weeks before the LSAT, this plan is not quite for you. You need to spend at least the last three days before the test reviewing your strategies for the entire test, not just logic games. Adjust this plan accordingly – give yourself those three days at the end to review the whole test. Since you have embarked on a two-week crash course, I will assume you are willing to spend all 14 days of those two weeks studying. Week One The goal of this week is to learn the fundamental steps of logic games, and understand how to apply these steps to any game. No work you do in this week should be timed. Our first goal is to learn the steps. Read all the chapters up to (but not including) Intermediate Techniques. Follow all instructions in the chapters, including those at the end under the heading "What Do I Do Next?" Make sure you apply all the techniques discussed in the Studying Guide when you study (not this chapter, but the one coming up about how to study). Read the chapters in order, but, since the chapters involve a lot of information and many of the chapters require you to work along with them, getting through them may take you a couple of days. Don't redo the games after you've read the chapters, as they tell you to, because you don't have the time. Make flash cards and memorize the steps as you go through this week (see the end of The Fundamentals for a quick how-to on flash cards). Spend the next two days practicing games from the "Recommended Games" list at the end of Game Three. Our next goal is to learn how to apply these steps to any game, including the more difficult ones. Once you have memorized the steps (including how to approach every type of question), read the chapters starting with Intermediate Techniques and up to (but not including) Advanced Techniques. Follow all instructions in these chapters. This will take you a day or two. Week one is almost up. Spend the rest of the week working on games from the "Recommended Games" lists at the end of Game Three and Game Eight. Week Two The goal of this week is to get used to applying what you know about logic games under timed conditions. Skip the Advanced Techniques chapter. Read Game Nine through Game Twelve; read the chapter on Timing. From this point forward you will time yourself on every logic game

8

Studying Timeline

you do. Follow the instructions in the "What Do I Do Next?" section at the end of the Timing chapter. On the second to last day of week two, read the chapters Before the Test and During the Test and follow the instructions therein. This gives you one extra day to review your notes and make sure you have internalized everything you need to.

Normal Plan (At Least Four Weeks) This plan is for people who have more than two weeks to study. If you have less than four weeks, spend less time doing what I describe in "Week Three." The instructions in the "What Do I Do Next?" sections at the end of the chapters assume you are following this plan. This plan assumes that you spend four to five days per week, 2 hours per day, studying. Week One The goal of this week is to get comfortable with the fundamental skills. Read and work through the chapters up to (but not including) Intermediate Techniques. Follow all instructions in the chapters, including those at the end under the heading "What Do I Do Next?" Make sure you apply all the techniques discussed in the Studying Guide when you study (not this chapter, but the one coming up about how to study). Reading through the chapters may take you several days, especially if you work through each of Game One through Three on your own after reading their chapters. Make sure you give yourself a couple of days at the end of the week to practice; spend these days working on games from the "Recommended Games" list at the end of Game Three. Week Two The goal of this week is to cement your comfort with the fundamental skills and start building mastery of them. If you don't yet feel like you understand the fundamentals, or don't have them memorized, feel free to continue working on games from the "Recommended Games" list at the end of Game Three for the first day or two of this week. Once you have reached the point where you do feel comfortable with them, read from Intermediate Techniques up to (but not including) Advanced Technique (so stop after Game Eight). Spend the rest of the week working on games from the "Recommended Games" lists at the end of Game Three and Game Eight. Make sure you use the studying techniques I talk about in the Studying Guide. Week Three, Week Four The goal of these weeks is to learn to apply what you know quickly and efficiently. If you don't feel comfortable applying your skills to more complex games, continue to work on games untimed for a few days. Don't do this beyond midweek of week three, though. When you are ready, read Advanced Techniques through (and including) Timing. You may or may not want to apply the advanced techniques, but you should be aware of them. Follow the instructions in the "What Do I Do Next?" section of the Timing chapter. Three or four days before the end of week four, read Before the Test and do what the chapter tells you. At some point in these days you should also read During the Test. You have now learned everything I have to teach you.

Studying Guide

9

Studying Guide The Why, What, How, When, and Where of Studying Most of us have only a limited amount of LSAT studying time (or energy). Nevertheless, we want to get a good score. This means that we absolutely must maximize the little time that we have. Simply plugging through questions will not get you a good LSAT score, because it reinforces your bad habits as well as your good ones. This section provides you with a clear and proven effective system for studying for the LSAT logic games (although it can easily be generalized to the other sections of the test, as well). It won't be easy to use at first; sometimes it may seem overly burdensome. But, used correctly and consistently, it is the only way to guarantee improvements. Read this section, think about what it says, and then read it again and take notes. If you really want to improve your LSAT score, begin implementing these strategies today. You'll end up studying less than you might expect, yet learning more every time you study.

Why Study? The answer to this question is so obvious that you were probably tempted to skip this section. But an understanding of why you study underpins the what, how, when, and where. You study because you want to get a good LSAT score. This is the only thing you should be concerned with when you study. If you ever wonder whether or not you are doing the right thing when you study, ask yourself, "Is this going to help me get a better LSAT score?" If it is, right on. If not, stop. This may seem obvious, but most people don't act like this is their goal when they study. For example, one thing I commonly see people doing is studying when they are exhausted, such as immediately after getting home from work. Now, is studying when you can't focus on what you are doing helping you get better at the LSAT? Of course not, because you are going to not do what you should, being too tired to practice new skills. Most people act like their goal is to do a lot of practice games before they get to the LSAT. That is, their entire studying plan is to do game after game, without really thinking about what they can learn from each game. Doing a lot of games can be helpful, but it is only helpful if it improves your skills. If you continue to make the same mistakes over and over, doing those games is doing nothing but building bad habits. The point of doing practice games is to build up the skills that you need for the LSAT. Every practice question is a chance to practice at least one useful LSAT skill; if you don't use the right skills on the question, you have wasted your opportunity. If you don't learn from the question, and figure out how you should do similar questions in the future, you cannot improve. When we practice, we want to make sure we are practicing skills that we need to learn; after we practice, we want to review what we have done to determine what we now need to work on. Every time you sit down to study, ask yourself, "What is my goal? What can I do now to improve my LSAT skills?" Here's a little story about how important it is to know your goals when you study. Once upon a time, back when I briefly practiced law, I went to the UCLA law library to do some research. I was sitting outside the library thinking about such and such and I overheard a conversation between two 1st year law students (this was during the middle of their second quarter of school).

10

Studying Guide

their second quarter of school). One student was complaining to another about her contracts teacher. Every week, she said, he assigned them tons of reading. She could barely get all of it done and briefed (which is a way law students often take notes on the cases that they read) before class, and it consumed more time than any of her other classes. Yet, every week, the teacher never once talked about any of the reading he had assigned. This upset her quite a bit. This, clearly, was a student who didn't know what her goals were. I could see three possible goals she might have: 1) learn the material, 2) impress the teacher, or 3) do well in the class. If she wanted to accomplish 1), then she should do exactly what she was doing and stop complaining, because she was doing what she wanted to do and it didn't matter what the teacher asked or didn't ask. If she wanted to do 2), she should stop bothering to read the material, since the teacher clearly didn't care whether the students read it or not. Likewise, if she wanted to do 3), she probably didn't have to read all the material either, because in my experience most cases you are assigned to read in law school are not relevant to the final exam. She should have been well aware of that, having already been through one series of final exams. If the cases were necessary to do well in the class, though, she should also stop complaining, because, again, she was working towards her goal. The reason she was so unhappy was either because she didn't realize that she was doing exactly what she wanted to do, or because she was doing work which was irrelevant to her goals. If you are aware of your goals, necessary work isn't always pleasant, but it is easier to accept it and be satisfied that you are doing it; as far as unnecessary work goes, you just shouldn't bother doing it.

What to Study? Your goal in studying is to improve skills. Before you can do this, you need to determine what the skills are you are trying to improve. Every time you sit down to study the first thing you should do is decide what it is you are going to work on. Never study without first identifying the specific skills or goals you will work on in that session. Making a "long list" As you work through each chapter in this book, take notes on what you learn. Everything underlined should definitely go in your notes, but don't limit yourself just to that. Your notes should include enough information that you can understand them without having to go back to the chapter itself; don't just jot down a phrase from the book, but rather explain the concept to yourself. Each chapter will briefly summarize itself at the end; use this to check your notes and make sure you covered everything. This summary won't include every single concept, just the key ones, and it won't explain the concepts to you, which your notes should (otherwise you can't use the concepts they contain). Don't be lazy and wait to take notes until the end of the chapter; the act of taking notes forces you to think about what you are reading while you are reading it, which will cause you to understand things better. After working through a chapter in this book, you should review the notes you took and the questions you did during that chapter. You should do this no more than 24 hours after finishing the chapter. However, don't start reviewing immediately after finishing; give

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yourself at least an hour of rest after the session before you start reviewing. Reviewing means reading through your notes and making sure you understand them; add anything you need to clarify what you wrote. Again, write your notes with the intent that, when you review them later, you will understand exactly what they mean and be able to implement what they say without a lot of head-scratching. After you write everything down, you may want to type it up and organize it in some way that makes sense to you. Organizing this stuff is helpful in that it forces you to think further about how everything fits together, rather than viewing every little tidbit as a completely separate idea to be memorized on its own. Use an organizational scheme that makes sense to you; you may want to put all the techniques about a certain type of question together, or group techniques by aspect of the test (timing, eliminating answers, etc.). These notes are your long list. The long list will contain everything that you want to know for the LSAT. Prioritize: make a "short list" As you learn more and more, your list of things you want to learn is going to get rather long. You won't be able to learn everything on it at once. You will also need a shorter list of things you want to focus on right now. This is the short list. Typically, your short list will contain issues of procedure and technique, such as a list of steps to follow for certain question types. The short list should be easy to read and understand at a glance. It should only have a few points on it, just the number of things you can focus on learning in one sitting (generally 3-5). Put this short list right next to you when you study, so you can refer to it easily. The point of the short list is that you will refer to it constantly as you work through practice questions. The point of doing practice questions is to practice new skills; if you don't actually use your new skills as you practice, you won't learn them. The short list reminds you what these skills are and how to use them. By referring to it constantly (at least before every question) you will keep these skills at the forefront of your mind, which helps to guarantee that each question brings you closer to mastering and habituating them. Making a short list – be specific This is crucial. The notes you take are meant to help you. They must give you instructions you can implement without too much thought. Your notes, both the long and short lists, should contain ideas that you can look at in the middle of doing a problem, read, understand, and implement immediately. Bad notes example  Be careful - don't make stupid mistakes  Learn question types! The above notes (either as a short list or a piece of a long list) give important goals. However, there are no instructions on how to actually accomplish those goals. These notes are the equivalent of writing yourself a note to "Get answers right!" They are useless.

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Studying Guide Good notes example  Be careful:  Read every word in a sentence  Write down any information given  If I need to test something out, make a new diagram  Go through all the rules  Learn question types:  On "Can be true" questions, test each answer and see if it can be true  On "Must be true" questions…  [and so forth]

Notice that the good list expands on the goals of the bad list in very concrete ways. Every time the list gives a more complicated concept, it breaks it down into smaller steps. These notes give thought processes that can be used on the test. These notes answer the question "What should I do in a given situation?"

How to Study Now that we've talked a bit about how to figure out what to study, lets talk about how to study it. When you first start studying you will be learning new skills. You can't worry about how fast you are at this stage. You must learn a skill before you can do it quickly, and if you try to get fast too early you will become sloppy. In this section I will talk only about studying without timing yourself. Studying is actually harder than taking the test – it requires more effort because you are learning new skills, whereas taking the test is just following a path you've already set out for yourself. Taking the LSAT is just a matter of showing up; all the real work is done beforehand, when you study. The right approach to studying will make the real LSAT a breeze (relatively speaking). Studying consists of three stages. You must do each of these stages every single time you sit down to study. Stage 1: Preparing – what will you practice? As discussed above, before you can learn a skill, you need to know what the skill is you are trying to learn. The first step in studying is reviewing your long list and putting together your short list. You will be creating your long list as you read through this book; your short list will either be created from scratch when you finish a new chapter or will be based on material you've been working on already. Once you have a short list, you must spend some time reviewing it before you do any problems. Make sure you know what each item on the short list means, and how to go about implementing it. Before you go on to stage 2, visualize doing a game or two. What this means is closing your eyes and imagining working through a game. This may sound bizarre, but it is extremely useful. Walk yourself, in your mind, through all the things you should be thinking about when approaching a game, from the setup stage to answering questions. Think about the skills to employ, the tricks to watch out for, the possible mistakes you might make. Why is this useful? When you are actually doing a game, you typically focus on the game

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itself, which means you aren't thinking so much about the skills you are trying to practice. This means that it will be hard to use these skills. By visualizing, you get a chance to practice using the skills without distractions; this gives you an opportunity to practice (rehearse) the skills themselves before you have to use them. If you do this correctly, when you actually do problems you will simply be following a plan you have already laid out for yourself. Visualization is a technique useful in any situation where you have to employ a complex skill under pressure, from cooking to archery, and will really help your LSAT practice. Always visualize using your new skills before you do any set of questions. Stage 2: Practicing Once you have identified what you want to work on, you must actually work on it. This means you must do practice questions. The point of doing practice questions is to practice your new skills so that they can become habits. Habits are things you do without having to think about them much. If you develop good habits, when you take the actual LSAT you'll be able to focus on doing the questions, not on trying to remember how to do them. As you do each question, make sure you do everything exactly the way you are supposed to. Constantly refer to your short list to make sure you are working on the skills identified there. This is absolutely crucial because it leads to forming proper habits, so let's repeat. When you are doing practice questions, you must make sure that you are following the correct procedure; that is, that you are doing the right steps in the right order, without skipping steps or doing anything extra. This is the only way to form habits. Start this from the very beginning. The more you do this in practicing, the better you will do on the actual test. If you come across something you have done before, but forget how to do it, stop and look it up in your notes. It is better to take the time to do this and be slow than it is to do the question the wrong way. Don't worry about memorizing things yet; you'll end up memorizing most skills through use (I'll note in the chapters where you should take extra, non-practice, time to memorize things). Every time you skip a step, get sloppy, or allow yourself to lose concentration, you are reinforcing bad habits which will cost you points on the test. Conversely, every time you do the right thing on a question you are reinforcing good habits which will help you get questions right on the test. People fall back on their habits when tired or under pressure. If you have the right habits, you will do the right thing when things get tough on the test. Follow all the steps you have learned, even when you feel that they are unnecessary, or that a question is easy without them. Practicing good habits even on easy questions means that you will have these habits on hard questions, which will make them easier. Initially, do only one game at a time. At this point don't worry about how long each game takes you. You only do one game at a time because there is a chance that you will do some questions the wrong way. If you only do a few questions, you can catch your mistakes before you repeat them and make them a habit. In addition, doing only a few questions allows you to devote all your attention to the questions you do; do too many games in a row and you will get tired and sloppy, creating or reinforcing bad habits. Once you finish a game, stop and take a break. You may do more games that day, so don't worry that you'll only be doing one game a day, but you have to do step 3 before you do any more questions (and then step 1 again, as well).

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Remember, no one cares about how many games you did when you practiced for the LSAT. No one will ever know, unless you tell them, and this fact will never make a difference in getting into law school. What matters is your actual LSAT score. This studying method puts a lot of emphasis on thinking about questions before and after you practice them, not on cranking through as many questions as possible. This may be frustrating at first, but the only way to improve what you do (and eventually improve your LSAT score) is to know what you are supposed to do and make sure you do it. Stage 3: Review After you have finished your game you must check your work. This doesn't just mean seeing if you got the answers right; this means checking your work to see if you used the right approach to each question. No one cares how many questions you get right when you practice; all that matters is how you do on the LSAT. If you get questions right, but use skills that won't work on the real LSAT, then you aren't improving. When you review questions, you are checking to see if you used the skills you will need for the LSAT. In the beginning, review questions you got right as well as those you got wrong. See if you did everything you were supposed to do, or if you did work that you shouldn't have. If you did get questions wrong, try to reconstruct why, and ask yourself what you could have done to avoid your mistakes. Try to see how the general principles in this book apply to the games you do; don't try to construct overly specific ideas that will only apply to games exactly like the one you just worked through. If you find you are making mistakes, look back through this book to find where I talk about similar issues. Here you will find concepts and skills you will want to use in the future to avoid these mistakes. Add these to your notes. Notice patterns of mistakes you make. Think about how you can avoid making these mistakes in the future. Don't just tell yourself, "Don't do this," but think about what you should do to avoid that mistake. For example, you might say to yourself, "Don't read too fast!" A better note would be, "Read carefully by stopping after every sentence and writing all the information down." Notice that the second note is something you can do to solve your problem, rather than simply an instruction not to have a problem. If an issue comes up often enough, put the solution on your short list, or (if it's already there) highlight it to make sure that you work harder on it in the future. Anything you learn about the test or yourself through this review should be added to your notes (at least to your long list). You should also notice what you did well. People are usually good at beating themselves up, but don't notice what they are improving at. Spend at least a few minutes every time you study thinking about what you are getting better at – what you do better now than you did before. There are two reasons for this. One, it will make you feel good, which will help you continue to work hard. Two, you will eventually move some things off your short list as you get good at them. One quick note: don't laugh off stupid or sloppy mistakes. Making careless errors is the result of improper technique. People who miss their score goals on tests often do so not because they didn't understand the material, but because they deviate from what they have learned – that is, they get sloppy under the pressure of the test. The techniques in this book are designed to make it very hard to make dumb mistakes; learn and use them. If you keep making dumb mistakes, figure out what you are not doing. If you don't learn how to avoid sloppy mistakes now, then you will be more likely to make them on the test when

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you are under more pressure. It is crucial that you build good habits now, when you are studying, so that they will be present on the actual test. If you make sloppy mistakes you must force yourself to stick to the techniques you have learned and slow down. This is why you only do one game at a time, so you can constantly assess yourself and reprioritize. Doing 100 questions in a row does no good if they are all done wrong. In fact, it will probably hurt you more than anything else, since you will have built up some really bad habits. Stopping frequently and checking your work allows you to nip problems in the bud. It also keeps you from dying of overwork. Return to Stage 1: Set new goals and start over After having done a game you will know more about what you should be working on. You may continue on the same types of problems, or move on to something else. You may have changed your short list of things to focus on. You may be feeling confident about a lot of things which troubled you up to then. Your self-assessment, performed during stage 3, should help you to change your short list periodically. If you feel that you have reached a point where you automatically use one of the skills on your short list, take it off the list. Add new high-priority skills to the short list as you master old ones. Take a break. Think about whether or not you have the energy and focus to do more work this day. Maybe you need a significant, 20 minute to several hour break, maybe you can start right up, or maybe you need to stop for the day. If you are going to study more this session, take some time to think about what the questions you have done have shown you, and what you should be working on. Then repeat the process: review or remake your short list, visualize using the new skills you want to learn, do another game, and review it. All studying should consist of these three steps – preparing by making or reviewing your short list, doing some questions to practice your skills, and assessing your progress. You cannot eliminate any of these steps if you want to study efficiently. Studying under timed conditions Studying under timed conditions is a lot like normal studying, which I just described. I'll let you know later in this book when I think you should start timing yourself. When you do, you will still go through steps 1, 2, and 3 as I describe above. However, in step 2, you will generally do whole test sections – four games – in 35 minutes, or sometimes do just one game, allowing 8 minutes to do it. Your goal is to answer as many questions as possible in the time given. Don't allow yourself to go over time; stop doing questions when your time is up. You should be practicing everything you normally practice, but paying extra attention to watching if you do extra stuff you shouldn't be. The key to speed is to eliminate excess work (anything I don't tell you to do in this book), not to rush through necessary work. When you review the game (step 3), you can do all the extra stuff you didn't do in your 35 or 8 minutes – answer questions you didn't get to, try alternate diagrams for the game, try to make deductions you missed. The goal during your timed practice is to simulate the LSAT, which means not doing anything you haven't already mastered. When you review you can think about what else you would like to learn and practice.

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Take frequent breaks It is important to be able to concentrate when you study. Remember, you are trying to build habits for the test. Being sloppy and unfocused is a bad habit. When you start to feel fuzzy, take a break. The best kind of break involves some minor exercise – a little walking, for example. If you allow yourself to recharge often you will get more out of the time you spend studying. Take a significant break every half hour or 45 minutes, even if you feel fine. This break should be at least a few minutes long. A few minutes of break time is very helpful. Of course, you won't be taking breaks this long when you take the LSAT, but remember, studying is actually harder than taking the test. Thus, you need more energy when you study, which means you need to take more and longer breaks. You should also take shorter breaks more frequently; take a 30 second to 2 minute break every 8 minutes. This is the same frequency at which you should take breaks during the actual test (you'll take a break after finishing each game); thus, taking these breaks is a way of practicing for the LSAT. These breaks help maintain concentration at peak levels, break up the tedium of questions, allow your blood to move more actively, and combat eye strain. During this break you should breathe deeply while not moving, move your head and shoulders to stimulate blood flow, focus away from your book or computer (preferably at something far away), and adjust the way you sit to be more comfortable.

When to Study? The goal of studying is to learn. You should only study when you are capable of learning. Following the three-stage study process requires that you be alert, focused, and somewhat energetic. Do not study when you don't feel alert, focused, and somewhat energetic. Studying when tired or distracted leads to studying wrong. Studying wrong leads either to wasted time or to the learning of bad habits, which leads to bad test scores. What time of day is best for studying? If you work, you should probably study before work on a regular basis. If you can't, then you should not study immediately after work. Allow yourself an hour or two of rest and have a light meal, and then study. Don't watch TV or listen to music when studying. In addition, the times you study should reflect your natural cycles of attention. Every human body follows a 25 hour cycle called the circadian rhythm. Although this rhythm is not exactly as long as our 24 hour day, it is reset every morning by exposure to bright light, usually sunlight. The circadian rhythm causes humans to experience two major alert and two major sleepy phases. The sleepy phases are (generally) from 2 to 7 am and 1 to 5 pm. The alert phases are roughly 9 to 11 am and 7 to 9 pm. Thus, try to avoid studying between 1 and 5 pm. In addition to the circadian rhythms, humans also have natural ultradian rhythms. These rhythms are a cycle that re-occurs through the day; we experience approximately 90 to 120 minutes of alertness, followed by 20 minutes of "recovery," during which thinking and concentration are more difficult. Because of this, you should not expect to be able to study for more than 90 minutes without a significant break (remember, you should be taking

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short breaks periodically – every 8 minutes, or at the end of every game). This significant break should be 20 minutes long; during these 20 minutes you should not study or think about the test at all. Because the exact length and effects of these two cycles can vary from person to person, you should spend some time trying to figure out when your two main circadian sleepy times are, as well as when your 20 minute ultradian down times occur. In addition, don't consider these hard and fast rules; in general, try not to study during these down times, but sometimes it may be unavoidable. It is OK to break up your studying so that you do different stages of studying at separate parts of the day. For example, you might do practice questions in the morning (stage 2), and then review them and prepare for the next set (stages 1 and 3) in the evening. This is fine, as long as you always precede practice questions with stage 1, and follow it with stage 3. If you do break up your study times, make sure you do some visualization right before doing practice questions. One note: the practice stage of studying (stage 2) requires more concentration than the other stages. Try to time your studying so that you are doing this when most focused. If you have to do one stage in the morning and the rest in the evening, do most of your practice questions in the morning. You won't be able to follow these guidelines all the time – no one lives an ideal LSAT studying life. But do your best to make your LSAT studying productive. If you never have time to study when you are alert, you aren't going to improve much. If this is the case, you need to reconsider your priorities. How often should I study? You should study at least three or four times a week, but generally not more than five. It is more important to study often than it is to study for a long time each session. Preparing for the LSAT is all about building good habits. Habits can only be built by consistent repetition, over the course of days and weeks; it can't be built by cramming. This is for two reasons: first, your ability to acquire the habit diminishes as you do something for consecutive hours (you need to recharge); second, if you wait between studying sessions, you begin to lose your habit. Sports, or other difficult physical activities, are good analogues to preparing for the LSAT. If you want to improve your free throws, your golf swing, or the amount you can bench press, you have to practice consistently. If you play golf once a month, you will get better only slowly, if at all. This is because your muscles build up in certain ways when you use them, so that next time you use them in that way they function more efficiently; if too much time passes between these types of use they break back down, and any gains you made are lost again. At the same time, practicing too often is bad for you as well. Weightlifting is a great example. If you go into the gym every day and work out your biceps, let's say, you'll make less progress than someone who went in half as much. This is because you aren't giving your muscles time to recuperate and build up in between uses. Your brain is like a lumpy gray muscle. If you use it in the same way consistently, certain neural pathways get reinforced, which makes it easier to use these pathways in the future; with time and disuse, these paths return to normal. At the same time, if you overwork your brain, it won't respond as well until it gets a chance to rest.

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If you want to be good at the LSAT, you have to train properly – practice consistently, don't over-train, and always use the right form. Each of these studying sessions should be 1 1/2 to 2 hours long (although you can break it up over the course of your day). Studying for much less than an hour is a waste. You need at least 20 minutes to prepare to do questions (reviewing notes and making a list of what to practice), at least 20 minutes to do questions, and at least 20-30 minutes to review the questions. If you study for less than an hour you will have to eliminate one of these steps. This means you won't learn anything from that time. Studying for more than a few hours in a row means you are going to be studying when you are very tired. No one can focus properly at a high level for this long. If you need to study for several hours in a day, take at least a 20 minute break every 1 to 1 1/2 hours. Studying consistently is much more important and useful than studying a lot. If you study 1 1/2 hours five times a week (total = 7 1/2 hours per week) you will learn more than studying 8 hours a day every weekend (total = 16 hours per week). Here, less than half the studying will result in more learning.1 Don't put off your studying until the weekend; you'll learn less in a weekend than you would in a week (even studying the same total amount of time) and you'll lose a lot of what you learned by the next weekend. Anyone can fit studying into their weekly schedule. You may have to make some sacrifices, but a month or two months of unhappiness is better than spending three years at an inadequate school, followed by several years in a lower-paying job. In summary, study consistently. Only study for as long as you can focus. Make sure that you give yourself enough time to preview what you will practice, do questions, and review the questions you did every time you study.

Where to Study? Study someplace where you can focus. Coffeehouses aren't very good places to study. No one ever gets much done in a coffeehouse. There are too many other people, some or all of whom you will be constantly aware of. There are too many noises. That said, they are great places to look and feel like you are studying while really just amusing yourself. Of course, you may not be able to avoid studying in coffeehouses, especially if your actual house is even less conducive. It's not impossible to learn at a coffeehouse, so if you have no other choice, don't give up on the LSAT. If you have a roommate, spouse, or children, your living room is also a terrible place to study. If you have no one at home, but own a TV, stereo, or computer, the living room is still bad. Never, ever, ever study while watching TV. The best place to study is someplace quiet outside your home (but not so far as to discourage you from going there). Having to travel is useful psychologically, to focus you and keep you from stopping too soon – since you had to drive or walk to get there, it makes

1

Roughly speaking; it's very difficult to quantify learning, and people vary, etc. etc. The point is, studying less, but consistently, is much more effective than studying more, but with large gaps between study sessions.

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that travel time seem wasted if you go home early. I prefer studying in libraries (as long as I stay away from the fiction section).

Summary The goal of studying is to improve your LSAT score. If, when studying, you do anything that doesn't, directly or indirectly, help you improve your score, you are wasting your time. You should study at least three times per week, and at most five. Learning new skills takes consistent practice. If you wait too long between study sessions you lose whatever skills you built up. If you study too much, though, you might burn yourself out. Study someplace you can concentrate, where distractions will be minimal. Before you do practice questions, you should put together a long list and a short list. A long list contains every skill and concept you'll ever want to learn for the LSAT. You create your long list as you work through this book, and as you pick up new pieces of knowledge while practicing. A short list contains the skills and information you want to practice right now. You can't learn everything on your long list at one time, so you prioritize and put your high priorities on your short list. This list will change as you learn the skills on it; you'll take off the skills you have mastered, and put new ones on. Immediately before doing practice questions, visualize the processes you want to practice. When visualizing you should imagine that you are doing a game or games, and walk yourself through the process you want to follow. You should visualize before doing any set of practice games. Visualizing helps focus you on what you are trying to practice, so that when you actually do games you do them properly. The point of practicing is to learn habits, and you can only learn habits by repeating a process over and over. When you do the actual LSAT, you will tend to do questions in whatever way is habitual for you. If your habits are good, you'll do well. Build habits by always doing the questions the right way – following the proper steps, leaving nothing out – no matter how easy or hard the question is. Look at your short list constantly as you do practice questions, at least before every new question. Start out by doing practice questions in small sets – one game at a time. After you finish a set of practice questions, review what you did and think about what you did well and what you should do differently in the future. Don't worry about getting the right answer or not; worry about following the proper procedure. Remember to be aware of what you are doing well, and give yourself positive reinforcement. Use this review to change your short list and guide your future practice. You should take breaks whenever you need to, and at least every 10 minutes. This keeps you alert and focused when studying, and also simulates what you'll do during the real LSAT, thus building good test-taking habits. To summarize the summary – before you do questions, figure out what you want to learn and make sure you understand it. As you practice, constantly focus on practicing what you are trying to learn. After you practice, figure out what you have learned and what you need to learn in the future. Use this information and start the process over again. This will help to ensure that your studying time is always concentrated on changing your logic games habits for the better.

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What Do I Do Next? Do you have the energy to keep learning? If not, take a break or stop for the day. Otherwise, continue. Now that you've learned how to study, read the next chapter – How to Take the LSAT Logic Games Section – taking notes for your long list as you go. Don't forget to take breaks as needed. Pretty soon you'll be doing practice games, putting everything from this chapter into effect. I hope you're as excited as I am.

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How to Take the LSAT Logic Games Section Let’s be honest: the LSAT logic games are hard. Let’s take a second to be upset about this… Darn it! OK, feel better? That done, let’s see what we have to do to get a good score. The LSAT logic games are hard for two reasons. First, the test just is hard – there is a certain amount of hardness built right into the test that is basically unavoidable. Second, the way most people take the test makes it even harder. We can’t avoid the built-in hardness unless we skip the test, so we have to prepare for it and know how to deal with it. At the same time, we clearly don’t want to make the test any more difficult than it has to be, so we need to know how not to do the stuff that makes it harder.

Built-in Difficulty There are several aspects to logic games that make them inherently difficult: 1. 2. 3. 4. 5.

You have to know logic The games, questions, and answers are worded confusingly There is a lot to think about at once There are a lot of questions There isn't a lot of time

Let’s go through these issues one by one and discuss why they make the test tough and what we are going to do to overcome them. I'll develop all of these ideas in more detail later in this chapter, but for now I want to get us thinking about how we are going to make the test easier. 1. You have to know logic What are we going to do about this? Well, we can't avoid it – we'll have to learn the logic we need to know. That's part of what this book is for, to teach you all the logical concepts and skills you'll need to succeed on the LSAT logic games. It's not so hard – what makes the test difficult is not the logic, but the way in which it is presented to you. 2. The games, questions, and answers are worded confusingly You may actually know the logic involved in a question, but if you can't figure out what the question is asking you to do there is no way you'll do it. The easiest way to understand questions is to first know what types of questions will be on the test. There is a limited number of types of questions they can ask, and every question of a given type is answered in the same way. It's easier to identify an oddly worded question as being a certain type than it is to figure out what it means from scratch. On the test, once we figure out which of the question types we are presented with, we know exactly how to go about answering it. This eliminates a certain amount of difficulty; we no longer have to think about how to answer a question, we just have to answer it. In addition, we are going to need to read slowly and carefully. It's easy to miss a "not" or "exactly" or "at least," and thereby to miss the question. We need to take in and understand what we read, and this requires reading carefully. 3. There is a lot to think about at once Games involve a lot of information – not just the information the games give you in the form of rules, but also the steps you need to remember to go through for the questions. If

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How to Take the LSAT Logic Games Section

you try to manage all this information in your head at one time, you'll get confused and make mistakes. You'll also get tired, which will slow you down and make you more prone to make mistakes. We deal with the information the game gives us by writing it down so that we don't have to remember it. The more we rely on writing things down, the less we need to think. The less we think, the less open we leave ourselves to making mistakes and the less tired we get. In addition, we need not just to memorize all the steps for doing questions and so forth, we need to make these steps into habits. Habits are things we do without thinking. We can form habits only by studying properly. 4. There are a lot of questions What is so difficult about this? Well, we will eventually get tired. When we're tired the questions will be a lot more difficult. Also, even if we don't get tired, we may not have enough time to answer all the questions. We don't want to use any more mental energy on a question that we have to. One way to avoid using too much energy is to write everything down, as I said above. We also need an approach to the test that is simple and doesn't require too much thought. That way, when we get tired (and we will), we can still stick to our system and do well. As we go through my approach to games you will see that I have tried to make it as methodical and memorizable as possible; I've done my best to eliminate unnecessary details and useless information from the approach. A simple, memorizable system is one that can be applied even when you are tired and not thinking as clearly as you normally do. It is also crucial to have techniques to help you maintain focus and regain it when it has been lost. The best technique for this is taking breaks during the test. We'll talk more about that later. Because we may not have time to do all the questions, we need to have a system that maximizes the number of questions we do do. In part we do this by speeding up on each question – having a simple and efficient approach. But we also need to do the questions in the right order. We want to do the easiest and fastest questions first, because we can do more of these in less time. I'll teach you a quick and easily memorized way to figure out what order to do the questions in on every game. 5. There isn't a lot of time Given the time limits of the test, it is crucial that you maintain the proper pace and don't waste any time. On the logic games section you have 35 minutes to do four games. You are capable of doing every game within these limits. You may not answer every single question on every game, but we are going to get pretty close. However, you don't have a lot of extra time – if you spend time doing stuff that doesn't help you answer questions, that is going to cost you points. It is amazing how much time students waste on the test. Yet students generally don't think they are wasting time – they think that the steps they spend the most time on during the test are helping them, when an objective observer would realize that these steps don't get them points in proportion to the time they take. For example, students often want to figure out as much as possible about a game before they look at the questions. This can be helpful; it can save you a little bit of time on the questions. But I often see students spending several minutes doing this. There is no way that this is worth so much time. You only have about 8 minutes per game (35 divided by four). You probably spend at least a minute, and more like two, understanding the structure of the game and the rules that are given to you. Spending an additional 3 minutes figuring out how the rules can be combined, and what may or may not happen in the game, gives you only 3 or 4 minutes to answer the questions. That's not enough.

How to Take the LSAT Logic Games Section

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Given that you don't have enough time, you can't afford to waste it. The key to speed on the LSAT is not rushing through the questions. There is certain work that has to be done slowly and carefully. The key to speed is avoiding doing anything that doesn't have to be done. We're going to figure out just what you have to do to get a great score, and we won't do anything else.

What Makes the Test Harder Than it Has to Be? Here is a list of the most common ways test-takers hurt themselves on the LSAT: 1. 2. 3. 4. 5.

Multitasking Not knowing what to do Not doing what they need to do Working through fatigue Worrying and/or changing your strategy

1. Multitasking Multitasking is doing more than one thing at the same time. It is inevitable and not always bad in the real world. For example, I am pretty adept at walking and chewing gum, or even walking and talking at the same time. Neither of the tasks in these pairs uses the same skills or the same part of the brain; only one of the two requires much (or any) concentration. Now imagine you had to do two tasks simultaneously, both of which required the same mental resources. Could you recite poetry while reading the newspaper? Maybe, but only if the poetry were gobbledygook, or you didn't really pay attention to what you were reading. The same problem arises when you do two tasks that both require concentration. You can walk and talk, but could you walk on slippery ice while closing an important business deal? On the LSAT logic games section, every task uses the same part of the brain – they are all logic games – and every task requires a decent amount of concentration. Doing more than one task at a time on logic games means that you'll do each task slower and less accurately than you would normally. Multitasking doesn't save you time, it slows you down. Multitasking is a great LSAT sin, and it comes up in a variety of ways, such as thinking about what you are going to do for the next step in a question before you've finished the step you are on, or in trying to combine a rule with other rules while you are still writing it down. 2. Not knowing what to do It's perfectly OK to look at a question and not know what the answer is. Finding the answer takes time and working through a process – you don't get answers just by looking. However, given that there are a relatively small number of question types for the logic games section, and each type is always answered in the same way, there is no excuse for not knowing the next step to take at any given stage of the section. This doesn't mean that you have to be able to look at a game and know exactly how everything fits together. It doesn't mean that you have to look at a question and know what the answer is. You are going to have to work through a system; you are going to have to figure things out slowly and carefully. But, you should know exactly how to do that, and you will, because I'm going to teach you. As an LSAT tutor, students often ask me for help with games that they can't figure out. Typically, these are really challenging games (otherwise they wouldn't need help with them). I can't count the times a student said, "What's the answer to this question?" or "What's going on in this game?" and I said (after looking at it for a second or two), "I have no idea, it looks really tough."

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How to Take the LSAT Logic Games Section

"What's going on in this game?" and I said (after looking at it for a second or two), "I have no idea, it looks really tough." So what do I do in those circumstances? Tell the student sorry and refund their money? Of course not. Instead, we go through the game or question step by step; we read the first rule or the first answer and figure out what we have to do with that. Then we go to the next one, and figure out what we have to do with it. By the time we get to last step we have answered the question or we understand the game well enough to start working on the questions, and it hasn't taken us that much time, either. This happens all the time; when I first started tutoring, it scared me silly, because I didn't have enough experience to trust my methodology. After a while, though, I started to take these almost miraculous solutions to complex questions, which just emerge from doing the work, as normal. What's the lesson here? Even the best test-taker (me, by the way) can't look at a hard question or game and instantly figure it out. But, any good LSAT-taker knows all the steps to go through, and they can tell them to you at a moment's notice. 3. Not doing what you need to do There are certain steps that have to be taken in order to answer a question. For example, you have to read the question. Most of the time you have to write out a diagram or two. This involves going through the rules one by one. These steps are vital – without them you cannot get the right answer. Each of these steps takes a certain minimum amount of time; you cannot do them properly in less time than this. Yet most people feel like the only way to be good at the test is to rush through these most important steps. What happens when you rush through the most important stuff? You end up making mistakes, getting confused, and/or getting tired. You don't want that. What happens if you slow down? You get the questions right, and everything feels much easier. In the long run, you'll be faster overall because you'll be less tired and wont have to double-check your answers. Why don't people slow down? Because they feel like they can't afford it – if they don't go faster, they won't finish the test. This is a very common and very dangerous mistake to make. Let's analyze it: the goal is to do well. If you don't rush (you assume), you won't do well because you won't finish in time. But, if you do rush, you won't do well, because you can't be accurate if you are going too fast. Damned if you do, damned if you don't. Except you don't have to rush. The people who wrote the LSAT wrote the test to be possible; if a high score were un-gettable (by regular people, not just by professional test prep teachers), the test would be a waste. The people who wrote the LSAT know their business; they know how long it takes to do the steps necessary for a question, and they know what these steps are. Each game is written to be doable in the given time, doing all the required steps. If you do what you need to do on a game and you do it in the amount of time it takes (not rushing through), you will have enough time to get most of the questions right. I promise. Of course, this assumes that you aren't wasting a lot of your time wondering what to do, or worrying about the test… Wouldn't you rather give those things up, and be able to do the logic games more comfortably?

How to Take the LSAT Logic Games Section

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4. Working through fatigue It's midnight. You're exhausted from a hard day at work or school. How do you become un-exhausted? Go to the gym? Read a bunch of philosophy? Plan a new business venture? No, of course not – you go to sleep. The only way to relieve fatigue is through rest. If you are fatigued on the LSAT, what should you do? Another question? Same idea – that question is not going to make you less tired; in fact, you are more likely to miss it because you are tired. What should you do? REST. While you are resting, you won't be doing any questions, and that's scary, isn't it? But, if you don't rest, you'll keep slowing down (and missing questions) as you get more and more tired. If you do take a short rest (20 minute naps aren't necessary) you'll come back faster and more accurate, more than compensating for the time "lost." Resting time is never wasted time. 5. Worrying and/or changing your strategy The LSAT is going to be psychologically difficult; it's a tough test and at times you will feel like you are getting questions wrong. Worrying about it doesn't do you any good (exactly what my mom used to tell me in fifth grade) and it actually hurts you – it wastes time and distracts you (it’s a form of multitasking). It's tough, but work on putting how you are doing out of your mind when you are practicing; eventually you will get used to focusing on what you are doing, rather than on how well you did earlier. During the LSAT, people often feel like they're doing badly when they are in fact doing quite well. This causes them to change their approach to the test – they deviate from the strategy they've been using (the same strategy that has caused them to do well thus far). This, in turn, causes them to do worse from that point forward. Don't do this, either when practicing or during the test. Trust yourself and stick to what you know works; you aren't going to be able to figure out a better strategy in the middle of the LSAT.

Putting It All Together There are several key skills that we have discussed above. These are the things that you are going to do to make the test easier. They are so important that I'm going to say them again. 1. 2. 3. 4. 5. 6.

Learn the logic Have a system for everything that might be on the test Have an energy-efficient approach to work Read carefully Do one thing at a time Take breaks when needed

I want you to notice something – each of these points is phrased as a positive, something for you to do, not something to not do. People tend to focus on negatives, but it is more important to know the right thing to do. The only way to avoid mistakes and problems is to do the right thing. It's important to avoid bad things, but you only get points by doing the right thing. When you notice yourself making mistakes, don't just ask "What did I do wrong?" Also ask, "What should I have done? What will I do next time in this situation?"

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How to Take the LSAT Logic Games Section

1. Learn the logic I'm going to devote sections of this book to teaching you the logic you need to know for this test. It's not as complex as you may think, and it is all based on common-sense ideas you probably already understand. 2. Have a system for everything that might be on the test This is most of why I wrote this book. The logic you are tested on in the LSAT logic games is, like I said, fairly straightforward. What makes the test so difficult is the way in which you are tested – the number of questions, the phrasing of the sentences, and the time pressure. Knowing exactly what you are going to do, and in what order, at any given moment of the test will relieve pressure, and it will eliminate time wasted wondering what to do. And, if it is a good system (and my system is the best there is) it'll help you answer the questions as accurately and efficiently as possible. That said, I want to give a little warning. Once you learn a way of doing things from this book, stick to it. The more you do it, the better you'll be at it – faster and more accurate – and the less you'll have to think about it, which will make the questions easier. One of the big time-wasters I see is that students look for a faster or better way of doing a question or diagramming a game, even though they already know a viable method for it. Be consistent in your approach to games. The best way to be good at the test is to have good habits, and habits are formed by repetition. 3. Have an energy-efficient approach to work Being efficient means minimizing waste. People waste energy on logic games by thinking too much. Typically this involves trying to figure things out in their head, as opposed to writing them down. Writing everything down and doing all your work on the page, rather than in your head, seems slower because it involves the extra step of writing. But, in fact, it is more efficient than just thinking questions through. There are several reasons for this. First, if you write down everything you do, you can "forget" each step after you do it, since your notes will remember all the relevant information for you. You can focus all your attention on each step you do, rather than splitting your attention between what you are doing now and what you just did. In addition, writing things down allows you to involve more parts of your brain – the visual and tactile – in the test process. You are more likely to catch mistakes you make when they are written down, and you are less likely to make those mistakes in the first place. Finally, you can use your written work to help you out on later questions. We'll learn an efficient method as we go through the book. Often, as students get better, they feel that they can be a little sloppier on questions – doing things in their head and/or doing several steps of a question at once. This inevitably leads to them missing more questions. The reason you can get answers quickly and accurately is that you are good at doing what needs to be done on a question. Trying not to do this will make you miss a question. Trying to do it in your head will, in the long run, tire you out. Don't try to change the way you approach a question once you get good at it – this totally negates the advantage of having learned to do it. 4. Read carefully Every single word in the Logic Games section is crucial. You don't want to miss a single one of them. Read everything – the rules, the questions, the answers – carefully, making sure you take everything in. You aren't reading slowly for the sake of reading slowly, you are reading carefully – understanding every single thing said.

How to Take the LSAT Logic Games Section

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5. Do one thing at a time Focus on the step you are doing while you are doing it, and ignore everything else. Don't worry about what equation you'll solve next, or what you are going to do with the information you get out of this diagram; once you've finished doing what you are doing, then you can think about the next step. 6. Take breaks when needed There is a science to taking breaks. This takes a bit of explaining, so get ready and pay attention to this. The first rule is: when you feel the onset of stress or fatigue, take a break. If you feel your concentration slipping, stop working for a bit. Stare at the ceiling. Rotate your shoulders. Breathe deeply. In other words, relax. Do this for as long as a minute or as little as a few seconds, whatever you need. It is perfectly OK to spend 60 seconds doing nothing at all during a test, as long as you are doing it on purpose. Take these breaks every time you start to lose concentration. This may mean taking a short break every four or five questions towards the end of the test. It is better to do this than to lose focus. When I took the Bar exam I went to the bathroom three or four times per section (a section is three hours long). Was I nervous? Had I drunk too much coffee? No; I didn't even use the facilities most of those times, just looked myself in the mirror, smiled, maybe splashed some water on my face, and walked back to my seat. Just walking to the bathroom took at least a minute, so these breaks probably lasted at least 3 minutes each. This time was totally refreshing, and really useful in keeping me on track. I ended up finishing each section before the majority of people taking the test, despite having "wasted" 10 minutes a section going to the bathroom, in good part because I was always focused. Plus, since I was wearing boots, I made a lot of noise, and everyone had to look at me… I was wearing a three-piece suit, because I believe in dressing for success, so that made me think of how good I looked, and how everyone was looking at handsome me, which boosted my confidence and got my mind off the test. Ridiculous, I know, but these little confidence builders can be very useful; I'll talk more about them in the chapter called During the Test. This will require that you learn to tell when you need a break. There are several ways to do this. One is to be aware that you will inevitably lose focus when you are studying; if you are ready for it you'll notice it when it happens, and take a break. Let me repeat that: when you study, take a break every time your concentration starts to slip. This is practicing what you should do on the actual LSAT; by the time you get to the real test, you'll be good at this. You'll also get better at noticing when you need a break. Another method of learning when to take breaks is to look at your performance on a series of questions after the fact. If you tend to miss questions in blocks – missing several in a row, rather than spread out – that is a sign of fatigue. Questions aren't grouped by difficulty or skill; if you are missing a group of questions, that's a sign that the problem is you and not the questions. Notice how often these blocks of missed questions occur. If they occur with some regularity, that shows you when you are getting fatigued. For example, I had a student who, like clockwork, would get five questions right, three wrong, five right, right wrong. This told me that she got tired every five questions. Patterns don't have to be so clear-cut; they are more likely to be a tendency, such as missing a few questions in a row every ten or so questions. Once you notice a pattern of when you get fatigued, start taking breaks at regular intervals – right before when you would normally get tired – so as to break the pattern. The clockwork five-right three-wrong student needed to stop after every fifth question and take a break.

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How to Take the LSAT Logic Games Section

have to be so clear-cut; they are more likely to be a tendency, such as missing a few questions in a row every ten or so questions. Once you notice a pattern of when you get fatigued, start taking breaks at regular intervals – right before when you would normally get tired – so as to break the pattern. The clockwork five-right three-wrong student needed to stop after every fifth question and take a break. This isn't so relevant to logic games, because people also often miss questions in groups because they didn't understand the game, rather than because they got tired. But this is a very useful technique for analyzing your performance on Logical Reasoning, so I thought I'd throw it in for free. You should also have a rule that you follow when studying, and when taking the test. My rule is to take a break after every logic game, no matter what. This means that, even if I feel great, I take a short break, generally just looking up from what I'm doing and moving my shoulders and neck around. This gives me a chance to get that game out of my mind, and to get sharp for the next game. Oftentimes you'll be too worried about the test, or too keyed up, to notice if you need a break. This rule guarantees that you'll maintain your focus and stay fresh. Follow this rule every time you study; by the time you take the LSAT, it'll be a habit, and require no thought.

What Do I Do Next? Feel tired? Take a break. When you feel mentally ready, begin reading the next chapter – The Fundamentals. Make sure you took notes on this chapter and that you use what you have learned here. I'll expand on much of it in later chapters, especially in Game One through Game Three, but I'll expect you to remember to take breaks, read carefully, and not multitask.

The Fundamentals

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The Fundamentals Let's get our terminology straight before we start discussing things in depth. Every logic game will start with a short paragraph explaining the situation you are dealing with. I call this paragraph the setup. After the setup, there will be a series of sentences describing the restrictions on the game. I call these the rules. After the rules, you will be asked questions. The setup and the rules give you a lot of information; the questions will ask you to put this information together and make determinations about what can and cannot happen in the game. There is going to be too much information for you to simply remember; you are going to have to write most of it down. Typically, it will be easiest for you to organize your information around some kind of chart or list. We'll call this the diagram: the diagram is the way in which you visually organize the data you are given in the setup and rules. There are three steps that you have to go through in every logic game. They are done in a certain order: it would generally be odd to read the rules before the setup, since the setup will give you the context for understanding the rules; likewise, it doesn't make any sense to answer questions first and then read the setup or rules. Here is the order in which the steps would normally be done: Steps in Chronological Order 1. Read the setup and make a diagram 2. Read the rules and write them down 3. Answer questions Before we discuss these steps in detail (and we are going to do so in great, great detail), tell me which of these steps is the most important? Take a second to think about that before looking at the next paragraph. Answering the questions is the most important step. Your goal on the LSAT is to get a high score. It is impossible to get a high score without answering questions. You can answer questions correctly without doing any other step, although you aren't likely to do that well (this is called guessing). But, even if you do all the other steps perfectly, you can't get a high score without answering the questions. What's the next most important step? Well, what step is most necessary to answer the questions? Each question will be based on understanding the rules, so step 2 is the next most important. It is very difficult to answer the questions correctly without a solid understanding of the rules, but not impossible (you have a one in five chance of getting a question correct if you just pick an answer randomly). What's next? Well, the questions are a lot easier if you have a good system for organizing your information. Thus, having a good diagram is important to answering the questions, but it is not necessary. Any diagram, as long as it doesn't contradict what you have been told, can be used to organize the information and answer questions. There is no "correct" diagram for a game, only diagrams that are more helpful than others. You need to know what is most important because that should dictate how you divide your time on the LSAT and in studying – you should spend more time answering questions on the LSAT than you do on any other step, and you should spend more of your study time

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The Fundamentals

learning how to answer questions. Don't obsess over trying to find the "perfect diagram," or in writing down rules in the most concise possible way (I'll talk about both of these topics in more detail later), just make sure you understand what is going on, get it down on paper, and get to the questions. Deductions Often, several of the rules have some common element. These rules can be combined to give you a new rule. For example, if one rule says "R is after P," and another rule tells you that "P is second to last," we know that R has to go last because that is the only position after P. Combining the rules to find out new information that always has to be true is known as making deductions. In some cases, as you answer the questions you will realize that rules can be combined in this way (more often, though, the answers just ask you to figure out what would happen in specific cases, not what has to be true generally). People frequently try to make deductions before they look at the questions in order to know as much as possible about the game before they answer questions. The importance of making deductions before you look at the questions – of trying to put rules together as you look through them (what I list as step two), or after you have looked at them but before looking at the questions (step three) – is misunderstood by many, if not most, students preparing for the LSAT. Most students feel that they must make deductions before they look at the questions. They think that if they don't make deductions early on, they won't be able to do the questions fast enough. I strongly disagree, however. I know, both from first-hand experience and from working with hundreds of students, that making deductions before looking at the questions is not necessary either for speed or for accuracy on LSAT logic games. In fact, trying to make deductions before looking at the questions is, for many students, the number one reason why they can't finish the logic games section in time. If these students just read the rules and began answering the questions, not trying to make deductions early on, they would be able to do all four games, whereas with looking for deductions they can only do two or three. For the majority of students I work with, including students who can and do get scores in the 90th percentile on the LSAT, trying to make deductions before answering questions hurts their score more than it helps it. Here's why looking for deductions before answering questions deductions is unnecessary and often harmful on the LSAT: First, you can answer any question on the test without having made any deductions prior to answering that question. If the question requires you to make a deduction, it will push you in that direction. The question will either give you a hypothetical situation to deal with ("Suppose X was 4th") that will lead you in the right direction, or the answers to the question will give you concrete possibilities that you can then test out. Having something concrete to work with makes combining the rules much easier. In either case, you don't need to have thought out the deductions beforehand. Second, many games have no deductions, or very few; in most other games the deductions aren't terribly helpful. Looking for deductions in these cases wastes valuable time that you need to spend answering the questions. Finally, making the deductions is difficult to learn to do consistently. It can be learned, but the payoff for learning it is often not worth the time and effort it costs. Most of you probably have a limited amount of time to devote to studying the LSAT. Using that time most efficiently means learning the most useful skills before any others.

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This isn't to say that making deductions prior to answering the questions is useless; on the contrary, deductions often make the games easier and faster. But, it is generally better to wait to make deductions until you start working on the questions, and it is never necessary to make them sooner. As I wrote this book, I did every logic games section in every LSAT released since June of 1996. I purposely avoided making any deductions until I started working through the questions. I used only techniques contained in this book. I finished each section in the time given (35 minutes) with my normal (high) level of accuracy. For this reason, I won't teach you to make deductions until much later in this book. For now, we'll understand the rules individually, and only put them together if the questions make us. We'll focus on learning the most important skills, the ones that will make the biggest difference to our score. All those skills are contained in this chapter. Later on, once you have mastered them all, you can learn to make deductions, which may help you improve your score a little more. Those of you who haven't done any LSAT preparation before now may not be surprised by this. Those of you who have previously taken an LSAT preparatory course or read a book on the LSAT may be taken aback. You should read the accompanying boxed text before going on. If making deductions is so unimportant and potentially harmful, why do test preparation courses stress it so much? Well, making deductions is difficult – it's the hardest part of logic games. Naturally, students want to learn how to do it. Students almost always spend most of their time studying what is most difficult for them, rather than what will help them get the most points. In addition, teachers enjoy teaching deductions more than anything else. It allows them to show off their intelligence and LSAT skills, and it is an interesting challenge to teach well. So there is great commercial and personal pressure to spend a lot of time teaching deductions. How to waste time on logic games The biggest logic games time-waster is looking for deductions that you can't find. These include deductions that don't exist and deductions that you are not capable of figuring out. If you are going to make deductions, don't spend so much time making deductions that you have insufficient time to answer all the questions. Another big time waster is looking for the "perfect diagram." It is generally worthwhile to put together a diagram that you can understand and use well, but trying to find some mythical Platonic ideal of a diagram is foolish. The difference in efficiency between a "great" and a "decent" diagram, or even an "excellent" and a "barely adequate" diagram is not worth a lot of time and effort. I'll teach you how to put together good diagrams quickly. However, you will get into some situations where the diagram you come up with just doesn't feel perfect. Forget about it. If you come up with a diagram that accurately represents the game, but doesn't feel like the best possible diagram, don't worry about it – get on with the game. I get calls from students all the time who say, "Brian, I can't figure out the diagram for this game. I spent 10/20/30 minutes trying to do it, but I can't get a good diagram." I ask them to describe the diagram they have, and then I say, "Let's use that and just go through the questions." Almost every time, they get all or most of the questions right; they could have done it themselves, but they were so freaked out about their diagram that they didn't bother to actually do the game. Don't let this happen to you, especially on the LSAT. Worst-case scenario – you miss one or two questions because you have an inadequate diagram. That's a lot better than running out of time and missing half the game because you spent so much time on your diagram.

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The Fundamentals

A note on pedagogy I'm about to talk in detail about the theory and practice of each of the three steps. On the one hand, it's going to be difficult for you to understand and digest all this information right now, without any examples to work through. I really think people learn best by doing. On the other hand, I think you need all the information to be located in one easy-to-find place so that later on you can read through it and see how it fits together. So I'm going to say almost everything I want to say about the steps in general right now. The next few chapters will be us going through some logic games from past LSATs and seeing how to apply everything I've just talked about. As we do that, I'll repeat a lot of this stuff and show you how it works in specific cases. After you've read through that, I really encourage you to reread this section; it'll make a lot more sense and you'll see how everything fits together. But you should still read this section now, before going on to Game One, because what we do in the rest of the book won't make any sense unless you understand the foundations I'm about to give you.

Step 1: The Setup and Diagram As you might be able to tell from my above rant against "perfect" diagrams, this is a much misunderstood step. In this step, you are reading through the setup – the initial paragraph of the game – trying to figure out what is going on. You may also spot some rules as you read the setup. I'll talk more about those in the next section. After you read through the setup, you will want to figure out how to organize the game in a diagram. There is only one kind of logic game, so you only need to learn one way of diagramming, which will work for every game. Let me say that again, for those of you who don't believe me: there is only one type of logic game. This is something that might shock those of you who've done LSAT preparation before, but it's true. Every LSAT game involves at least two types of things. There might be several things of each type. The game will ask you to match up things of one type with things of the other type. Take the following three examples I just made up: A tutor is going to schedule the appointments of seven students – P, Q, R, S, T, U, and V – one per day on Monday through Sunday of the same week. Six boys – A, B, C, D, E, and F – are being grouped by height; three boys are of average height, two are short, and one is tall. Five flowers will be selected for a bouquet from a stall containing nine flowers: begonias, daisies, irises, jasmine, lilies, orchids, poppies, roses, and snapdragons. Each of these examples has two types of things. The first has students and days, the second has boys and heights, and the third has the bouquet and the flowers. In each case, you want to match up one type of things with the other. You want to match students with days of the week, or boys with heights, or flowers with the bouquet. It is possible that the game may contain three types of things. For example, the second game could go on to say: "Two boys are blonde, one is a redhead, two are brunettes, and one is bald." Then you'd be trying to match boys to height and to hair color. That doesn't really change anything, as we'll see.

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In every game, one of the two types of things is going to be more definite. That is to say, it will change less, and/or you know more about it. In the first game you know more about the days of the week. Why? Because Monday will always be next to Tuesday, which will always be next to Wednesday, etc. This will never change. You know nothing about the students, though – you have no idea where P or Q or R will be. In the second game you know more about the heights – you know that there are three average kids, two short kids, and one tall kid, which will never change – but you know nothing about the boys, since which boy is of which height might change. In the third game, you know more about the bouquet – it must always contain five flowers – than about the flowers. We are going to build our diagram around the definite group. The definite group is the one we know the most about. Every other type of thing in the game is variable. I'm not going to use these words ("definite" and "variable") much in the rest of the book, so you don't have to memorize what they mean; you just need to remember that there are types of things that you know more about and types of things you know less about, and your diagram should be built around the ones you know more about. Making the diagram is simple enough – just write the names of the definite group members (abbreviate if you want) in a row, horizontally or vertically. I generally prefer horizontally for some reason, but it really makes no difference. There are occasionally games where it makes more sense to do it one way or another – for example if you are listing the floors of a building you might want to do it vertically, since buildings are built up and down – but it is never necessary to go one way or another. Here are our diagrams thus far: Mon Short

Tues

Wed

Average

Thurs Fri

Sat

Sun

Tall

Bouquet: Now, each definite thing will have a certain number of the other (variable) things associated with it. Draw that number of blanks under (or next to) each definite thing (use lines to show where the blanks are). Each day of the week will have one student, so each gets one blank. In the next game, there are two short students, so Short gets two blanks, where Average gets three and Tall gets one. There are five flowers in the bouquet, so Bouquet gets five blanks. If the game doesn't tell you how many variable things go with each definite thing, don't worry, just don't put any blanks. Mon ___ Short ____ ____

Tues ___

Wed ___

Average ____ ____ ____

Thurs Fri ___ ___

Sat ___

Tall ____

Bouquet: ____ ____ ____ ____ ____

Sun ___

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Write down the names of the variable things someplace so you can reference them (again, feel free to abbreviate). Label them (heights, flowers, etc.). And that's it. That's it. We have just generated what I call the original diagram; we'll recopy this diagram whenever we want to test something out (see Making Test Diagrams later in this chapter). What if there are three (or more) types of things? If there are more than two types of things, go through the same process, and add blanks for the third type of thing; it can be helpful to label the two types of blanks you have. For example, if each of the boys gets a height and a hair color, then I'd just put a place for hair color next to every blank for a boy (since every boy gets a hair color); I label the "boy" blanks b, and the "hair" blanks h (or if I trust my memory, I just remember which blank is which). Short b h __ __ __ __

Average b h __ __ __ __ __ __

Tall b h __ __

The short boys' names go under the "b" in the "short" group, and their hair color goes next to their name (under the "h"). Wait! What if you can't figure out which type thing is more definite? If you can't figure out which type of thing is more definite, just pick one of the types of things and base your diagram on it in this way. Don't worry about whether or not you are "right." Like I said above, the difference between a "perfect" and a "decent" diagram is not that big. There is one type of game that doesn't diagram quite like this. This is where the definite things have a certain spatial orientation. For example, they could be seats around a circular table (see Game Seven). In that case your diagram should mimic the orientation. In a circular table, the "last" person is next to the "first" person, so your diagram should include this, probably by being a circle itself. This is rare, and circular tables are about the only situation where it comes up. You now know everything there is to know about diagramming logic games. After this it is all just practice. Let's summarize: every game has two or more types of things in it, and the game just consists of matching a thing from one category with one or more things from another category. Figure out which type of thing you know more about, and write those things down in a line. Figure out how many of the variable types of things (the ones you know less about) go with each thing you have just written down (the ones you know more about), and make that many blanks under each definite thing. Don't worry about the vocabulary "definite" and "variable"; that's just for me to avoid clunky sentences, and isn't that important for you to master. I recently taught a student who had gone through a course with a major test prep company whose name I won't mention. He told me that diagramming the games always confused him. I taught him exactly what I just taught you and he stared at me in disbelief. He couldn't accept that the diagrams were so straightforward. In fact, I thought he was on the verge of getting mad at me. He kept asking why he had been taught that it was so complicated and difficult. I couldn't tell him, and I can't tell you. Maybe test prep companies want you to think the LSAT is harder than it is so you feel like you're getting your money's worth (but I doubt it). My theory is that this just never occurred to them. It took me years of constant one-on-one interaction with LSAT students (and the help of some very smart people) to come up with this. I've never found a game that couldn't be easily diagrammed like this. In fact, I've found that diagramming this way often gives me a better diagram than the more complex approaches I've seen, and it never gives me a worse one. And the student I told you about? He went from getting about 12 questions right per section to getting about 20, in just a few days.

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diagrammed like this. In fact, I've found that diagramming this way often gives me a better diagram than the more complex approaches I've seen, and it never gives me a worse one. And the student I told you about? He went from getting about 12 questions right per section to getting about 20, in just a few days.

Step 2: Read the Rules When you read the rules you are trying to understand them. If you don't understand a rule, you can't apply it, and if you can't apply it, you are going to miss questions. This means that you need to read the rules slowly and carefully, one at a time. As you read each rule, think about what it means and what it doesn't mean. For example, if you are told that "A is next to B," you aren't being told what order they come in (B might be before A or after – BA or AB). It is much worse to think a rule means more than it really does than to think it means less. Most of the time, rules will be easy to interpret. They will look like rules you have seen and understood before. In the few cases where the rules aren't easy to understand, try making them specific in order to make them clearer. If a rule says something like "No professor teaches a class taught by a professor with the same specialty," try out some examples: say to yourself, "What if professor X taught class A? What would happen?" Trying out specific examples will make understanding the rule much simpler because people think about the concrete better than the abstract. Some seemingly difficult types of rules come up again and again. One of the most common types of rules, called "If… then…" rules, typically takes the form "If such and such happens, this other thing has to happen as well." These rules are so important that I will provide an in-depth explanation of how they work in their own separate chapter ("If… then…" Rules and Negations), which comes after Game One. I wait until after Game One because that game doesn't have any "If… then…" rules, and it gives you an opportunity to get used to the general format of games, as well as all these fundamental concepts, before adding new ideas. Once you understand a rule, you need to write it down. You will need to look at the rules over and over, often several times for each question. The LSAT doesn't write the rules in the clearest or most useful language; reading what they have written again and again will just waste time. Instead, we write the rules in a way that makes sense for us. When writing down a rule, make sure what you write is clear, complete, and accurate. In other words, you need to be able to understand what you have written down, it needs to include all the information in the rule, and it needs to be right (hopefully that last part is obvious). One common mistake that people make is to try to write their rules in the most compact form possible. They learn and try to use all kinds of strange symbols. This is fine if you are completely comfortable with the symbols. If you aren't, don't use them. Don't be afraid to use words when writing down rules. You don't need to write in complete sentences, but there's nothing wrong with doing so if you wish. You wrote the rule down well as long as you can understand what you have written. My rule of thumb for writing down rules is this: I assume that I will turn dumb 10 seconds after writing down the rule. I write every rule in a way that the dumb version of me can understand. I figure if I have an opportunity to make a mistake I will make it, so I write the rules in a way that I can't possibly misinterpret.

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The final rule is this: be consistent. If you use a symbol or phrase to mean something, always use it this way. Don't use a symbol one way in one game and another way in another game. Otherwise you will get confused. Symbols Used in This Book __ This is a space that must be filled by someone XY X is right next to Y in this order (or in the same group as Y) X _ Y (X _ _ Y, etc) There is one space (or two, etc.) between X and Y in this order Those are all of them. The rest of the time I use English words and phrases. A final point: go through the rules one by one. When you are thinking about rule 2, don't worry about rule 1 or rule 3. Don't try to put the rules together at this stage; do one thing at a time. Otherwise its easy to get sidetracked or confused. Let's summarize. Read the rules one by one, slowly and carefully. Make sure you understand each rule. Once you understand a rule, write it down. Write it down in a way that you will easily understand later on. Don't leave out any information. If you use symbols, use ones you understand and always use them in the same way. Another note on deductions This note is especially for those of you who've done some LSAT practice before this. I mentioned before that making deductions before you do the questions is not necessary and can be bad. It can be helpful, too, and I'm here to help. I will teach you how to make deductions eventually, but I'm not going to tell you how to make them now. As we practice games we'll look at the rules individually, rather than trying to combine them. As you go through the book you may see ways in which the rules can be combined. Please don't try to look for these and don't use them if you see them; I don't want you practicing the wrong skills. Instead, do the games as I do. You need to learn and get close to mastering these fundamentals before you try to learn to make deductions. Even if you have studied for the LSAT before and consider yourself pretty good at logic games, go through this book in order; learning the most important skills will help your score more than jumping straight into the more advanced ones (and you really won't be able to understand and apply the advanced techniques without understanding my view of the fundamentals). We are going to do the first eight games in this book without making a single deduction. Why? For a couple of reasons. First of all, because you don't need to. In fact, trying to make deductions is often a huge waste of time. By doing games without making deductions I demonstrate that it is not just possible, it's often faster and easier. Second, by doing games without deductions I will give you a solid grasp of the most important aspects of games. Deductions are often a distraction at the beginning; once you have mastered the most important skills you can turn your attention to the little things, like deductions. Third, by not learning to make deductions you save studying time. Given that most LSAT students have a limited amount of time to prepare for the test, and a lot of skills to master, limiting the number of skills you try to learn is good for you. You should focus on the skills that make the most difference to your score. Finally, many of the skills you will learn as we go through the games in this book will be helpful in making deductions. When you finally turn to the Advanced Techniques, deductions will make a lot more sense and be a lot easier.

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Step 3: Answering the Questions All right, you excited? We're about to go over the most important step. Fasten your seat belts. Remember, I'm about to inundate you with information. You won't be able to take it all in right now. In fact, a lot of it won't make sense until we start doing games. Still, read through this, skimming if you have to, before going on to the next chapters. After you've read through the first couple of games I explain, you'll know what in all of this you need to reread and make more of an effort to understand. The order of the questions Before we talk about answering a single question, we have to talk about the order in which we will answer the questions. If you've ever done an LSAT logic game before, you've probably noticed that the questions for each game are not given in order of difficulty. To a certain extent, the first question is often the easiest and the last often the hardest, but this is frequently not true, and even when it is true the middle questions don't follow any pattern of difficulty. This is important, because you have only a limited time to answer questions on the test. There is a chance that you will run out of time and not be able to answer every question in the games section. Since that is the case, you'd better do the easiest questions first. Why? Two reasons: they take less time, and you are more likely to get them right. If you run out of time and have been doing the easy questions first, rather than just going through the questions in order, you will have answered more questions and gotten more right than you would have otherwise. In addition, working through certain questions first will make other questions easier. Some questions will help you understand the game better, and will generate scratch work that you can use to eliminate answers on other questions. It's better to do these questions first, then, so as to make the later questions easier. Fortunately for us, the easiest questions are also the ones that give us the most helpful scratch work. There is a science to the order in which you will do the questions. That is to say, you can memorize the procedure ahead of time and simply go through a series of mechanical steps to determine what questions you want to do when. Sound easy? Well, it is! Logic Games Questions in Order of Difficulty (Easiest to Hardest) 1. What can be true? and If-questions 2. What can't be true? 3. What must be true? 4. What can be false? 5. Which is a complete and accurate list? 6. What is the maximum/minimum number of …? 7. How many diagrams are possible? These are all the question types you'll ever see on the games section. (Notice that I've italicized the "is" in "Which is a complete and accurate list?" That's because sometimes you will see "Which could be a complete and accurate list?" which is actually the same as a "What can be true?" question, a much easier question type) Now, questions will often be asked in different words. For example, "Which of the following is possible?" means the same as "What can be true?" I'll list common equivalent questions in the accompanying boxed text.

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Also, questions will generally involve more words than this. For example, a question could ask, "Who can be in position 3?" This is a "What can be true?" question, because it asks for what can happen. If the question asks, "Who must be in the same group as Todd?" this is a "What must be true?" question, because it asks for something that must happen. Common Equivalents for Each Question Type Here are some different ways questions can be phrased. 1. What can be true?  Which could be true?  Which of the following is possible?  Which of the following is acceptable?  Which one of the following could be a complete and accurate list of …?  Each of the following cannot be true EXCEPT (see #2 for equivalents of "cannot be true"; any of them can be substituted for "cannot be true") 2. What can't be true?  What must be false?  What is impossible?  Which of the following cannot be a complete and accurate list of …?  All of the following can be true EXCEPT (see #1 for equivalents of "can be true") 3. What must be true?  All of the following can be false EXCEPT (or "could be false") 4. What can be false?  All of the following must be true EXCEPT Question types 5 doesn't have any common equivalents. 6. What is the maximum/minimum number of …?  What is the greatest/smallest number of …?  What is the earliest/latest…? 7. How many diagrams are possible?  For how many of the … can the position be determined?  In how many distinct orders can …?  Which of the following, if true, would allow … to be determined?  There is exactly one way in which … if which of the following is true? If-questions (these words mean "If")  Suppose…  Assume… There is one additional complicating factor. Some questions start out, "If such and such happens…" and then go on to ask a question (such as, "If such and such happens, what must be true?"). We call these If-questions (as opposed to "If… then…" rules). These questions ask you to imagine a hypothetical situation, and then they ask a question about that situation. The question can be any one of the seven types I've listed above. For example, they might ask, "If M is in the first position, what must be true?" If-questions give you new information about the game, but this new information pertains only to this question. All the normal rules apply. These questions are easier than other questions because they give you more information, and more information makes things easier. We

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want to do them early on for that reason. In addition (as I'll explain in more detail later), these questions give you helpful information for later questions, but you can't use the notes from your previous questions to help you do them. Thus, if you do them sooner they will help you with later questions, but there is no advantage to doing them later. Thus, we do If-questions (those starting with "If such and such happens" before most other questions. So, here is our procedure. We do all the If- and "What can be true?" questions first. Then we do "What can't be true?" questions. Then "What must be true?", and so forth. It doesn't take any significant amount of time to go through the questions and pick out the one you want to do next, but it does save a lot of time to do the easier questions first. Why this order? I suppose you want to know how I arrived at the order I use for the questions. Like I said, there's a science to it. First of all, you have to notice that there are more wrong answers than right answers. Four out of five answers are wrong. To answer a question you have to look at the answers. This means that you spend most of your time looking at wrong answers, not right answers. For any given question, the easier it is to figure out if an answer is wrong, the easier the question is. Second, answer a question. What is easier to determine: that an answer follows all the rules of the game, or that an answer breaks a rule? It is easier to determine that an answer breaks a rule. To determine that an answer follows all the rules, we have to look at all the rules, and make sure every person in every slot of the game follows all these rules. To see if an answer breaks a rule, we typically only have to look at some of the rules and some of the parts of the game. It is almost always less work to spot answers that break the rules of the game than answers that don't. Put the two points together. We evaluate the easiness of a question based on how easy the wrong answers are to spot. The easiest answers to spot are those that break rules. Therefore, the easiest question should be the question where the wrong answers break rules. Et voila! Look at question type 1. If the question says "What can be true?" you know that the right answer can be true. Which tells you what about the wrong answers? Yes! It tells you that the wrong answers can't be true, which means that they break the rules! This is as easy as it gets. Now, question type 2 asks "What can't be true?", which means that the correct answer breaks a rule, and the wrong answers follow the rules. Not so easy. But it is much easier than question type 3, which asks "What must be true?" On one of these questions we know that the right answer must be true, but the wrong answers can be true, right? That is, they might be true sometimes, but not all the time. So on one of these questions, potentially no answer breaks a rule. That makes the answers more difficult to evaluate (there are other difficulties, as we'll see later on). The other question types take even more work to evaluate, but for now you'll have to trust me on that. There is an additional consideration, which is how much we can use our previous work to help us on a question. As we do the questions, we will generate diagrams which we use to test out possible answers. Each of these will show us a possible way the people in the game could be placed. Many questions require us to think about what is possible. For example, in a "What can't be true?" question, we know that the wrong answers all describe possible

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situations. That means that if we see the situation described in the answer in a diagram we already have written down, we know that it is possible without doing any more work. In question type 1, "What can be true?", only one answer (the right one) describes a possible situation. That means that the wrong answers break the rules, so the situations they describe won't show up in the diagrams we've previously generated. So there is little point in waiting to do these questions – not only are they pretty easy, they also aren't going to get any easier if we draw more diagrams. But the other questions, types 2–7, will be made a lot easier by having other diagrams to look at. This is why we do If-questions the first time around. If-questions are pretty easy, because they give us more information. Also, we can't use diagrams from other questions to help us on If-questions (I'll explain this later). But we can use the diagram we make on an Ifquestion to help us on other questions. Which means that If-questions won't get any easier if we wait, but doing them sooner will make other questions easier. Science.

Making Test Diagrams You will often have to test answers. This means that you will have to see if the situation described in the answer is possible. You do this by making a new diagram and trying out the situation described in the answer. Why do we make a new diagram? Well, when we test something out we have to try it out, which means we have to write it down in a diagram (we never do things in our heads, because that is too hard). We are going to have to test out many answers. If we use the diagram we made originally (in step 1 of the game), we'll have to erase what we put in it when we want to test another answer. This is a waste of time, and, in addition, it means that we can't reuse the diagram we just made (and erased) later on. So, whenever we want to test something out, we draw a new diagram. Our new diagram should contain everything we put in our original diagram (see Step 1: The Setup and Diagram earlier in this chapter), but we don't have to recopy our rules (since we aren't going to add anything to them). Once we have a new diagram, we add to it whatever we are trying to test out. If the answer says "M is in group Z," we put M into a space under group Z. After we've added anything to our diagram, we go through our rules and see if anything else has to happen. For example, maybe N always goes with M. If M is in group Z, then N has to be there too. If anything has to happen, we put that in the diagram. Then we go back through the rules again, because, as I just said, after we've added anything to the diagram we go through our rules. If we go through the rules and find that nothing else has to happen, we then try to fill out any empty spaces that are left. Put whoever remains in any empty space, as long as it doesn't break a rule. Keep trying each space until you find one for each person. If you can fill all the empty spaces, you have a possible diagram. If you can't fill the empty spaces without breaking a rule, you don't have a possible diagram. Knowing this one way or another is the key to answering every question. If you have a diagram that doesn't work (meaning it breaks a rule), cross it out (erasing takes too long). We don't want to look at the diagram ever again, because it will just confuse us.

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Don't erase or cross out diagrams that work. We'll call these previous diagrams and we can use them to help us figure out later questions. Each previous diagram gives us a possible situation, and that can be helpful, as we'll soon see. Marking with a dot or star Often the answers don't seem to give you enough guidance about where to put things. But to complete your test diagram, you have to fill every spot; this means that you have to put each thing someplace. Here is the worry students often have: "If I put this thing in one place, maybe it won't work there, but it would have worked someplace else. I'll mark the answer wrong, when it really is right. How do I know where things are going to work?" Well, sometimes you just don't. But you have to draw a test diagram, which means you have to put the person (or thing) someplace. Have no fear. You don't need to be able to figure out the best possible place in your head. Instead, when you are uncertain where to put someone, put them in the first available place. Then mark that person with a little dot or star. This tells you that you made a decision where to put that person, but they might be able to go someplace else. Then, if the diagram ends up not working out, try moving the person you have dotted/starred to the next available place. This usually means moving them from left to right. If you have multiple people marked, move the last one you put in. Keeping doing this until you get a diagram that works, or you run out of places (which tells you that it will never work). I use an asterisk (*) in this book when marking things in this manner. In real life, I use little dots, because they are quick and easy to put in; but they are hard to see in a book, so I'll stick with the big, obvious asterisk. Once you have dotted one person, you will often be forced to put other people in definite spaces. Don't mark these people, just put them in. Again, only dot when you make an arbitrary decision, so that you know where to go back and make a different decision. And, finally, don't do this when you know already where the person can't go – you are wasting your time trying them in places that you see are impossible. We are going to spend a lot of time making test diagrams as we work through the games in this book; soon this will all become habit for you.

The Question Types Let's take a detailed look at each type of question. In order to answer a question, you need to know how to figure out what the right answer is and what the wrong answers are. The question always describes the right answer to you. If it says "What must be true?", you know that the right answer is a situation that must be true. Since each question describes the right answer, it also describes the wrong answer: the wrong answers are those that don't have the quality the question describes. For every type of question, you need to know what you are going to have to do to test out the answers. In addition, you need to know whether or not you can use previous diagrams to help answer the questions. We'll examine all these issues for each question type, and for If-questions. These next sections contain a lot of information. You will eventually have to memorize it. I am totally serious – you can't do well on logic games without knowing how to answer the questions. As you read through the section on each question type, write out the important

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points – what you know about the right answer, what you know about the wrong answers, how to test the answers, and how to use previous diagrams. Don't try to memorize this yet – read through one or two games in this book to get a feel for how these things work in practice. Then memorize. The sooner you understand each type of question, the better you'll do on the test. I have a summary of this information in the Glossary. I've had students who were really smart, and really good at understanding the games, making diagrams, and making deductions. But they kept forgetting how to do the questions. Once I reminded, them they'd do great, but they didn't bother to memorize the processes on their own. Their scores suffered as a result. Eventually I had to yell at them a little to get them back on track. But this is the most basic kind of knowledge, and the most important. Remember, doing the questions is the only part of the test that impacts your score, and you aren't going to get many right if you don't remember quickly and easily how to do the questions. In fact, think how much less stressful the test will be if you never have to struggle to think about how to do a question – you can spend all your energy just doing them, rather than trying to remember how. 1. What can be true? questions What do we know about the right answer to these questions? We know that it can be true – that is to say, it is possible. This means that it follows all the rules of the game. What do we know about the wrong answers? They can't be true – they must break at least one rule. How do we test out the answers? We test out the situation the answer describes (see Making Test Diagrams earlier in this chapter). We draw a new diagram and put in it the situation the answer describes. We see what has to be true from the rules. Then we fill in all the empty spaces. If this works – if we can fill the empty spaces without breaking a rule – the answer can be true and it is the right answer. If you see that you are going to break a rule, stop, cross out the diagram, and cross off the answer. It is wrong. Notice that you aren't going to get a lot of mileage out of previous diagrams. Most of the answers are going to break the rules, which means that they won't show up in previous diagrams (since your previous diagrams are all of possible situations).2 Once you've found the right answer, go on to the next question. There is only one right answer; have confidence in yourself and don't keep checking answers. Look at it this way: if you don't know what you are doing, you probably aren't going to get the right answer no matter what, so you might as well get it over with quickly. If you do know what you are doing, then you've already got the right answer, so looking at the other answers is a waste of time. One more thing. Very often the first question of the game is a special kind of "What can be true?" question. The answers to this question will actually be a complete spelling out of a potential scenario. For example, the answer could list everyone in each position from 1 to 7, in order (see Game One question 1). These are the easiest type of questions. You don't 2

Some of you may be thinking, "Ah, so we should keep all of our previous diagrams – even the ones that break the rules, so we can use them on these questions." But then you have to distinguish between diagrams that break the rules and those that don't. This is confusing and you will end up making mistakes. Also, you won't know what caused the diagram to break a rule – was it the situation your answer describes, or something else? Finally, it is so much easier to spot answers that break rules that looking at previous diagrams is more trouble than it's worth.

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have to draw a diagram for these at all, since everything is already spelled out for you. You just go through each answer and compare them against the rules. Once you have found the right answer, though, I recommend rewriting it yourself, so you can easily see it later as a previous diagram. Often people overlook these diagrams and they can be very helpful (as we'll see in Game One). 2. What can't be true? questions The right answer to these can't be true, which means it breaks a rule. What does this tell you about the wrong answers? They can be true, which means that they follow all the rules. Previous diagrams will be very useful on these questions. As you look at each answer, first see if you have a previous diagram which contains the situation described in that answer. For example, if the answer says "Q is with P" and the diagram from another question has Q with P, you know that can be true. Cross the answer off (the answer, not the diagram!), since it can be true. If the answer isn't in your previous diagrams, skip it. Look at the other answers first. Hopefully you will be able to eliminate all of them using your previous diagrams, so you won't have to do any work for the question. If you end up having to test out one or more answers to the question, test out the situation described in the answer as I talked about in Making Test Diagrams earlier in this chapter. If it works – that is, if you can fill out all the spaces in the diagram without breaking a rule – you know that the answer is wrong. If it doesn't work – if you are forced to break a rule – then the answer is right. You are done. If you eliminate all but one answer, pick it but don't test it out. You know it has to be right, because there has to be a right answer. Trying it out is just a waste of time. Here's a pet peeve of mine (and all of my pet peeves relate to things that make students miss questions, so you should be interested): I really don't like it when students say a diagram, or an answer, that breaks the rules is wrong. It doesn't work, it breaks the rules, it can't be done, maybe you can even say it's false, sure, sure. But wrong? Not always. On a "What can't be true?" question, the answer that breaks the rules is right. Breaking the rules is a separate issue from being right or wrong. The reason I don't like this is that when students start calling diagrams that break the rules "wrong," on some level they are thinking that this answer can't be right. But that's not true; best case scenario, this sort of confusion slows you down. Worst case scenario, it confuses you to the point that you miss the question (I see it happen a lot). Lesson: don't confuse breaking rules with being wrong, or following rules with being right. Don't call the two different things by the same name. 3. What must be true? questions These are probably the most misunderstood type of question in the games section; they are also one of the most common (there being five or six of them on the average LSAT). They are going to confuse you until you memorize the process for them and understand how and why it works. Once you've done that, though, they aren't that much harder than the first two types of questions. What does it mean for something to have to be true ("have to be true" is the same as "must be true," but it conjugates better)? It means that the thing must be true no matter what. If something must be true, it will be true in any possible diagram for the game. Notice that

44

The Fundamentals

this is an "If… then…" sentence, so give me the contrapositive. That's right: if something is not true in every possible diagram for a game, then it is not something that must be true. People generally test the answers to these questions by trying out the situation the answer describes. If the answer says "A must be first," then they put A first and see what happens. Now, what if A works in the first position? Does this mean that A must be first? No. It just means that A can be first. Typically, most answers to these questions can be true, so you haven't really gotten any closer to the answer. To test an answer, you need to see if you can make the game work in a different way. If the answer says "A must be first" and you see that A could be second, then you know that the answer is wrong. So here's what you do. First, look at your previous diagrams. You are looking for a diagram which contains a situation other than what is described in the answer. If you see one, you know that the answer doesn't have to be true – it could be the way the previous diagram shows. So cross it off. If you don't find what you are looking for in previous diagrams, skip the answer. Hopefully you'll eliminate all the others and you won't have to test anything out. If you have to test out an answer, test out a situation other than what the answer describes. If the answer says "A must be first," try A second, or third, or anyplace except first. If you can make it work – that is, if you can fill all the spaces in the diagram without breaking the rules, doing something different from what the answer says – the answer is wrong. If you can't make it work, then the answer is right. I talk about this in more detail, and give examples of how it works, in the chapter entitled "If… then…" Rules and Negations. Now this is backwards thinking, and it is confusing at first. If you generate a working diagram, the answer is wrong, and if you are forced to break rules, the answer is right. But it should make sense. If you can make a diagram work that doesn't do what the answer says, than the answer doesn't have to be true – you've got a diagram where it's false. If you can't make it work any other way then it has to be true. 4. What can be false? questions The right answer to this questions can be false. What does this mean about the wrong answers? They can't be false. We have just talked about answers that can't be false – this means the same as "must be true." On a "What can be false?" question, the wrong answers must be true, and the right answer is possibly false (if it has to be false that's fine as well – something that has to be false is also possibly false). These questions are the mirror image of "What must be true?" questions, just like "What can be true?" and "What can't be true?" questions are inverses of each other. How do we do "What can be false?" questions? We test each answer as we would the answers in a "What must be true?" question. Try and make a diagram which contains a situation other than what the answer describes. If you can't make something other than what the answer describes work, the answer must be true, and is the wrong answer. If you can, the situation described in the answer doesn't have to occur, and the answer is correct. You can use previous diagrams on these questions, but they aren't that useful. Look for previous diagrams which contain something other than what the answer says (as we do in "What must be true?" questions). If you see one, then you know the answer doesn't have to be true, and it is the right answer. If you don't have any previous diagrams that show situations other than what the answer describes, then the answer might have to be true, but you won't know until you test it out. Don't eliminate the answer in this case.

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These questions are a bit time consuming, but they are very rare, occurring less than once per LSAT. 5. Which is a complete and accurate list? questions Notice that this question says "Which is a complete and accurate list?" not "Which could be a complete and accurate list?" The second version is actually a "What can be true?" question (see above). These questions ask for a list of things that fit a certain description. The list must be complete, so it has to include everything that fits that description, and it has to be accurate, so it shouldn't include anything that doesn't fit that description. If the question says, "Which of the following is a complete and accurate list of boys who can have red hair?", the answer must have all the boys who could be redheads, and no boys who can't. Complete and accurate lists include all the things that fit this description in any possible diagram. If only two boys can be redheads at one time, the list of possible redheads might still be four or five boys long. Any of those four could have red hair in some possible diagram, but only two at once. The wrong answers to these questions are going to leave someone off the list, or will have someone in the list that shouldn't be there. Previous diagrams are going to be very useful here. Any person or thing that fits the description in any previous diagram should be in your list. You can cross off any answer that leaves one of these people/things off. Thus, if you see that A can have red hair in one diagram, and B in another, then any list without A or B is wrong. If you don't eliminate all the wrong answers using previous diagrams, you are going to have to test out at least one answer. Look at your remaining answers and pick a person/thing that at least one of them lacks (if they all have that person/thing, you know it has to be in the list, so don't bother testing it). Draw a diagram where that person/thing has that quality, and test it out. If you can make the diagram work, then any answer without that person/thing in it is wrong. If you can't make it work, then any answer with that person or thing is wrong. Do this until you have one answer left. 6. What is the maximum/minimum number of …? questions These questions ask you to determine the largest or the smallest number of things that can have a certain property. For example, they might ask you, "What is the maximum number of students who can be scheduled before A?" The right answer will be the largest or smallest number that can have that property, and the wrong answers will be less or greater than this. First look at your previous diagrams. Find the largest/smallest number of things fitting the description. If you have two diagrams, one where A is 4th and one where A is 5th, the largest number of students before A is at least 4 (there are 4 people before the 5th position). Thus, we know that any answer less than this is wrong. Often you will be pressed for time by the time you get around to these questions – this is one of the last question types you will do. You may need to guess; you can pick any one of the answers you didn't eliminate, but I think you are safest picking the number you know can happen. That is, pick the one that you see in a previous diagram. If you have time, and haven't eliminated all but one answer using your previous diagrams, here's how to answer the question. Look at the largest (or smallest) answer (whichever the question asks for). Try to make that work. Imagine the question asks for the maximum number of students who can be scheduled before A. There are seven slots in the game.

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The Fundamentals

The largest answer is six. If this were right, then A would have to be seventh. Put A seventh and test out the diagram. If you can make it work you have the answer. If you can't, go to the next largest answer, and so forth. If the question asks for the minimum, start with the smallest answer and work your way up. 7. How many diagrams are possible? questions These questions all rely on your ability to figure out who in a diagram can be moved without breaking a rule and who cannot. They are not terribly common – in the last ten years, they have appeared slightly less than once per LSAT. In their most common form, these questions ask how many different ways the game could be worked out, usually given some condition specified in an "If." For example, "If X was fourth, how many different ways could the people be ordered?" Since these are usually If-questions, previous diagrams aren't terribly helpful. We generally don't use previous diagrams in If-questions (see If-questions later in this chapter). To do these questions, we draw a test diagram, putting in any conditions the question stipulates (if it is an If-question). We then go through the rules and see if these conditions cause anything to have to be true. After we've gone through the rules, we fill the remaining spaces in the diagram. Be sure to mark anything that might have gone elsewhere with a dot or a star (see Marking with a dot or star under Making Test Diagrams earlier in this chapter). Once you have created a diagram that works, move the first thing in your diagram that is marked with a dot or a star. See if this allows you to make a new diagram. Keep moving things that you can move until you run out of ways to change the diagram. Count up the number of new diagrams you've made; this is the answer to the question. There is a simpler variant of this question, which asks "For how many of the things can the position be determined?" These are usually If-questions as well, so previous diagrams aren't helpful. You need to count up the number of things that can only go one place. Generally, you will have a good idea of who can and can't be moved – the conditions in the question, together with the rules, will cause certain people to have to go in certain places. If you think someone's position can be changed (for example, if they are marked with a dot or star), try to put them someplace else. If there is no place else to put them, their position is determined. A final variant of this question type asks for information that would allow you figure something out for sure. For example, the question could ask, "Which of the following would allow you to determine who is in the seventh position?" or "Which of the following would allow you to determine what group A goes in?" This is really asking, "Under what condition is only one diagram possible?" That is, which answer makes it so that things can only be put in the diagram one way? The wrong answers will be conditions that allow more than one diagram. Previous diagrams aren't terribly useful on this variant of the question either. You want to see if knowing the information in the question forces something to happen. You would need two previous diagrams, both of which match the scenario in the answer. If they differ as to what the question asks – if, for example, a different person were in the seventh position in each diagram – then you know that scenario doesn't force anything to happen. You can see that this is hard to do. I recommend skipping these questions unless you have plenty of time; if you have the time, just work through the answers. In these questions, you check an answer by drawing a diagram that matches the scenario in the answer. You then try to see if there is only one way the position or person in the

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question can go. For example, if the question asks about the seventh position and the answer says "B is fourth", you would put B fourth and see if there is a definite person who must go seventh. If there doesn't seem to be, try putting each person seventh, one by one. If more than one person can go seventh without breaking any rules, the answer is wrong. For an example, see Game Eleven, question 16.

If-Questions As I said earlier, If-questions give you a hypothetical situation. This situation is almost always compatible with the rule you are given in the beginning. If it isn't, the question will explicitly say so (see below). If the question doesn't explicitly say it is changing a rule (and they almost never do), then all the rules are in effect. So If-questions give you more information. This makes them easier than normal questions. Because they are easier, we want to do them early on. If-questions can ask any question – you can have an If with a "What can be true?", a "What can't be true?", a "What must be true?", and so forth. But, generally, If-questions, no matter what they ask, are as easy as "What can be true?" questions and we should do them first (along with "What can be true?" questions). If-questions give you new information. Because of that, you can't use previous diagrams from other questions – these diagrams don't always match the scenario given in the Ifquestion, and so are irrelevant.3 However, and this is important, the scenarios in If-questions don't break any rules. Because of that, any possible diagram you generate for an If-question will be possible for any question (except other If-questions). So you can use previous diagrams from Ifquestions when doing other questions (except other If-questions). Let's review: If-questions should be done first, along with "What can be true?" questions. You can't use previous diagrams to help you with them. You can use the diagrams you make on If-questions to help you on other questions. How to do If-questions This is hugely important, because If-questions make up about 50% of logic games questions. We'll go through a lot of If-questions as we do the games in this book; here is the process we will use: Steps for Doing If-Questions 1. Draw a new diagram. 2. Put in your diagram whatever the "if" part of the question describes. 3. Go through the rules and see if anything has to be true based on that; if so, write it down. Also write down things that can't be true (e.g. "X can't go in space 3"). 4. Answer the question based on the question type ("What can be true?", "What can't be true?", etc.).

3

There is an exception to this, but it is complex to learn and not necessary for doing well on logic games. I will talk more about it in Advanced Techniques, but you will do just fine not thinking about it. Don't use previous diagrams with If-questions and you will do great.

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Step 3 is a crucial step, and involves a repeated process: Every time you figure out something that has to be true (or can't be true) from the rules, go back through the rules again and see if that makes something else true. Do this until you go through the rules without learning anything new. Don't put anything into your diagram that might or might not be true – if you aren't sure who goes in a certain blank, leave it blank. Then go through the answers in the way relevant to the type of question it is – "must be true," "can be true," etc. – using the diagram you just made. You may have to recopy it a couple of times since you may have to test out several answers. If-questions that break rules Once in a while an If-question will tell you that it is changing the rules – either taking a rule away or modifying one (an If-question that adds a rule is just a regular If-question, giving you new information in addition to what you already have). These If-questions will be very clear about what they are doing. They will tell you explicitly that they are changing or removing a rule. It might say, "If the rule about blah blah were changed to say such and such, but all other conditions remained the same…" Save If-questions that change or remove rules for last. We can't use the diagrams from these questions on other questions, because they don't follow all the rules. Other than that, do these questions as you would any other If-question. These questions are rare. About 2% of the logic games questions since 2000 have changed or removed rules. This works out to less than one of these questions per LSAT, on average.

What Do I Do Next? Well, you've just worked through a huge mass of facts and concepts. You might not have understood them all – many of them won't make sense until you've used them – and you definitely won't have memorized them all. At this point don't worry about that too much. Go and work through Game One. Don't try to do the game on your own; instead, work through the game along with my explanation in the chapter (later I'll tell you when you should do a game on your own before reading the chapter). You'll start to see how all this fits together and what it all means. Then you can start thinking about memorizing things. Much of this chapter – for example, how to diagram games – you will memorize without trying to, as you work through the games in this book. If you find that you don't remember general concepts – like how to diagram games or how to write down certain types of rules – even after going through a couple of games, then make a conscious effort to memorize them. Flash cards are helpful (see below). Other things are more detail-oriented, and you'll certainly have to make an effort to memorize them. Things you should make a conscious effort to memorize are: the order in which you do the questions, the common ways of phrasing each question (Common Equivalents for Each Question Type earlier in this chapter), and the way to answer each type of question (including how to use previous diagrams on each). I recommend making flash cards for each question type.

A Note on Flash Cards Flash cards should help you prepare for the test. The test will use certain ways of talking which are different from my way of talking, and probably from your way as well. You don't want to memorize vocabulary words like "deduction" or "definite entity" because these won't appear on the LSAT. I try to use vocabulary like these as little as possible in this book so as to save you the work of learning them. The LSAT will use certain words and phrases over and over again though, like "What must be true?" or "exactly." You want to memorize what

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to do when you see these words and phrases. On the front of your flash card, you'll have the word or phrase that will appear on the LSAT. On the back, you should have exactly what to do when you see it. You should have a flash card for each question type, and a separate flash card for every alternate way of asking the same sort of question. So you should have different flash cards for "Which of the following is possible," "Which of the following could be true," "Which of the following is acceptable," "None of the following can be true EXCEPT," and so forth (all of those are different ways of asking the same type of question, which is "What can be true?"). The back of the flash card for a question type will say how to test the answers, how to use previous diagrams, and when you should do that type of question. For different cards that mean the same thing, as I've just listed, the back of each will have the same stuff on it. Why should you have several different cards for each question type? Why not just put all the ways of asking the same question on the same card? Well, putting them on the same card gives you a hint about what they mean – you might not remember what "acceptable" means, but you would know that it means "could be true" because they are on the same card. This doesn't help you prepare for the test. The LSAT won't give you any hints, so if you don't know what the question means just by looking at it, you aren't going to do too well. You should also have flash cards for important LSAT words like "exactly" or "at least." I'll point out words like these as we go through the rest of this book. Run through these flash cards regularly (mixing them up periodically). You should spend more time on the cards you have a hard time remembering – put them in a separate pile and go through them more often – but don't neglect the cards you remember easily. Every so often, shuffle all the cards together, even the ones you know well, and go through the pile. Your goal is to know every card without pausing to think – the instant you look at the card, you should know exactly what you are supposed to know. Having to pause to remember slows you down on the test and forces you to think, and thinking makes you tired. If you take a look at the Big Fat Genius website (www.bigfatgenius.com), there should be a set of flashcards available for you to download for free (I can’t give you an exact address in this book because nothing on the internet ever stays the same for long; look around, they should be easy to find). These should give you a useful starting place for making your own cards.

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Statistics on Question Frequency Here are some statistics on how often each type of question has appeared in LSAT 19 through 48 (the most recent LSAT as of the writing of this book). I consider the LSATs before 19 not representative of modern logic games. I've broken the statistics down into two groups: before 2000 and 2000 and after; the frequencies have changed slightly in recent years. Notice, for example, that these days you are somewhat more likely to see the more difficult questions types, like "What is the maximum/minimum?" or "How many diagrams are possible?", although you still are not likely to see more than one of these on a given LSAT. I've given the following statistics: what percentage of the total questions are of each type, what the largest number of that type on a single LSAT has been, what the smallest number of questions of that type on a single LSAT has been, and the average number of that type of question per LSAT. Percentages may not add up to 100 due to rounding. If the average is less than one, this means that there is a significant chance that an LSAT will not have a single question of this type on it. One thing to point out is that each If-question is also another type of question – the question will say, for example, "If such and such, which of the following can be true?" Don't try to add the percentages for If-questions with the other types of questions. If-questions that change or remove rules are counted separately from regular If-questions. Before 2000 Since 2000 (2000 and later) "What can be true?" questions Percentage: 45% Largest number: 13 Smallest number: 8 Average: 10.75

"What can be true?" questions Percentage: 41% Largest number: 14 Smallest number: 5 Average: 9

"What can't be true?" questions Percentage: 15% Largest number: 5 Smallest number: 1 Average: 3.5

"What can't be true?" questions Percentage: 21% Largest number: 9 Smallest number: 3 Average: 5

"What must be true?" questions Percentage: 32% Largest number: 10 Smallest number: 6 Average: 7.5

"What must be true?" questions Percentage: 24% Largest number: 10 Smallest number: 3 Average: 5.5

"What can be false?" questions Percentage: 1.5% Largest number: 1 Smallest number: 0 Average: .3

"What can be false?" questions Percentage: 2% Largest number: 3 Smallest number: 0 Average: .6

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Before 2000 (continued)

Since 2000 (continued)

"What is a complete and accurate list?" questions Percentage: 4% Largest number: 2 Smallest number: 0 Average: 1

"What is a complete and accurate list?" questions Percentage: 4% Largest number: 3 Smallest number: 0 Average: .9

"What is the maximum/minimum…?" questions Percentage: 1.7% Largest number: 2 Smallest number: 0 Average: .4

"What is the maximum/minimum…?" questions Percentage: 5% Largest number: 4 Smallest number: 0 Average: 1

"How many diagrams are possible?" questions Percentage: 1% Largest number: 1 Smallest number: 0 Average: .25

"How many diagrams are possible?" questions Percentage: 1% Largest number: 3 Smallest number: 0 Average: .3

If-questions Percentage: 52% Largest number: 17 Smallest number: 9 Average: 12.4

If-questions Percentage: 50% Largest number: 16 Smallest number: 8 Average: 11

If-questions that change or remove rules Percentage: 2% Largest number: 1 Smallest number: 0 Average: .5

If-questions that change or remove rules Percentage: 2% Largest number: 2 Smallest number: 0 Average: .4

52

Game One Game omitted from electronic version of book.

Game One

53

Game One (From LSAT 28)

Step 1: Read the Setup/Draw a Diagram Every game involves two types of entities that you match together. What are the two types of things in this game? They are the racehorses and the positions 1 through 6. The next question we ask is, which is more definite? That is, which do we know more about? We know more about the positions, because 1 is always next to 2, which is always next to 3, and so forth. Thus, we are going to base our diagram around the positions. When you see an LSAT game involving numbered positions, your diagram will almost always be based around the numbers, as numbers are pretty definite (numbers don't move or change). We write the numbers 1 to 6 out in a row, which is what we always do with the definite things. Now we ask how many of the variable things will get matched up with each definite thing. How many horses per position? The game says "one horse per position," so there's your answer. Each position will get one blank associated with it. This is a very simple diagram: 1 __

2 __

3 __

4 __

5 __

6 __

Write down the names of the horses (K, L, M, N, O, P) somewhere off to the side so we can remember them. We end up with something that looks like this: 1 __

2 __

3 __

4 __

5 __

6 __

KLMNOP

Now, here's a question you might be asking: where do you draw the diagram? You don't get any scratch paper on the LSAT, so you've got to fit all your work in the blank space provided for you. Put the diagram any place you want; don't write it so big that you don't have any space for test diagrams, but don't write it so small that can't read it. Many people prefer to put it at the very top of the page; I have no strong feelings either way.

Step 2: Read the Rules Let's go through the rules one by one, making sure we understand them and writing them down in a clear and complete manner. Ready? Let's rock! First rule: "K and L must be assigned to positions that are separated from each other by exactly one position." What does it mean for K and L to be separated by exactly one position? It means that there will always be one (and only one) space between them. The word exactly is an important LSAT word; it means "this much and no more or less." Now here's the second question: what does this rule not mean? Specifically, does it tell us who comes first, K or L? I ask about who is first because order is very important in this game – it is a game about putting horses in order. The rule doesn't explicitly say anything about the order of K and L, so either of them can come first. For the rule to tell us explicitly, it would have to mention order. It could say "in that order" or "L is before K" or something like that. So we know we have either K and a space and then L, or L and a space and then K. These are the only two options. The

54

Game One

easiest way to write this rule is to write the options down. When a rule only gives you two options, write both of them down. So here is our rule: K __ L or L __ K This is the best way to write down the rule, but it isn't the only way. You could have written: Exactly one space between K and L (or L and K) This is much longer, but it communicates everything in a clear fashion. Memorize and try to master my guidelines for writing the rules (so you can use them without having to think about them much), but if you forget them on the test, or you can't figure out how they apply to a certain rule, never forget this: it's better to write down a rule any old way than to waste time trying to figure out the best way to write it. Next rule: "K and N cannot be assigned to positions that are next to each other." What does this mean? It means that K and N will never be next to each other; that is, you'll never have them in consecutive positions. If, for example, K is in 1, N won't be in 2. What does it not mean? Do we know what order they will come in? Well, the rule doesn't say explicitly, so we don't know. They might be in either order. There are many ways K and N could be situated. There might be one space between them, or two, or three, and so on. But there are only two ways they can't be – we can't have KN and we can't have NK (when I write the horses next to each other I mean that they are in consecutive spaces). So our rule is No KN no NK Of course, we didn't have to write this down so nicely. K and N aren't next to each other That works pretty well, too. I don't mean to say that it's not good to write the rules down nicely. It is – it's easy to read (usually) and it means that you understand the rules. But it's not absolutely necessary. It's supposed to save you time overall, so if it takes you a long time to figure out the best way to write the rules that defeats the purpose of writing them. Do your best to learn how to write rules well, but don't spend more time studying it than you do something really important, such as memorizing how to do each type of question. Third rule: "N must be assigned to a higher-numbered position than M." This is an easy rule to misinterpret and to write down badly. First ask yourself what it means. I'll give you a second to think. OK, here the answer: it means that the space N is in has a higher number than the one M is in (but we don't know how much higher, because it doesn't say). That means that N is further to the right and M further to the left, because we write low to high from left to right. When you write this rule down, make sure that this relationship is in what you write. Many people write something like N>M. This is very confusing – it has N on the left of M, not on the right. If you write something like this, you are almost guaranteed to make a mistake (oh, how many times have I seen this!).

Game One

55

If a rule talks about a spatial relationship, make sure that the way you write the rule mimics that relationship. That is, if a rule tells you that someone is to the left of someone else, you should show that in the way you write it. If you are told that someone is above someone else, make darn sure that they are above them on the page when you write it down. Here is our rule as we write it down: M before N Last rule: "P must be assigned to position 3." Not a hard rule to interpret. Put P directly in position 3. If a rule can be written directly into your diagram, do so. But also write this with our other rules so that we don't forget it. Cross P off the list so we know we don't have to worry about him. As things get assigned to spaces, cross them off the list. So now here is what you should have written down on your page: 1 __ 1. 2. 3. 4.

2 __

3 P

4 __

5 __

6 __

KLMNOP

K __ L or L __ K No KN no NK M before N P is 3

You don't have to number your rules (really, there is absolutely no reason why you should). I'm doing it so that I can refer you back to them quickly and easily as I work through the questions. Some of these rules can be combined to give you new information (deductions), but we aren't looking for that sort of stuff at this stage in our LSAT life. Let's just focus on learning the fundamental, and most important, skills.

Step 3: Answer the Questions Here is where the magic happens. We are going to walk through the questions one by one. If a question is one that we should do, we'll do it; otherwise we'll skip it and come back to it later. It will all make sense as we go through. Question 1: A "What can be true?" question – do it now The word "acceptable" means "can be true," and "What can be true?" questions are the first ones we do. We are going to do this question now. Notice that each answer fills out every space in the diagram, in order. This is going to make the question pretty easy, because we don't need to make our own diagrams. We know that the right answer can be true, so it follows the rules. This means that the wrong answers break the rules. When going through the rules to check whether something follows them or not, always go through the rules in the order in which you have them written down. We do this because it is easy and it ensures that we don't skip a rule. This means that we actually look at our

56

Game One

diagram first, because the diagram is the first thing we have written down. So we are going to look at rule 4 (P is 3) before any other rule because it is written directly into our diagram. Answer A OK, P is third, so that's good. Next rule says K and L are one space apart, but here K is next to L. That breaks a rule, so this is wrong. Cross it out and go on. Answer B P is third; good. K and L have P between them, so that's good. The next rule says that N is not next to K, and it isn't. Finally, M must be before N, and it is. This follows all the rules, which means what? It is correct. Since this follows all the rules, it gives us a possible diagram. We'll want to use this later. People often forget to look at the answers to this type of question when looking at previous diagrams to see what they know can be possible. To avoid this, we are going to recopy this answer ourselves, putting it into a diagram, so we'll recognize it as such. 1 M

2 K

3 P

4 L

5 N

6 O

Question 2: A "Which is a complete and accurate list?" question – skip for now Question 3: A "What can't be true?" question – skip for now Question 4: A "What must be true?" question – skip for now Question 5: A "What can't be true?" question – skip for now Well, we just skipped all the questions. Did we do something wrong? No, the game just gave us only one of the easiest kind of questions. Now we go back and do the "What can't be true?" questions – numbers three and five. Question 3: A "What can't be true?" question – do the second time through We know that the wrong answers are things that are possible, since the right answer is impossible (can't be true). We want to use our previous diagrams to show us quickly what is possible. We only have one diagram, which we found in answer B on question 1. Answer A Look at our previous diagram. It shows us K in position 2, so we know that this is possible. We cross off this answer. Go through the rest of the answers in order. We can also eliminate answer C, since M is in position 1 in the previous diagram. We can't eliminate any of the others, because the situations they describe (e.g., L in position 2, or M in position 5) are not shown in our previous diagram (e.g., the diagram has K in 2 and N in 5). We are going to have to test out at least some of the rest of the answers. Answer B We have to test this and see if it is possible. So we draw a new diagram (copying our original diagram, so putting P in 3) and put L in position 2. Also, cross L off the list because we've placed it. 1 __

2 L

3 P

4 __

5 __

6 __

KLMNOP

Game One

57

Now we go through the rules one by one and see if anything has to be true. Rule 1 tells us that we must either have K __ L or L __ K. We can't have K __ L because that would put K off the chart (there is nothing to the left of position 1), so we have to have L __ K. Thus, K goes 4th (cross K off). 1 __

2 L

3 P

4 K

5 __

6 __

KLMNOP

The next rule says that N and K aren't next to each other. So N can't go in position 5. Write that down next to position 5 (so it is easy to see). But we don't yet know where N has to go (as far as we can see so far it can go in position 1 or 6) so we don't put N in anyplace. 1 __

2 L

3 P

4 K

5 6 __ __ no N

KLMNOP

The last rule says that M has to go before N. This is going to limit where M and N can go. To see how, we look at each empty space in the diagram, one at a time. M can go 1st or 5th, but not 6th – if it were 6th, N would have to be 7th, and there is no 7th. N can't go 1st, because then M would go off the chart. It can't go 5th, because we wrote down "no N" under 5, but it could go 6th. N has to go 6th – that's the only place it is able to go, and it has to go somewhere. If you aren't sure what a rule tells you, look at each person in the rule and each empty spot in the diagram. Earlier, rule 2 told us that N can't be next to K. Since we knew were K was, it was clear that this told us only that N couldn't be 5. The rule we just looked at, though (M before N), doesn't clearly tell us anything, since we don't yet know where either M or N goes. But it seems like it should tell us something, so we try it out, trying both M and N in each empty space. And this gives us new information, that N has to be 6. 1 __

2 L

3 P

4 K

5 6 __ N no N

KLMNOP

All that are left are M and O. They can go in either 1 or 5 (we already tried M in both spaces, and we have no rule about O). We can either write "M/O" in either space to show that they can go either way, or just put them in someplace. Let's just put them in, in alphabetical order to be systematic. 1 M

2 L

3 P

4 K

5 6 O N no N

KLMNOP

This works. We've filled every space without breaking any rules. So it is possible for L to be in position 2. This may seem like it took a long time, but after you practice this a bit, it will become second nature and you'll soon be whipping right through it. And now we have an additional diagram to help us out in later questions. Use this new diagram to see if we can eliminate our remaining two answers (D and E). Does the situation in D or E appear in this diagram? Unfortunately not; D talks about M being 5, but here M is 1, and E talks about O in 2, but here O is 5. We've already eliminated answer C based on the diagram for question 1, so go to answer D.

58

Game One

A quick point. In this book, as we test one answer, I redraw the diagram every time I add something new. I'm not saying you should do that; I'm doing it to show you how the diagram evolves. In these cases, where you are adding something to a diagram you already have, just add the new information to the same diagram. Draw a new diagram to test a new answer or a new question. Answer D Let's try this; recopy your diagram and put M 5th.4 1 __

2 __

3 P

4 __

5 M

6 __

KLMNOP

The first rule says that we have to have K __ L or L __ K. Where can we put in L and K? When you don't know where someone has to go, but you have to put them someplace because you are drawing a test diagram, put them in the first available space. But you want to remember that they didn't have to go there – putting them there might make the diagram break a rule later on, and you might want to move them someplace better. So put a little dot or star next to them; this will tell you that their position was your choice. When you choose where to put someone, mark them with a dot or star (see Making a Test Diagram in the chapter The Fundamentals). Here, we want to put K and L in the first available spaces. Position 1 is first, but if we put K or L there, the other would have to be 3, so this won't work. You can put one of them in 2, because spot 4 is empty. Put K there (since it is before L in the alphabet); however, it may turn out that this breaks a rule, so mark it to remind us that this was our option. L, however, will now have to go 4th because of the rules, so we don't mark L. 1 __

2 K*

3 P

4 L

5 M

6 __

KLMNOP

The next rule says that N can't be next to K. Write "no N" under position 1. There is only one place left for N to go, space 6, so put N there. Because N had to go 6th, we don't mark it. 1 2 __ K* no N

3 P

4 L

5 M

6 N

KLMNOP

The next rule tells us that M is before N. This agrees with what we have here, which is good. This leaves O 1st. There is no rule against this, so put it in. 1 2 O_ K* no N

3 P

4 L

5 M

6 N

KLMNOP

We've filled every space without breaking a rule, so this is possible. We can cross off answer D, so the answer has to be E. Don't bother checking it, we know it has to be the answer. 4

When we did B, we could have put M 5th. If you remembered this, then you would just cross off this answer and be done with it. If not, you'd have to test it out.

Game One

59

This wasn't too hard. We only had to test out two answers, and they were pretty straightforward. Notice how systematic we were – we went through the rules in order, we put people in the first available spaces, in alphabetical order. Don't be afraid to put people wherever it seems they can go. Sometimes you'll have to move them later on, but this is no big deal. Question 5: A "What can't be true?" question – do the second time through Let's use our previous diagrams, because we can do that on "What can't be true?" questions. If we see that what an answer describes occurs in a previous diagram, we know it is possible, so it is wrong – the right answer can't be true. Answer A Notice that this answer doesn't specify an order. If we have LN or NL we know that this is possible. Check your previous diagrams first. We have the diagrams from answer 1B and from answers 3B and 3D. The diagram for 1B has L next to N, so we know that this is possible. Cross off the answer and move on. Answer B The diagram for 1B has M and K next to each other, so this is possible. Cross it off. Answer C We don't have M and O next to each other in any previous diagram, so skip this. Remember, if you are using your previous diagrams, skip answers that you can't eliminate with the diagrams. Hopefully you will be able to use your previous diagrams to eliminate all the other answers and won't have to test the answer you skipped. Answer D What does this mean? It means that there is one space between L and N, but no order is specified. We could have L __ N or N __ L. We see this in the diagram for 3D – L is 4th and N 6th. O is in the only position between them. So we know that this is possible and we can cross off this answer. You might be wondering, what would we do if our previous diagrams weren't so helpful? Well, we'd have to do some more work – we'd have to test these answers. That's not so bad. In most games, our previous diagrams should do some work for us because it's very difficult to write 20 or more answers that are wholly unique. Answer E This is similar to D, except we are looking for M __ P or P __ M. Look for it in your previous diagrams and … there it is! In the diagram for 1B (as well as in 3B and 3D). We've eliminated every answer except C, so C is the answer. Now do you see why we skip answers we can't use our previous diagrams on? We've made our second pass through the game. Now we do the third-easiest type of question – the "What must be true?" questions.

60

Game One

Question 4: A "What must be true?" question – do the 3rd time through The answer to a "What must be true?" question must be true in every possible diagram. So if an answer is false in a possible diagram, it is wrong. When we look at our previous diagrams, we look to see if we have a diagram where something other than what the answer describes happens. Answer A "Either" means K could be 2nd or L could be 2nd. We want something other than this, so we look for a diagram where K and L are not in position 2. Someone else – maybe M, maybe O, maybe N – will be there. But you don't see it. 1B has K 2nd, as does 3D. 3B has L there. Skip this answer. Answer B Again, look for a diagram where someone other than K or L is in position 4. We don't see it. Skip this answer too. Answer C Look for a diagram where someone other than M or N is 2nd. All of our previous diagrams have someone other than M or N in position 2 (they all have K or L 2nd). So M or N doesn't have to be 2nd. Cross this off. Answer D The diagram for 3B has O in position 5, so M or N doesn't have to be there. Cross this off. Answer E 3B and 3D have N 6th, so M or O doesn't have to be there. Cross this off. We still have A and B left. Let's test A out. Answer A To test the answers on a "What must be true?" question, we make a test diagram doing something different from what the answer describes. We don't want to put K or L in position 2. Write this in your diagram. 1 __

2 3 __ P no K no L

4 __

5 __

6 __

KLMNOP

Now go through the rules and see what has to be true. We know from rule 1 that K and L have to be one space apart. Let's put them in the first available space. Figure out what this is on your own before looking further. OK, done? Here's what you should have seen. Neither can go 1st, because the other would have to go 3rd, and P is already there. Neither can go 2nd, because that would defeat the purpose of what we are doing: we want to see if we can avoid putting them 2nd. We can put one 4th, and the other would have to go 6th. Notice, by the way, that neither can go 5th, because the other would have to go 3rd or 7th. So they have to go 4th and 6th – that's the only way they can fit. Put them in, in alphabetical order. Since the order is our choice (although not the position), mark K with a dot or star (only K, because once K is in, L has to be 6). If the order ends up mattering, you can always switch them later.

Game One 1 __

61 2 3 __ P no K no L

4 K*

5 __

6 L

KLMNOP

The next rule says that N can't be next to K. So N can't be 5th. 1 __

2 3 __ P no K no L

4 5 K* __ no N

6 L

KLMNOP

The next rule says that M has to be before N. See where M can go. It can go 1st, because then N would go 2nd. Put it there and mark it, because we haven't figured out that it has to go there. (By the way, M can't go 2nd, because then N would have to go 5th, but N can't be 5th. So M has to be 1st). N has to be 2nd because it can't be 5th. This leaves O for 5th. 1 M*

2 3 N P no K no L

4 5 K* O no N

6 L

KLMNOP

This works. That means that the answer is wrong – remember that when you test something out in a "What must be true?" question and you make the diagram work, the answer is wrong. That's because you tested out something other than what the answer describes. If the diagram works, it means that the scenario in the answer doesn't have to be true; something else (that you just tested) could be true. Here, we've just learned that we don't have to have K or L 2nd. Notice how important it is to memorize the procedure to answer the question. We just did a lot of reverse thinking – we tested out something different from what we were told, and we crossed off the answer because the diagram works. That's weird, and it can be confusing if you don't have it thoroughly memorized. I beg you, memorize this. Please… Anyway, we've eliminated every answer except B, so B is the right answer. I want to point something out. Notice that once we write something down like "no N" under position 5, we don't question this later on. Imagine the following internal dialogue: "Well, hmmm, can M go 2nd? Well, if it went 2nd, then N would be 5th. Can N be 5th? I don't know. I wrote down that it can't, but why did I do that? Let's work it out." What a massive waste of time and effort. Once you write something down you have to trust that it is correct. Don't question what you write down later on. There's only one question left.

62

Game One

Question 2: A "Which is a complete and accurate list question…" – do it our fourth time through The question asks about K. The right answer has to include every place K could possibly be. We have diagrams with K 2nd and 4th. We can eliminate any answer without 2 or 4 in it. That gets rid of A and B. Now, to eliminate D, we wonder if K can be 5th. Try this out. 1 __

2 __

3 P

4 __

5 K

6 __

KLMNOP

Our first rule tells us that we have either K __ L or L __K. If we have K __ L, L is 7th, which won't work. If we have L __ K, L is 3rd, which also won't work. So we can't have K 5th. Any answer with 5 is not an accurate list, so it's wrong. Cross off answer D, and cross off this diagram. Always cross off diagrams that break rules so that you don't try to use them later. I know that this is the last question of the game, and that there won't be any "later" for this diagram, but always be consistent. That's the only way to build good habits. Now let's try K 6th. 1 __

2 __

3 P

4 __

5 __

6 K

KLMNOP

Our first rule tells us that L will have to be 4th (so no dot or star for L) 1 __

2 __

3 P

4 L

5 __

6 K

KLMNOP

Our next rule tells us that N can't be 5th. 1 __

2 __

3 P

4 L

5 6 __ K no N

KLMNOP

Our next rule tells us that M is before N. Let's see where they can go. M can go 1st, which would put N 2nd. (M can't go 2nd, because that would put N 5th) O has to be 5th. 1 M

2 N

3 P

4 L

5 6 O K no N

KLMNOP

This works, so K can go 6th, which means that the answer has to have 6 in it. Only E has 6, so E is the right answer. And we are done.5 Notice that if we were running out of time we could make a really quick guess at this answer. It's pretty easy to see that A and B are wrong, and it looks like L and K can go 4th and 6th, so E is pretty likely the answer.

5

Some of you may have noticed that we could just switch K and L in the diagram for 4A and see that K can go 6th. This is true, but it doesn't always work. I'll talk about when you can and can't do this sort of thing in the Advanced Techniques section. For now, if you don't see something in a previous diagram, use a new diagram to test it out (unless you are really pressed for time; then just make the best guess you can).

Game One

63

That's It – Summary Well, congratulations. You've either done your first game, or you've done your first game the right way. Let's see what we've learned:     

Be methodical in looking at the rules: start with the first rule and go through the rest one by one When testing answers, put in people where you can as rules about them come up When testing answers, fill in any empty spaces after looking at all the rules Doing the questions in the right order sure makes things easier Always try things out on paper – it is easier, and it gives you diagrams to look at later on

At this point there are a couple of things we haven't seen. We haven't seen any "If… then…" rules, and we haven't seen any If-questions. We'll see both in the next game, though.

What Do I Do Next? What should you do before you go on? Well, at the very least you should go through the notes you took as you worked through this game. What? You didn't take any notes? Well, go back through this game and write down everything that seems useful or important. Then go through those notes and think about what they mean and how it all fits together. I want you to visualize working through a game or two; imagine yourself going through these steps. This will allow you to practice these steps without having to do any questions. This game should have helped you to understand a lot of what we covered in The Fundamentals. At this point you should be a bit tired. Take a break. Think about what you have learned and how it all relates. Then work through this game on your own and try to apply what you have learned here (although feel free to use your general notes on the steps and so forth – just don't look at the answers until you are done). Once you have done that, you are in a position to think about what you need to start memorizing. Go back and read What Do I Do Next? at the end of the chapter The Fundamentals. There I talk about what you'll need to work on memorizing, and how to do so. Put together some flash cards. You don't need to memorize them right now, but go through them for a few minutes every day as you practice logic games. Your goal is to have memorized them by the time you get to Game Four through Game Eight. Once you've made up a list of things you need to memorize (and hopefully made some flash cards), proceed to the next chapter, "If… then…" Rules and Negations.

Answer Key 1. 2. 3. 4. 5.

B E E B C

64

"If… then…" Rules and Negations

"If… then…" Rules and Negations "If… then…" Rules "If… then..." rules generally, but not always, are sentences containing the words "if" and "then". For example, If a creature is a human being, then they have a heart and kidney(s). Let's take a look at this sentence. First of all, it is true – human beings have hearts and at least one kidney (assuming that they are alive, but let's ignore the philosophical question of whether or not a corpse is a human being). So any time I meet a human being, I know (without surgery) that they have a heart and kidney(s). However, there are plenty of animals who have hearts and kidneys but aren't humans. For example, my dog has a heart and two good kidneys, and, while she thinks she's a human and tries to sit on the couch, she really isn't. What we've just seen with this "If… then…" sentence can be generalized to all "If… then…" sentences. Here, then, is the first thing we've learned about "If… then…" rules: when the "if" part is true about a thing or situation, the "then" part has to be true as well. If I say that it is true that so and so is a person, then it has to be true that they have a heart and kidneys. In other words, the truth of the "if" part guarantees the truth of the "then" part (or, as philosophers say, the truth of the "if" is sufficient to show the truth of the "then"). However, the truth of the "then" part doesn't tell you anything for sure about a given person or situation. If I know that it is true that Edward has a heart and kidneys, I don't know that it is true that Edward is a human (in fact, he is my cat). Let's look at another example: If Fred eats ice cream, then he is happy. Let's say you knew that Fred was eating ice cream. What else would you know? Right, you'd know he was happy. What if you were only told that Fred was happy? Would you know that was eating ice cream? No, because "is happy" is in the "then" part of this sentence, and knowing that the "then" part is true doesn't tell you anything for sure. The contrapositive Let's see what else we know. Sticking to the first example I gave, "If a creature is a human being, then they have a heart and kidneys," let's say I know that Mothra doesn't have a heart or kidneys. Can Mothra be a human? Well, if Mothra was a human, she'd have to have a heart and kidneys, right? But she doesn't have them, so she can't be a human. So we can say, If a creature doesn't have a heart or kidneys, then it isn't a human. This is always true about "If… then…" sentences; if the "then" part isn't true about a person or situation, the "if" part can't be true either. From this, we arrive at the idea of the contrapositive. The contrapositive is a way of rewriting an "If… then…" sentence. Let's take a look at the form this will take; here's a general example of an "If… then…" sentence:

"If… then…" Rules and Negations

65

If something is X, then it is Y. This means that if something isn't Y, it can't be X, because if it were X, it would have to be Y. If something isn't Y, then it isn't X. Remember that the "if" part being true guarantees that the "then" part is true. Whenever something is X, we know immediately that it has to be Y. We can say that the "then" part being true is a requirement for the "if" part to be true (another word for "requirement" is "necessity"). This means that the "if" part can't be true without the "then" part being true; for example, something can't be X without also being Y. But the "then" part might only be one of many requirements, so knowing that it is true doesn't tell us that the "if" part is true. We might have something that is Y, but not X, but we can't have something that isn't Y and is X. Let's look at another example and see how it works like these X and Y examples: If you have read The Brothers Karamazov, then you think Dostoevsky is a genius. If X, then Y. If you don't think Dostoevsky is a genius, then you haven't read The Brothers Karamazov. If not Y, then not X. These two sentences are the contrapositives of each other. Notice that the two sentences are structurally the same as the examples with X and Y – that is, the second sentence tells you that if the "then" part (the Y) isn't true, the "if" part (the X) can't be true. The contrapositive of an "If… then…" sentence is a way of expressing the fact that if the "then" isn't true, the "if" can't be true. There is a simple rule for making the contrapositive out of an "If… then…" sentence. To make the contrapositive, do two things: 1) make the "if" part into a "then," and make the "then" into an "if"; and 2) make both sides negative. If one side is already negative, make it positive (two negatives make a positive). Look at the Dostoevsky example and see that this is what I did there. Take the following example with negatives. The contrapositive of If something is A, then it is not B. is If something is B, then it is not A. We switched the "if" and the "then" and made both negative; but since the "then" is already negative, it becomes positive. This works because we always know that when the "then" part isn't true (when it is negative) then the "if" part can't be true (so it will be negative as well). The contrapositive of every "If… then…" sentence is true, and it is useful. So every time you have an "If… then…" rule, always write down the contrapositive of the rule.

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"If… then…" Rules and Negations

Some examples OK, here is a true sentence (I'll put Xs and Ys below the clauses to show how this sentence relates to the more abstract examples above): If someone lives in Los Angeles, then they live in California. If X, then Y. Imagine that I have a friend who lives in California. Do you know that this friend lives in Los Angeles? You don't know – they may or may not. Now imagine that I have a friend who doesn't live in California (let's say they live in Oklahoma). Do they live in Los Angeles? Of course not; they haven't met the requirement for living in Los Angeles. The contrapositive of the sentence is If someone doesn't live in California, then they don't live in Los Angeles. If not Y, then not X. Second example: If Mary goes to the dry cleaner, then Bob will eat a hamburger. If X, then Y. Here we can't rely on our intuitions. We have to apply the rules. Now, what happens every time Mary goes to the dry cleaner? That's right, Bob eats a hamburger. What if we know that Bob eats a hamburger? Do we also know that Mary went to the dry cleaner? No, we don't – since Bob eating a hamburger is on the "then" side, it tells us nothing about Mary. What's the contrapositive of this sentence? If Bob doesn't eat a hamburger, then Mary doesn't go to the dry cleaner. If not Y, then not X. Now imagine that we know Bob doesn't eat a hamburger. What does this tell us? It tells us that Mary doesn't go to the dry cleaner. What if we know that Mary doesn't go to the dry cleaner? This tell us nothing, because it is on the "then" side. Now let's look at an example with negatives: If I ate lunch, I will not order pizza for dinner. If A, then no B. Notice that the "then" part has a negative in it ("will not order pizza"); this negative will become a positive when we form the contrapositive. If I order pizza for dinner, then I didn't eat lunch. If B, then not A. What does this mean? If I ate lunch, what do you know? You know that I won't order pizza. What if I order a pizza? Then I didn't eat lunch. What if I didn't eat lunch? Well, I may or may not order a pizza; knowing that the "then" part ("didn't eat lunch") is true doesn't tell you anything about the "if" part.

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A sentence with negatives in the "then" part, or in both the "if" and "then" parts, follows the same rules. For example, these two sentences are contrapositives of each other: If you don't like to laugh, then you won't like Happy Gilmore. If you like Happy Gilmore, then you like to laugh. To summarize: whenever the "if" part is true, the "then" part is true too. But when the "then" part is true, we don't know anything about the "if" part.

"If… then…" Equivalents There are many ways the LSAT will state "If… then…" rules. For example: All kittens are cute. is really an "If… then…" sentence. It means If something is a kitten, then it is cute. When you see something that means "If… then…", rewrite it as an "If… then…" sentence; we know how to deal with "If… then…" sentences, and we know how to form their contrapositives, so we like the format. Here are some common things you will see on the test and how to rewrite them as "If… then…" sentences; memorize these sentences and how they are equivalent to "If… then…". Each of these sentences means "If something is an X, then it is a Y." All Xs are Ys. Any X is a Y. Every X is a Y. When something is an X, it is Y. Nothing is an X unless it is a Y. No one can be an X without being a Y. Only Ys are Xs. Something can be an X only if it is a Y. To illustrate how to use this list, let's look at the sentence "Only mammals are cows." "Mammal" is the Y in the "only" version of the sentence, and "cow" is the X. Each of the sentences on the list means "If X, then Y"; we replace X with "cow" and Y with "mammal" and get "If something is a cow, then it is a mammal." X and Y can be replaced with anything in these sentences; for example, "Something is a monkey only if it is mean," means "If something is a monkey, then it is mean." Remember, this tells you that all monkeys are mean, but something can be mean and not be a monkey (because "mean" is the "then…" part). One way of understanding why all these are equivalent is to think about guarantees and requirements. If I tell you that "All monkeys are mean," this tells you that being a monkey guarantees that something is mean (because all monkeys are mean). But being mean is a requirement – you can't be a monkey without it. Since it is a requirement, it might not be the only requirement; just because you are mean doesn't mean you have to be a monkey, because you might not have met the other requirements to be a monkey (like having a tail).

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So "monkey" is the "if" part and "is mean" is the "then". Likewise, if I say that "Only Americans are Californians," this means that being an American is a requirement for being a Californian. However, it isn't a guarantee – you can be an American without being a Californian. People often have trouble remembering how to translate "unless" into "If… then…" Here are some tips for dealing with these sentences: "Unless" An "unless" sentence has to have two parts. Take the following example: "You can't dance well unless you have the right shoes." (It's true – have you ever tried to dance in combat boots? It's tough, real tough.) The two parts are "can't dance well" and "have the right shoes." One of the two parts will become the "if" and the other the "then" of an "If… then…" rule. Whenever you have a sentence with "unless" in it, replace "unless" with "if not," and put a "then" in front of the other part. Applying this to our example "You can’t dance well unless you have the right shoes," we get: Then you can't dance well if not you have the right shoes. Sounds weird, but we'll fix it. Change the order to put the "if" first (this is perfectly acceptable, and something you commonly have to do with "unless" sentences): If not you have the right shoes, then you can't dance well. Now, what does "if not you have the right shoes" mean? It means "if you don't have the right shoes" – that's how we'd say this in English. Putting "not" in front of a word or phrase negates it; later in this chapter we’ll talk about how to negate some common LSAT words and phrases. Now we have If you don't have the right shoes, then you can't dance well. and its contrapositive: If you can dance well, then you have the right shoes. Perfect. To summarize, "unless" means "If _______ is not the case…" After you’ve made this substitution, you may have to move the "if" part of the sentence to the beginning. I recommend that you don't rely on your intuition in interpreting "If… then…" rules. Memorize these equivalencies (but use the idea of guarantee and requirement, or necessity and sufficiency, to help you understand and memorize them) because logic games will give you situations that you have no intuition about, such as "Sally wears a hat only if Jane doesn't."

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Complex "If… then…" Rules Sometimes "If… then…" rules will be more complex than this. The "if" part or the "then" part will contain several pieces. For example, If you drive too fast or run a red light, then you will get a ticket. Complex "If… then…" rules should generally be split into two "If… then…" rules. For example, in this case we know that both of these are true: If you drive too fast, then you will get a ticket. If you run a red light, then you will get a ticket. Splitting these rules into two rules makes them easier to think about and much easier to do the contrapositives for. Sometimes (but very rarely) these rules can't be split. For example, If you drive 35 mph and you are on the freeway, then you will get a ticket. Driving 35 mph won't guarantee a ticket by itself, and being on the freeway won't guarantee a ticket by itself – you need to do both together. So we can't split this into two rules. More often than not, you can split a complex rule into two rules. I am about to give you a list of times when you can and can't split the rules. This should be low priority on your list of things to memorize – generally, just split the rules unless that clearly doesn't make sense – but if you find that you get everything else under control and still have time and space left in your brain, go ahead and memorize these. If If If If

X X X X

or Y – split and Y – don't split then Y and Z – split (If X then Y, If X then Z) then Y or Z – don't split

Here are the contrapositives of the two you can't split: If X and Y, then Z – If no Z, then not both X and Y (which means one or the other of X and Y won't be true) If X, then Y or Z – If no Y and no Z, then no X. See why we split when we can? It makes the contrapositives sooooo much simpler. I'll explain more about what these complex contrapositives mean below, in Negations. To summarize, when you have an "If… then…" rule with more than one thing in the "if…" or "then…" part, you generally can (and should) split it into two rules.

Negations When we form the contrapositive, we have to make both sides of the contrapositive negative. We also need to know how to make things negative for "What must be true?" questions. On these questions, we test answers by seeing if a situation that is different from what the answer describes can work. To be different from the answer, a situation has to be the negation of the answer. There are certain terms and phrases on the LSAT that

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people often have a difficult time making negative. It's important that you understand how to do this, so let's spend some time going over it. We can define the negative of a sentence as anything that would make the sentence false. "Not A" refers to any situation other than A, because "A" can only be true if it is true, not if something different from it is true. So if the sentence says "X is 1st," then X being 2nd, 3rd, 4th, etc. would be the negation of the sentence, because in these cases it is false that X is 1st. Sentences, or answers, usually have more than one negation – a whole range of situations will negate a single sentence. Let's go through the types of sentences you will have to negate on the LSAT; you don't have to memorize all of these right now, but you should at least understand the type of thinking that underlies them. Later on, when you practice games, you will have to make negations like these. If you find that you have a hard time doing it, refer back here and then start to memorize. Negating negatives: (For example, "X is not large.") This is the easiest thing to do; the negation of a negative becomes a positive. So the negation of the example sentence would be "X is large." Negating positions: (For example, "X is 1st," or "X is in group A.") Some sentences talk about X being in one specific position. The negation of these sorts of sentences is having X not in the position described. Any situation where X is in a position or group other than the one described would be a negation of this type of sentence. Here's how it works in an example "If… then…" sentence: If X is 1st, then Y is 2nd. If Y is not 2nd, then X is not 1st. Here we have an "If… then…" sentence and its contrapositive. What does the contrapositive mean? Well, if you see Y in 1st, 3rd, 4th, and so forth, then you know X isn't 1st; it has to be 2nd or 3rd, etc. Now let's look at "What must be true?" questions. We test answers on these by looking for diagrams where the negation of the answer is true. If the answer says "X is 1st," then you want to look for a diagram where X is not 1st. This means that you are looking for a diagram where X is 2nd, 3rd, or 4th – any position but 1st. If you need to test the answer, then put "not X" under position 1 in your test diagram. Then go through the rules and see if you can fill all the spaces in the diagram without breaking a rule. Negating "before," "after," and "at the same time": (For example, "X is before Y.") Most games involving "before" and "after" don't allow things to be at the same time (like Game One), but some do. If a game doesn't allow things to be at the same time, ignore where I have "At the same time" in what follows. The negations of "before" are "after" and "at the same time." If X is after or at the same time as Y, you know X is not before Y. The negations of "after" are "before" and "at the same time." And the negations of "at the same time" are "before" and "after." Let's look at an "If… then…" sentence and its contrapositive: If A is before B, then B is before C. If B is not before C, then A is not before B.

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What do these sentences tell you? Well, if you see B after (or at the same time as) C, then B is not before C. This means that A can't be before B, so A has to be after (or at the same time as) B. Now let's see how this would work on a "What must be true?" question. Imagine the following was an answer to a "What must be true?" question: (B) G is before E To test this out, we want G to be not before E. So look for previous diagrams where G is after E (or at the same time as E); or, draw a diagram in which you put G after E. Negating "more than," "fewer than," and "exactly": (For example, "Group X has fewer members than does group Y.") This is very similar to before/after/at the same time, except "exactly" is a very important LSAT term and gets used all the time, whereas "at the same time" isn't and doesn't. The negations of "more than" are "fewer than" and "exactly"; the negations of "fewer than" are "more than" and "exactly", and the negations of "exactly" are "more than" and "fewer than." This means that if something is not more than three, it is either less than three or equal to three. If something is not exactly three, then it is more or less than three. Let's see how this works with contrapositives: If group A has more members than group B, then B has exactly as many members as C. If B doesn't have exactly as many members as C, then A doesn't have more than B. These are real mouthfuls. Let's see what the second sentence means. If you see that B has either more or fewer members than C – for example, B has 2 and C has 3, or B has 4 and C has 2 – then you know that A has to have either the same number or fewer members than B. If you saw one of these terms in a "What must be true?" answer, you'd test it by looking for a diagram which has the opposite. If the answer said (D) A has more members than B. you'd look for a previous diagram where A has fewer members than B, or the same number. To test it out in a diagram, you'd give B fewer or the same number of members as A. For an example of this, see Game Two, question 11. Negating "only": (For example, "Only X is in group B," or "X is the only red car.") Sentences like this mean two things. First, they mean that X has the property described – i.e., being in group B, or being red. Second, they mean that no one else has this property. In the examples I just gave in parentheses, group B has one member only – X – and in the second example every car other than X is a color other than red. Since "only" sentences require two things to be true, this tells us that we can negate these sentences in two ways. First, we could make X not have the property described – X could be in group C, or it could be blue. Second, we could give other people that same property. We could put more than one person in group B, or make another car red.

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Let's see this with contrapositives: If only X is red, then only Y is green. If not only Y is green, then not only X is red. What would tell us that "not only Y is green," as we see in the contrapositive? Well, if Y were not green (say, if it were red), or if someone else (say, Z) was green as well, then you would know that not only Y was green. If this were the case, we'd know that not only X is red. Unfortunately, that isn't terribly informative, because there are two ways "not only X is red" is true: X might be red, but someone else is red as well, or X might not be red at all. Here's a little bonus hint regarding the above. Let's say you knew that Z was green, but you didn't know anything about Y. What would this tell you? Well, it would tell you that not only Y was green. See, if Y ends up being green, then both Y and Z are green, so it's not only Y. And if Y ends up not being green, then not only Y is green. Now let's see how this works on a "What must be true?" question. Here's our sample answer: (A) Only X is red. To test this, look at previous diagrams. If you see one where X is not red (where it is green, or orange, or blue, etc.), then you know that not only X is red. If you see one where someone else is red, say Y or Z or Q, then you know that not only X is red. In either case, A doesn't have to be true. To test this out by making a diagram, you'd either make X not red (so make him green or orange, etc.) or you'd make X red and someone else as well. Negating "either/or": (For example, "Either X or Y is blah blah.") Whatever fills out the blah blah is going to be one of the things described above; e.g., "Either X or Y is 1st," or "Either X or Y is before Z" or "Either X or Y has fewer members than Z," or "Either X or Y is the only member of A." To be able to negate an either/or sentence, then, you have to be able to negate the type of sentence that fills out the blah blah – you have to understand "before," or "fewer than," or "only," and so forth. But, of course, that's not all. For an "either/or" sentence to be true, one or both of the people referred to have to have the property referred to. If it says, "Either X or Y is 1st," then if X is 1st, it's true, and if Y is 1st, it's true (and if they are both 1st? It's true!). The only way for this type of sentence to be false is for neither person to have the property in question. For example, If either X or Y is first, then either Z or W is fourth. If not either Z or W is fourth, then not either X or Y is first. You should notice that these are the sorts of "If… then…" sentences I told you above to split up into smaller sentences. I don't split them up here because I want to show how "either/or" is supposed to work, but you should do so on the LSAT. Since the "either" part is true if X is first or Y is first, you can split the sentences into two rules, one about X and one about Y: If X is first, then either Z or W is fourth. If Y is first, then either Z or W is fourth.

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Now the contrapositives are a little easier to make: If not either Z or W is fourth, then X is not first. If not either Z or W is fourth, then Y is not first. Of course, the question still stands: "What does 'not either Z or W is fourth' mean?" I'll answer this question just below. How do we know that not either Z or W is fourth? Simple – we know it if neither of them is fourth. We know this if both of them are someplace else, for example, if Z is 5th and W 3rd. And if that's the case, we know that neither X nor Y can be first – they both have to be someplace else. Let's see how this works with "What must be true?" questions. Take a look at this sample answer: (C) Either A or B is before C. If you see a previous diagram where neither A nor B is before C, you know that this doesn't have to be true. So look for diagrams where both A and B come after C. To test this out with your own diagram, you'd have to put both A and B after C. You'd try putting C first, and A and B somewhere after it; if that didn't work, you'd move C to spot 2, and so forth. (See Game One, question 4.) By the way, the negation of "neither/nor" is "either/or." A "neither/nor" sentence is false if one of the entities mentioned has the property mentioned. That sounds very abstract, so here's an example answer to a "What must be true?" question: (A) Neither X nor Y is happy. X being happy is a negation of this answer. Y being happy is also a negation (and both of them being happy is a negation as well). If you saw a previous diagram where X was happy, you would know that this answer doesn't have to be true. To test this out with your own diagram, you would make one of the two happy. If the one you picked didn't work, you'd try the other one. (See Game Three, question 8, answers C and D.) The LSAT can say "or" and mean "either… or…" For example, "A or B is before C" means "Either A or B is before C." Negating "both” and "and": (For example, "Both E and F are red-haired." "X and Y and Z are painters.") A statement with "both" is only true if both parts of it are true; "and" is just like "both," but with potentially more parts. Here, E would have to be red-haired and so would F. If either of them was not, then the statement would not be true; so if E was blond, or if F was a brunette, the statement would not be true. The negation of "both" is "not both," and it means that one or the other part isn't as described. Take the following "If… then…" sentence and its contrapositive as an example: If both E and F are red-haired, then both J and H are blondes. If not both J and H are blondes, then not both E and F are red-haired. You could break these rules down into simpler ones if you wanted. With the "if" part, you know that both E and F have to be redheads for the rest of the rule to be relevant. This means you can't break up this part of the rule – having only E be a redhead doesn't tell you anything, nor does having just F be red-haired – you have to have both of them. But you can break up the "then" part. If both E and F are red haired, J has to be blonde. So does H. You can make this into two rules, one with the "then" about J and one with the "then" about H:

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anything, nor does having just F be red-haired – you have to have both of them. But you can break up the "then" part. If both E and F are red haired, J has to be blonde. So does H. You can make this into two rules, one with the "then" about J and one with the "then" about H: If both E and F are red-haired, then J is blonde. If both E and F are red-haired, then H is blonde. Now the contrapositive is nice and simple. If J is not blonde, then not both E and F are red-haired. If H is not blonde, then not both E and F are red-haired. Breaking up "both," "either," "and" and "or" rules makes these sorts of sentences, or their contrapositives, much simpler to think about. What does "not both J and H are blonde" mean? It means that one of them, or both, is not blonde – they have some other hair color. So if you see J is a redhead, or H is bald, you know that not both of them are blonde. Then you know that "not both E and F are redhaired." What does this tell you? It tells you that one of them (maybe both) has to have a hair color other than red. You don't know which one it is, unless one of them is a redhead. Then you know the other can't be. Now let's take a look at "both" in a "What must be true?" question. Imagine this were an answer: (E) Both T and R teach English. The negation of this is that one of them doesn't teach English. If you see a previous diagram where one of them teaches a different class, you know that (E) doesn't have to be true. To test this by making a new diagram, you'd have to give one of them a different class to teach, but you wouldn't know which one to give it to. You might try T first, and give them every possible other class (while giving R English). If that didn't work, you'd try to give R every possible class other than English (and give T English). If no class other than English worked for either of them, you'd know that they both had to teach English. By the way, the LSAT can just say "and" and mean "both." For example, "X and Y teach English" means "both X and Y teach English." Negating “If… then…” sentences: (For example, “If A is 1st, then B is 3rd.”) This is very rare, but once in a while a “What must be true?” question will have “If… then…” sentences for answers (see, for example, LSAT 29, question 6 in the logic games section; each answer is an “If… then…” sentence). In order to see which answer must be true, you need to test the negation of each answer. Thus, you need to know how to negate “If… then…” sentences. Here’s how to do it: To negate an “If… then…” sentence, make the “if” true and the “then” false. For example, to test (B) If A is 1st, then B is 3rd. You would make a diagram in which A is 1st, but B is not 3rd. In other words, you’d write “No B” under space 3, and try to put B someplace else (2nd, or 4th, or 5th, etc.). If you can

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put B someplace else (other than 3rd), you know that B doesn’t have to be 3rd if A is 1st. Thus, the answer doesn’t have to be true. If you can’t put B anyplace else, you know that if A is 1st, B has to be 3rd, so the answer must be true. Like I said, this is very rare, so I wouldn’t put it high on your list of things to memorize. The moral of the story on negations Negations often confuse people because they involve negatives, but you generally can't see negatives – you see positives. That is, you don't see what X isn't, you see what X is. What X is tells you what it isn't – it isn't anything else other than what it is. What you have to do is learn how to recognize when one situation is the negation of another. If, to answer a question, you have to find a situation where X is "not such and such," you should be able to know, in advance, what types of actual situations you could see (X being something) that would mean "not such and such." Learn what actual situations are the negations of sentences, and you'll be able to spot right and wrong answers much more quickly and be able to apply contrapositives much more comfortably.

What Do I Do Next? You need to understand what "If… then…" rules mean and how to make contrapositives. If you don't, read the first part of this chapter again. Make up your own "If… then…" sentences and make contrapositives out of them. When you feel somewhat comfortable with that, go on to Game Two. Once you have "If… then…" sentences and contrapositives down, you need to think about equivalents of "If… then…", like "all," "any," "only," and so forth. You don't need to memorize these before you go on to the next chapters, but you should be memorizing them while you study the next chapters. You want to have the "If… then…" equivalents nailed down by the time you get to Intermediate Techniques. Try rewriting some of the "If… then…" sentences I told you to make a few sentences ago using the equivalent terms. You may also want to make flash cards out of some of these; most people find sentences with "unless" and "only" difficult, so I'd be especially careful to understand them. You don't have to have to be comfortable with negations at this point. Just be aware that they exist, and you'll be forced to think about them as you go through games. If you see that you have problems with them in general, or with specific types, refer back to this chapter and maybe make some flash cards.

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Game Two Game omitted from electronic version of book.

Game Two

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Game Two (From LSAT 28)

Step 1: Read the Setup/Draw a Diagram Every game involves two types of entities that you match together. What are the two types of things in this game? Read the setup and figure it out. We've got some researchers and some languages, and we are going to match one to the other. Which is more definite? Well, you don't know too much about either group. You are told that each researcher can only learn three languages at the most (which you should write down), but you don't know how many languages each will actually learn – one? two? or three? Since we don't really know which of the researchers or the languages is more definite, we don't know how to diagram this. Now, here is an important tip: When you aren't sure how to diagram a game, glance quickly at the rules and see if they help you. Take a quick peek at the rules. Go ahead… Now, notice that the first three rules tell you definitely how many times each language is learned. That makes the languages more definite. So our diagram should be based around them; write down their names (abbreviated) horizontally (or vertically, it doesn't matter). Under each language we are going to put a blank for each time it will be learned; those blanks will eventually be filled with the names of the researchers. But that information will come from the rules, so let's not get ahead of ourselves. Write down the names of the researchers off to the side. Also, I've written down the rule about how many languages each can learn. This is a rule, so I'm writing it where the rules go. R

S

T

Y

researchers: G H L P

Each researcher can learn 1 to 3 languages. Remember, this is the format of every diagram: the definite things are written down in a row, and each gets a blank for every variable thing that will be assigned to it.

Step 2: Read the Rules The first three rules tell us how many blanks to write under each researcher. Notice the word "exactly" in each, which means that each has to be learned by that many researchers, no more and no fewer. R gets one, because it will be matched with only one researcher, S gets two, and so forth. We put these directly into our diagram: R __

S __ __

T __ __

Y __ __ __

researchers: G H L P

Each researcher can learn 1 to 3 languages.

78

Game Two

Next rule: "Any language learned by the linguist or paleontologist is not learned by the geologist." First thing, you should have noticed the word "Any." The word "Any" tells you that this is an "If… then…" rule. The "any" part is the "if" part, and the other half of the sentence is the "then" (see "If… then…" Equivalents in the chapter on "If… then…" Rules and Negations). Second, this is a complex "If… then…" rule, because it has two things in the "if" part. When you see an "If… then…" rule with two things in the "if" part, ask yourself if you can split it into two rules. This can be split into one rule about the linguist and the other about the paleontologist. We know this because of the word "or." If either one of them (the linguist or paleontologist) learns the language then the geologist can't learn it. So we'll write this as two rules to make it easier to understand. If L learns a language, then G can't (learn that language). If P learns a language, then G can't (learn that language). You don't have to write the part in parentheses, but you might want to if you find the rule confusing. Now that we have "If… then…" rules, we want to write the contrapositives. Always write the contrapositive when you see an "If… then…" rule. We make the contrapositive by switching the "if" and "then" parts, and by adding negatives to both parts. Since the "then" part is already negative (G can't learn that language), we make it positive. If G learns a language, then L can't (learn that language). If G learns a language, then P can't (learn that language). What do these rules tell us? If you aren't sure you understand a rule, give yourself a specific, concrete example to make things clearer. What if L learns S? The G can't learn S. And if G learns S? Then L and P can't. Next rule: "Any language learned by the geologist is learned by the historian." How should we write this? I'll give you a second to think. That's right, this is an "If… then…" rule (the word "any" tips us off), so we write it with "if" and "then." If G learns a language, then H learns it (the same language). Write the contrapositive as well. If H doesn't learn a language, then G doesn't learn it (the same language). Does this mean that G and H always learn the same languages? No. This is a common mistake. The rule tells you that if G learns something, then H will, but what if H learns something? Since H is in the "then" part, it doesn't guarantee that G will learn it. H learns all of G's languages, but H might learn more than these. Get used to interpreting "If… then…" rules in this way.

Game Two

79

So here is our original diagram and rules (with optional words in parentheses): R __

1. 2. 3. 4. 5. 6. 7.

S __ __

T __ __

Y __ __ __

researchers: G H L P

Each researcher can learn 1 to 3 languages. If L learns a language then G can't (learn that language). If P learns a language then G can't (learn that language). If G learns a language then L can't (learn that language). If G learns a language then P can't (learn that language). If G learns a language then H learns it (the same language). If H doesn't learn a language, then G doesn't learn it (the same language).

This is a lot of rules, but they are simple to understand. The numbering is just so I can refer back to them, and it doesn't have much to do with the order in which they were told to us by the LSAT. There are several things we can figure out by combining these rules right now – deductions – but we aren't going to look for them. It isn't necessary and I don't want to distract you from the more important things you need to learn now. I point out that there are deductions because after we finish the game I want you to notice how well we did without making them.

Step 3: Answer the Questions We are going to walk through the questions one by one. If a question is one that we should do, we'll do it; otherwise we'll skip it and come back to it later. Question 6: A "What can be true?" question – do it now It's a "What can be true?" question, so we'll do it ("could" means the same as "can"). We have to test each answer out by drawing a new diagram and putting in the scenario the answer describes. Answer A Redraw your diagram and put the linguist in under each of the languages listed in the answer (R, S, and T). R L

S L __

T L __

Y __ __ __

Now let's go through the rules.

researchers: G H L P

80

Game Two

Rule 1 says that each researcher can only learn one to three languages. L has learned three, so it can't learn any more. This means that L is finished. Cross it off our list. Rule 2 says that G can't learn any languages that L learns. So G can't learn R, S, or T. Write this in the diagram. R L

S L __

T L __

no G

no G

no G

Y __ __ __

researchers: G H L P

Every time we learn something new about the game we have to go back through the rules from the beginning. Here, we've learned that G can't learn R, S, or T, so we start again with rule 1. It says that every researcher has to learn from one to three languages. That means that G has to go someplace, and the only place it can go is Y. We can cross G off the list because it can't go anyplace else. R L

S L __

T L __

no G

no G

no G

Y G __ __

researchers: G H L P

Keep going through the rules. Rule 3 says "If P learns a language," but we don't know what P learns. We could look at the "then" part of the rule, but we shouldn't. Remember, with "If… then…" rules, the "then" part doesn't tell you anything. When looking at "If… then…" rules, focus on the "if" part first. If it is true (if P learned some language here), then you know that the "then" part is true. If you don't know if the "if" part is true, then the "then" might be true or it might not. Rules 4 and 5 tell you that L and P can't go where G goes, so they can't go under Y. Rule 6 tells you that H has to go under Y. Put all this in. R L

S L __

T L __

no G

no G

no G

Y G H __ no P no L

researchers: G H L P

Skim through the rules one more time because we've added some new stuff. Nothing new happens. Now we are done with the rules. We have to fill in the rest of the spaces to see if we can't make this diagram work. We can put P or H under S and T, since there is nothing to say that we can't. Who do we put in the last spot for Y? We can't put P in, we can't put L in, and we've already used G and H. What does this mean? It means that there is no one that can go in that last space under Y. We can't fill all the spaces of the diagram without breaking the rules. This diagram doesn't work, so this answer is wrong. Cross off the diagram (always cross off diagrams that break the rules so that you don't use them later on by accident) and cross off the answer.

Game Two

81

Answer B Draw a new diagram again and put in the situation described in the answer. R __

S L __

T L __

Y L __ __

researchers: G H L P

Rule 1 tells us that we can cross off L because we have used it three times, and rule two tells us that G can't go under S, T, or Y, because it can't go with L. R __

S L __

T L __

no G

no G

Y L __ __ no G

researchers: G H L P

Since we've learned something new – that G can't learn S, T, or Y – we have to start again with rule 1. We know that G has to go under R, because it has to be used at least once. We cross off G because it can't be used any more times – there is nowhere else for it to go. R G

S L __

T L __

no G

no G

Y L __ __ no G

researchers: G H L P

Continue with the rules. Rules 4 and 5 tell us that L and P can't go under R (which is no problem because there isn't any more room under R). Rule 6 tells us that H has to go under R, because H goes wherever G goes. But there isn't any room under R, so H can't go there. This means that this diagram breaks the rules, so the answer is wrong. Cross off the diagram and cross off the answer. Answer C Again, draw a new diagram and put H in where you are told. R H

S H __

T H __

Y __ __ __

researchers: G H L P

Go through the rules. Cross off H because of rule 1. Rules 2 through 6 are "if" rules about the languages L, P, and G learn. But we don't know what languages they learn; when you don't know if the "if" part of an "If… then…" rule is true, we skip the rule. That brings us to rule 7. It says "If H doesn't learn a language." We know that H doesn't learn Y, because there isn't an H under Y, and there can be no more Hs in the diagram. Since the "if" part is true (H doesn't learn a language, Y), the "then" part has to be true as well. G can't learn Y. R H

S H __

T H __

Y __ __ __ no G

researchers: G H L P

82

Game Two

You might now notice that there are only two people that can go under Y – L and P. But there are three spaces under Y. This won't work, so this answer is wrong. Maybe, though, you didn't notice that. You can still get the answer right. We're done looking at the rules, and we have many empty spaces. We are just going to have to try things out and see if we can make it work. Start putting people in. When you have to just put people in a diagram, start with the first person and put them in the first available space (that's the first space that isn't filled and that has no rule explicitly saying they can't go there). Put G under S. Mark it with a dot or star, since we chose to put G there. R H

S H G*

T H __

Y __ __ __ no G

researchers: G H L P

Once we've added something to the diagram, we go through the rules. The only rules about G say that L and P can't go with G. There isn't any more space under S, so this isn't worth writing down. Now we have to put in L and P. Put L in the next available spot – under T. Mark it, because this is our choice. R H

S H G*

T H L*

Y __ __ __ no G

researchers: G H L P

Now we have three spots left under Y. Put P under Y because P is next on our list. Now we go back to the beginning of the list. G can't go under Y, and H is all used up. This leaves only L, which means that we can't fill all the spaces under Y. This won't work. Could we make this work by changing some people around? We can move G to T, but this won't make a difference in filling Y – the H's are all assigned by the answer, and we've already got L and P under Y. We can't move G to Y, because we have "no G" under it. Cross off this diagram and cross off answer C. Answer D Try this out on your own, then read my explanation. We put H where the answer tells us. R __

S H __

T H __

Y H __ __

researchers: G H L P

Then we go through the rules. Rule 1 tells us that H can't be used any more. Rules 2 through 6 are about the languages learned by G, L, and P, and we don't know what those languages are. Rule 7, though, tells us that G can't learn R. This is because H isn't under R, and if H doesn't learn a language, G doesn't either. This is all the rules tell us.

Game Two R __ no G

83 S H __

T H __

Y H __ __

researchers: G H L P

We just have to start putting people in. I'll put G in first. The first available space for G is under S, since there is a "no G" under R. Mark G because this was our choice. R S __ H no G G*

T H __

Y H __ __

researchers: G H L P

Look at the rules because we just put someone in. L and P can't go with G, but since S is now full this is no big deal. Now let's put in the next person on our list (who isn't crossed off): L. Put L in the first available space, which is under R, and mark this as our choice. R L* no G

S H G*

T H __

Y H __ __

researchers: G H L P

Now on to P. The first space open for P is under T. Put it there and mark it. R L* no G

S H G*

T H P*

Y H __ __

researchers: G H L P

Looking through the rules, we see that this doesn't tell us anything new (well, it tells us that G can't go under T, but T is filled anyway). Now we have two spaces left under Y. Start back at the beginning of our list. Put G under Y. Look at the rules again. They tell us that neither L nor P can go with G (you probably remember that without looking at this point), so we couldn't put anyone in the last spot under Y. This won't work, so we think about the last thing we put in. Let's not put G under Y. Instead, put L there. This is fine. Now put P in the last spot. R L* no G

S H G*

T H P*

Y H L P

researchers: G H L P

Check the rules one more time. This works, so it is possible; this (answer D) is the answer.

84

Game Two

Question 7: An If-question – do it now This is our first If-question. Let's savor the moment – as Sade says, it's never as good as the first time. If-questions give us a new piece of information that we assume is true (on this question only). The first step on an If-question is to draw a new diagram so we can put this information in. Then we are going to see if this new information, together with the rules, makes anything have to be true. R __

S __ __

T __ __

Y __ __ __

researchers: G H L P 3 Ls

We can't put this situation right into the diagram – we don't know where our three Ls have to go. So I wrote it off to the side. When you first look at an If-question, before you look at the answers, only put things in your diagram that have to be true. You have an original diagram which is true for the entire game – that's what you set up in step 1 of the game. You copy this diagram every time you do a question. We don't put stuff that might be true in this diagram, because it might be false, and we want this diagram to apply to every question. On an If-question, you have been given new information to put in your diagram; from this information you can usually but not always figure out other things that have to be true. These things will have to be true for every diagram based on the "If." That means that every answer you test out on that question will have to incorporate these. The "If" gives us a new diagram, which we use instead of the original diagram to test every answer on that If-question. But, we don't put things that might be true into this diagram, because we want it to use it on every answer (and stuff that might be true is not always true). Now, when we look at an answer, we want to see if it could be true. So we plug people in where they might go; we try things out that might be true, not just things that have to be true. The difference between this and what we do when we first look at an If-question is that the diagram we draw initially for the question has to be used on every answer, so it should only include things that have to be true for every answer. The diagram we draw to test a single answer only has to be possible, and we are only using it to test that one answer, so it doesn't have to be true for any other answer. Because we don't know exactly where the Ls will go, we probably aren't going to figure much out. Go through the rules quickly. Rule 1 tells us that we can have three Ls at the most, which just goes with what the question tells us. Rule 2 tells us that G can't be where L is. Great. Nothing else mentions L, so that's all we know. We are going to have to use the answers here. This might be an OK question to skip, since we didn't figure much out, but I'm going to do it because I have confidence in us. The question is a "What must be true?" question. How do we test the answers on this type of question? You should have this memorized by now. We do something other than what the answer describes and see if you can make it work. Remember, we have to have three Ls, as the question says. Also, we can't use our previous diagram because this is an Ifquestion.

Game Two

85

Answer A The answer says that L must be under T, so we are not going to put the L under T in order to test this out. Since we have to have three Ls, that means L goes under everyone else. Now that we've put our three Ls in, we won't put in any more Ls, so we cross L off. R L

S L __

T __ __

Y L __ __

researchers: G H L P 3 Ls

Let's go through the rules. Rule 2 tells us that G can't go where L goes. We can't have G under R, S, or Y; write this into your diagram. Go back through the rules because we've learned something new. We see that G has to be used at least once (rule 1), so it has to go under T. G can be crossed off, because there are no other places it can go. R L no G

S L __

T G __

no G

Y L __ __ no G

researchers: G H L P 3 Ls

Continuing through the rules, we see that H has to go with G (rule 6) (the other rules just repeat what we already know, that G can't go with L, or talk about things we don't know about, such as the language learned by P). This isn't the only place H can go, because H can go someplace G can't. R L no G

S L __

T G H

no G

Y L __ __ no G

researchers: G H L P 3 Ls

Going back through the rules one more time, we learn nothing new. Rules 2, 4, 5, and 6 talk about things we know (that G can't go with L or that G can’t go with P), and rule 3 talks about the language P learns, and we don't know which one that is. Now we just fill in our empty spaces. We have one under S and two under Y. We haven't used P yet, so put it under S (and mark it as optional). R L no G

S L P*

T G H

no G

Y L __ __ no G

researchers: G H L P 3 Ls

Looking through the rules, this tells us nothing new. We have to fill the spaces under Y. G and L are crossed off, so we have to put P and H there. R L no G

S L P*

T G H no G

Y L P H no G

researchers: G H L P 3 Ls

86

Game Two

This is possible, so the answer is wrong. The next thing we should do is see if this diagram helps us with the other answers. We can't use previous diagrams from other questions to help us on If-questions, but we can use them from previous answers within the same question. We can do this because the diagram will have to incorporate the situation described in the If-question, whereas diagrams from other questions might not. We want to see if the diagram we just made is different from the situation described in any other answer; if it is, we can eliminate that answer, because we know that it doesn't have to happen. Answer B has L under R, which agrees with our diagram. We can't eliminate B, then, because we don't know that that doesn't have to happen. Answer C has the L learning S. Our diagram has that, so we can't cross off C. Answer D has the paleontologist learning R, which is different from our diagram. We can cross that off. Answer E has the paleontologist learning S, which is in our diagram. We can't cross that off. We have to test out at least one more answer. Look at B. Answer B To test this answer, don't put L under R. Since we have three Ls, we have to put it under S, T and Y. R __

S L __

T L __

Y L __ __

researchers: G H L P 3 Ls

Look through the rules. Rule 2 tells us that G can't go with L, so it has to go under R. R G

S L __

T L __

Y L __ __

researchers: G H L P 3 Ls

Go through the rules again. Rule 6 says that H has to go with G, but there is no room under R. This won't work, so it (answer B) is the answer. Remember, when you can't make a diagram on a "What must be true?" question work, the answer is right (because this means that nothing other than what the answer describes can be true). Notice how this seemingly difficult question – we didn't figure out anything from what they initially told us – ended up being pretty easy. Why? Because we are comfortable going through the rules and trying things out. We know how the question works – that is, how to determine if an answer is right or wrong. And we know how to re-use the diagrams we create. Question 8: A "What can't be true?" question – do it the second time through This question looks like a "What can be true?" question, except for the word "EXCEPT." The word "EXCEPT" means that the test has just described the wrong answers to you, so the right answers are the converse. Here we know that the wrong answers could be true, so the right answers can't be true. We'll skip this and do it after we've done all the "What can be true?" and If-questions.

Game Two

87

Question 9: A "What can't be true?" question – do it the second time through This looks like a "Which is a complete and accurate list?" question, except that it says "could be a complete and accurate list…", which makes it a "What can be true?" question. Oh, and the word "EXCEPT," which makes it a "What can't be true?" question. Skip it for now. Question 10: An If-question – do it now Draw a new diagram and write down what you are told. R __

S __ __

T __ __

Y __ __ __

researchers: G H L P 2 Gs

Like the previous If-question, you can't do much with this information. The rules tell you that G can't go with L or P, and has to go with H. But we don't know exactly where G goes (it is possible to figure this out, but we'll talk about how to do this later in the Advanced Techniques chapter). Notice that it is also a "What can be true?" question. Let's go through the answers. We'll try out what they describe, and if it works, the answer is right. Answer A Since it's a "What can be true?" question, we just try out what the answer says. Put P under R. R P

S __ __

T __ __

Y __ __ __

researchers: G H L P 2 Gs

Notice that the answer doesn't say "The paleontologist learns only Rundi," so we can have P someplace else too. Don't read more into the rules than they say; if a rule says something happens, we know that it happens, but it isn't the only thing that can happen. Other things can happen too (unless it says "only"). Let's go through the rules. Rule 2 is about the language L learns, but we don't know what that is, so we skip it. We know that G can't learn Rundi from rule 3, but since there is no more room under R, it wouldn't go there anyway. The rest of the rules are about the languages learned by G or not learned by H, but we don't know anything about G or H, so these rules don't tell us anything. We now have to fill our empty spaces. Start by putting G in someplace because it is first alphabetically, and because we have lots of rules about it. We have to put G in twice. Put it under S and T because they are our first two empty spaces. Put marks next to them because we decided to put G here. Going through the rules, we see that H has to go with G. Since it has to go with G, H doesn't get a mark. R P

S G* H

T G* H

Y __ __ __

researchers: G H L P 2 Gs

We now have three spots left under Y. We can't put G there because we only get two Gs. We have H, L, and P left, so put them there. Remember, we can have H without G (but not vice versa).

88

Game Two R P

S G H

T G H

Y L P H

researchers: G H L P 2 Gs

This works, doesn't it (look at the rules and make sure). So this is possible, and it (answer A) is our answer. Don't look at any other answers. Really, I mean it. Don't do it. Looks easy, but what if we had done it differently for some reason? What if we had put G under Y? It wouldn't have worked – we wouldn't be able to fill the third space because neither L nor P could go there. When you come across a diagram that doesn't work, change the last thing you marked with a dot. We didn't have to put G under Y, so try someplace else. Well, hey, you can put G under S and T; you'd try that out and it would work. Don't be afraid to play around with the diagrams a bit if they don't work, if there are things that you can change (i.e., if you have marked something). If not – if, for example, you were told that G had to go under S or T – then don't change things. Note that it is important to mark things only if you chose to put them where they are, not if the rules forced you. Question 11 – A "What must be true?" question – do it the third time through Question 12 – An If-question – do it now Redraw your diagram and plug in what you are told. R __

S __ __

T __ __

Y __ __ __

researchers: G H L P 2 Hs

Again, we can't put what we are told directly into the diagram because we don't know where the two Hs have to go. We could put the Hs into places where we think they could go, but when we first set up a diagram for an If-question we only put things where they have to go. Look at the rules before you look at the answers. All we know is that wherever we put a G, we have to put an H, so at least one of the Hs will go with a G (since we have to have at least one G). Also, we can't put a G anywhere we don't put an H (rule 7), so we have two Gs maximum. On to the answers. Work through them yourself and then compare what you did to what I say; remember, this is a "What must be true?" question, so we test the answers out by doing the opposite of what they say. Answer A We test this by putting the paleontologist under Rundi (since the negation of "does not learn R" is "does learn R") and seeing what happens. R P

S __ __

T __ __

Y __ __ __

researchers: G H L P 2 Hs

Go through the rules. All you learn is that we can't put a G under Rundi (rule 3), but since there is no more room under R anyway, this doesn't tell us much. Let's fill in the spaces and see if we can make this work. We could start by putting in G, because it's first, but since the rule for this question tells us we have to have two Hs, put them in first. The first open spaces are under S and T. Mark the Hs.

Game Two R P

89 S H* __

T H* __

Y __ __ __

researchers: G H L P 2 Hs

Put a G and an L under S and T, since G and L are our first two researchers. Going through the rules, we learn that G can't be under Y, because H doesn't learn Y. Now we have to fill the three spaces under Y. We can't put in any more Hs because we've used both of them. G can't go there. That leaves L and P . This can't work. When you have a diagram that doesn't work, change the last dotted thing you put in. You can either draw a new diagram (cross off the one that broke the rules) or erase parts of the one that didn't work. We put H under S and T, but we don't have to do that. Let's put H under S and Y instead. I don't mark the second H because there is nowhere else it could go. R P

S H* __

T __ __

Y H __ __

researchers: G H L P 2 Hs

Go through the rules. They mostly talk about P and L, and we don't know where those two are, but rule 7 tells us that G can't learn T because H doesn't. Let's put G under S, the first open spot. R P

S H* G*

T __ __ no G

Y H __ __

researchers: G H L P 2 Hs

Let's fill the spaces under T with L and P, the next two researchers on our list. R P

S H* G*

T L P no G

Y H __ __

researchers: G H L P 2 Hs

By this point we probably remember that G can't go with L or P, so we put L and P, but not G, under Y. If you didn't remember that, you could try putting G under Y and marking it, because you didn't have to put G there. It would end up not working, since you couldn't fill the last spot, so you'd get rid of G (the last thing you put in) and put in L and P. R P

S H* G*

T L P no G

Y H L P

researchers: G H L P 2 Hs

This works, so this answer is wrong. Let's see if this diagram helps us to eliminate any other answers. See if this diagram differs from what other answers describe. We can eliminate B, since this diagram shows us that the Geologist can learn S. We can't eliminate any of the other answers, however, since this diagram agrees with what each of them say. On to C.

90

Game Two

Answer C Let's try to put the linguist under Rundi. R L

S __ __

T __ __

Y __ __ __

researchers: G H L P 2 Hs

Now we have to put our two Hs in. I saw that putting them under S and T was problematic in answer A, so I'll put them under S and Y again. R L

S H* __

T __ __

Y H __ __

researchers: G H L P 2 Hs

This doesn't tell us anything other than that G can't go under T (rule 7); let's put the G in the first available spot: R L

S H* G*

T __ __

Y H __ __

researchers: G H L P 2 Hs

Now I just fill out the spaces with Ls and Ps like before. R L

S H* G*

T L P

Y H L P

researchers: G H L P 2 Hs

This works also, so cross off this answer. Unfortunately, this diagram doesn't help us eliminate D or E, so we have to test one of them out (but only one, since it will be either right or wrong; if it's right, we're done. If it's wrong, then we know the last one left is right.) Answer D Put the historian under R. R H

S __ __

T __ __

Y __ __ __

researchers: G H L P 2 Hs

Game Two

91

Now we have one more H left. Our previous work showed us that we have to put one of the Hs under Y. R H

S __ __

T __ __

Y H __ __

researchers: G H L P 2 Hs

Go through our rules. We have to put in a G (rule 1), and the G has to go with one of the Hs. So we put the G under Y. R H

S __ __

T __ __

Y H G __

researchers: G H L P 2 Hs

Going through our rules again we see that L and P can't go under Y. But that means that we can't fill in all three spaces under Y. This can't work. Can we make any changes to fix it? Nothing here is marked, so no. The first H is stuck under R, because that's what we need to do to test out the answer; we can put our second H under S or T instead of Y, but then we couldn't fill all the spaces under Y (we'd have to put G, L, and P there to do so, and that doesn't work). There is no way this diagram will work, so D is the answer. Question 8: A "What can't be true?" question – we're doing it now, our second time through The question asks for something that can't be true about the researcher who learns R (although it looks like a "What can be true?" question, the EXCEPT makes it a "What can't be true?" question). So we are focusing on the person who is under R. Use our previous diagrams wherever possible; if the answer shows up in a previous diagram, we can cross it off because we know it can be true. Answer A When they say "the researcher" they mean "the researcher who learns Rundi," because that's who the question is asking about. So, do we have a diagram where the same person learns R and T, but not S? (Notice that the answer doesn't talk about Y, and doesn't say "learns only Tigrinya," so we don't worry about Y at all.) 12A and 12C have this situation (P learns R and T but not S in 12A, and L does so in 12C). You don't have to spot both of these – in fact, once you've seen one diagram that matches, stop looking – but I'm putting them here for your reference. Cross this answer off. Answer B In this case we want the guy who learns R to not learn T or S, and again we don't care about Y. Look at our previous diagrams. 6D and 10A contain this situation. In 6D, L learns R and Y but not S or T, and in 10A, P learns R and Y but not S or T. Cross this off. Answer C Look for a diagram where the same person learns R and T but not Y (ignore S, since the question doesn't mention it, nor does it say "learns only Tigrinya…"). None of our diagrams have this – in each case, the person who learns R also learns Y (and they may or not may not learn T). What do we do when our previous diagrams don't help us? We skip the answer and look at the other answers. If we can cross them off using previous diagrams, great! If we can't, well, then we have to do a little work.

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Answer D Look for a diagram where the same person learns R, T, and Y (they can't learn S in this case because they can only learn three, but you don't need to worry about realizing that, because the question doesn't even mention S). 12A and 12D all work. Cross this one off. Answer E Look for an answer where the same person learns R and Y, but doesn't learn T. 7A and 10A work. On 7A, L learns R, S, and Y; S wasn't mentioned in the answer, so it doesn't matter if L learns it or not. This answer is wrong as well. So the answer has to be C. Question 9: A "What can't be true?" question – we're doing it now, our second time through Make sure you understand the question. It says “EXCEPT”, so the right answer will give a list of people who can’t possibly all learn both S and Y at the same time (notice the answer doesn't talk about learning other languages, nor say "only S and Y," so the people on the list can learn more than these). That's the difference between questions that say "is a complete and accurate list…" and "could be a complete and accurate list…" The first will give you a list of people that could do whatever in any possible diagram, while the second will be a list of people that could do whatever in the same diagram. Answer A Look at our previous diagrams first. Do we have one where the historian, and only the historian, learns both S and Y? Where other people learn one or the other, but no one else learns both? Sure; 6D, 10A, 12A, and 12D. In each of these, the historian learns S and Y, and no one else does (because in each case G learns S, but doesn't learn Y). Sure, the historian learns other languages as well, but that's not important, because the question doesn't ask for people who only learn S and Y. So we know that A gives a possible list, which means that it is wrong (the "EXCEPT" in the question tells us we are looking for list that can't be complete and accurate). In going through your previous diagrams you might also have noticed that in question 7A, L and P learn S and Y. This allows us to eliminate answer E. We now have to look at answers B, C, and D. Answer B Put just the paleontologist under S and Y. R __

S P __

T __ __

Y P __ __

researchers: G H L P

The answer only lists P, so this means that whoever else goes under S can't go under Y, and vice versa (otherwise, if they went under both, the answer would have to include them, since it is a complete list). Go through our rules. Rule 3 says that G can't go with P. Write that in our diagram. R __

S P __ no G

T __ __

Y P __ __ no G

researchers: G H L P

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We know that whoever we put under S can't also go under Y. So let's see who can learn S. Not G, so try H; this would mean that H can't go under Y. Mark H with a dot or a star, because we don't know that H has to go here. R __

S P H*

T __ __

no G

Y P __ __ no G no H

researchers: G H L P

But who now can go under Y? Only L, and that doesn't fill enough spots. So H can't go under S. Try L instead; we put L under S, but then it can't go under Y (otherwise it would have to be in the answer, since it would be under both S and Y), so we put "no L" under Y to remind ourselves of this. R __

S P L no G

T __ __

Y P __ __ no G no L

researchers: G H L P

Same problem; we can't put enough people under Y. So there is no way to make this work – we've tried everyone under S, and no matter who we put there, we can't find enough people to put under Y. We can't make B work, so B can't be a complete list of the people who learn both S and Y at the same time. B is the answer. Question 11 – A "What must be true?" question – we're doing it now, our third time through Test the answers out by looking for a previous diagram showing that the negation of the answer can be true. Answer A The opposite of this is that H learns as many as P or more. You may not remember that "as many" (or "exactly") is the negation of "fewer," so I'm reminding you (see "If… then…" Rules and Negations). Even if you don't remember, you can still get this question right just looking for "more." Look for a diagram where H learns as many or more languages than P. In 6D, 7A, 10A, and 11A, H learns more than P. In 12C, H learns as many as P. Again, you only need to see one of these diagrams to eliminate the answer, but I'm giving you all of them just so you can see what you are looking for. Cross off this answer. Answer B This means that G learns fewer than H. So we want to look for a situation where G learns as many or more than H. Notice how useful it is to understand the answer (putting it in our own words) before figuring out what we are supposed to be looking for in the previous diagrams. We don't see any diagrams that show us what we are looking for; H always seems to learn more than G. Does this mean that this has to happen? No, just that it has always happened so far. Skip this answer.

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Answer C This means that G learns fewer than L. Look for a diagram where G learns as many or more than L. In 10A, we have two Gs, but only one L. Cross off this answer. Answer D This means that P learns fewer than L. Look for a diagram where P learns as many or more than L. In 10A and 12A, P learns more than L. Cross off this answer. Answer E This means that P learns fewer than H. Look for an answer where P learns as many or more than H. In 7A and 12C, they learn the same number of languages. In 12A, P learns three while H only learns two. Cross off this answer. The correct answer has to be B.

Summary What has this game demonstrated to us? Well, hopefully it's reinforced how to construct diagrams. You can use a different diagram – for example, try putting the names of the researchers along the top of the diagram, and leave blanks underneath them to put in the names of the languages. It'll work this way too, but it's a bit easier to do it the way we did. Also, I hope it helped you understand how to write the rules of a game; it was very easy for us to use our rules because we wrote them out so clearly. Here are some other key points this game illustrates about rules: You can use the rules to help you figure out how to diagram a game. Split "If… then…" rules into two rules whenever possible. On If-questions: Do them the first time through. Make a new diagram for the question, put in what you are told, then go through the rules and figure out what has to be true (put only these in the diagram). Use this diagram on all the answers; use diagrams from previous answers on later answers of the same question. Other points: don't read more into a rule, question, or answer than it says; if it says "So and so learns X," or asks you who learned X, don't assume that person has to learn only X.

What Do I Do Next? Take a break. Then read through your notes on this game and think about them until you feel like you understand how the various steps work. Then go back and do this game on your own. You can use your general notes to help you remember how to do the various question types. When you are done, go on to Game Three.

Answer Key 6. 7. 8. 9. 10. 11. 12.

D B C B A B D

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Game Three Game omitted from electronic version of book.

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Game Three (From LSAT 33)

Step 1: Read the Setup/Draw a Diagram Every game consists of two or more types of things which you have to match together, right? So what are the two types of things in this game? The setup mentions birdwatchers, but they don't actually do anything; they just explore the forest. The setup also mentions some birds. It may be unclear to you what you are matching the birds to – maybe bird-watchers? Where can we look for more insight into the game if the setup doesn't make the game clear? If we are uncertain how to diagram a game, look at the rules. Each rule talks about whether or not a certain bird (or birds) are in the forest. So that should make it clear that we have two types of things: birds and a forest, and we are matching birds to the forest. We are trying to figure out which of the six birds will be in the forest. Now here's the next question. Which of these things is more definite? We don't know how many birds are going to be in the forest (if we did, that would make the forest more definite). In fact, we know next to nothing about the forest, except that the birds are going to be in it. So we will base our diagram around the birds. Write down their names: G H J M S W Our other type of thing is the forest. Some of these birds will be in the forest, and some will not. That means that the game will divide up into two groups: the in-forest group and the not-in-forest group. We always label our groups, so label those: G H J M S W

in-forest: not-in-forest:

So we've written down everything we've been told. We are done. This is a common sort of thing to see in a game: picking things off a list to put in one or more groups. If some of the things won't be in the group (or any group, if there is more than one group), make a group for those excluded (here, the not-in-forest group). This allows you to keep track of who isn't in a group; often, although not here, only a limited number of people can not be in groups, so once you've filled the "not" group, everyone else has to go in a group (see Game Five).

Step 2: Read the Rules I'm going to warn you in advance that all of these rules are "If… then…" rules. So let's briefly review what "If… then…" rules mean and how we write them down (see "If… then…" Rules and Negations). "If… then…" rules give you two situations; one is in the "if" part and one is in the "then" part. Whenever you know that the "if" part is true, you know also that the "then" part has to be true. However, knowing that the "then" part is true doesn't mean that the "if" part is true. For example, imagine I say that "If X is true, then Y is true." Whenever I know that X is true, I know that Y has to be true. But if I know Y is true, X may or may not be true.

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The fact that every time the "if" part is true the "then" part is true tells us something else. It tells us that we can't have the "if" without the "then," because the "if" always makes the "then" true. So, if we don't have the "then" part, we can't have the "if." In our "If X is true, then Y is true," example, we know that "If Y is not true, then X can't be true." We know this because X being true would make Y have to be true. This is called the contrapositive. We always make the contrapositive when we have "If… then…" rules, and we make the contrapositive by 1) switching the "if" and the "then" (the "if" part becomes a "then" and vice versa); and 2) making both parts negative (something already negative becomes positive). Finally, some "If… then…" rules are more complex than they need to be. When we get these rules we are going to make them simpler by breaking them into multiple rules. First rule: "If harriers are in the forest, then grosbeaks are not." Our first rule is an "If… then…" rule. It is easy to write down – we just write it as it is, a little abbreviated: If H is in-forest, then G is not-in-forest. This means that whenever the H is in the in-forest group, we have to have the G in the notin-forest group. My way of writing things is a suggestion; you can abbreviate more than I have here (the "is" can be taken out in each clause without a problem) – write whatever makes sense for you, just make it easy to understand. In reality, I abbreviate even more than this, but I don't in this book to make it easier for you to read the rules. See the end of this section for the rules as I normally write them. We should also form the contrapositive; this tells us that whenever the G is not in the notin-forest group, the H can't be in the in-forest group. If G is not not-in-forest, then H is not-in-forest. This can be simplified. We only have two groups; if something is not in one group, it has to be in the other group; if something is not in the in-forest group, then it is in the not-inforest group, and vice versa. So, instead of writing "G is not in not-in-forest," we can write that "G is in-forest." Our contrapositive is: If G is in-forest, then H is not-in-forest. Whenever something has to be in one of two groups, instead of saying it is not in one group, say it is in the other group. Next rule: "If jays, martins, or both are in the forest, then so are harriers." This is a more complicated "If… then…" rule, because it has three things (jays, martins, both) in the "if" part. We want to break it down into simpler rules. So ask yourself, what if jays were in the forest? Well, harriers would have to be as well. What if martins were in the forest? Harriers would have to be as well. So we can break this into two rules, one about jays and one about martins, because the rule tells us something has to happen when we have just jays or just martins.

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If J is in-forest, then H is in-forest. If M is in-forest, then H is in-forest. Make the contrapositive of each. Switch the "if" and "then," so H goes in the "if" part of each and J (or M) goes into the "then" parts. Make both sides negative, which just means put each person into the other group, so we get If H is not-in-forest, then J is not-in-forest. If H is not-in-forest, then M is not-in-forest. We don't have to worry about the "or both" part – if both J and M are in the forest, then J is in the forest which means H will have to be in the forest. Next rule: "If wrens are in the forest, then so are grosbeaks." Another "If… then…" rule. Write it down and make the contrapositive. If W is in-forest, then G is in-forest. If G is not-in-forest, then W is not-in-forest. Last rule: "If jays are not in the forest, then shrikes are." If J is not-in-forest, then S is in-forest. If S is not-in-forest, then J is in-forest. One quick point. People are often very quick to try to combine "If… then…" rules and their contrapositives in order to make deductions. They generally do this incorrectly. For example, people might think that the last rule, together with its contrapositive, tells us that J and S can't both be in the forest. After all, if J is out, S is in, and vice versa. This is a mistake, though, because the rule only tells us about what happens if J or S are out of the forest. Remember, the "then" part of the rule being true tells us nothing about the "if" part. So if S is in the forest (the "then" part), J could also be in the forest. Take the rules as they come, and take them literally; don't try to think too much about them. So here is our original diagram and the complete list of rules. I'm spacing like I do to make them easier for you to read. G H J M S W 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

If If If If If If If If If If

H is in-forest, G is in-forest, J is in-forest, M is in-forest, H is not-in-forest, H is not-in-forest, W is in-forest, G is not-in-forest, J is not-in-forest, S is not-in-forest,

in-forest: not-in-forest: then then then then then then then then then then

G is not-in-forest. H is not-in-forest. H is in-forest. H is in-forest. J is not-in-forest. M is not-in-forest. G is in-forest. W is not-in-forest. S is in-forest. J is in-forest.

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Here is how I write these rules for myself, more abbreviated (I use arrows to mean "then;" it's just something I learned doing philosophy): H -> no G G -> no H J -> H M -> H no H -> no J no H -> no M W -> G no G -> no W no J -> S no S -> J I'm showing you this just to demonstrate that you don't have to write as much as I do when I write the rules, although there is nothing wrong with it. You only write the rules once, so spending a little extra time to write them isn't so bad. If you want to abbreviate, go ahead; just make sure that you use an abbreviating scheme that you like and use easily. Don't bother making one up; it's not worth the effort. Mine works well for me because I had it drilled into my head from years of doing formal logic for philosophy classes. Many of the rules we have can be combined to make deductions. However, even if you knew how to do this, there are so many rules and so many ways to combine them that trying to put them together would take you forever. In a game with this many rules, deductions definitely aren't worth it.

Step 3: Answer the Questions We are going to walk through the questions one by one. If a question is one that we should do, we'll do it; otherwise we'll skip it and come back to it later. Question 6: A "What can be true?" question – do it now This looks like a "Which is a complete and accurate list?" question, but the fact that it says "Which one … could be a complete and accurate list…" tells otherwise. The question is asking for a list of all of the birds who could be not-in-forest at one time. The right answer will be a list that could be true, that follows all the rules, so this is a "What can be true?" question. Let's do it now. Each answer will tell us a complete list of birds in the not-in-forest group. That means that no other birds (no birds not on the list) are in the not-in-forest group. What does that tell you about the other birds? It means that they have to be in the in-forest group. Remember, when we have only two groups, if you are not in one group you are in the other. It is crucial to understand what the answers are supposed to mean before you evaluate them. Answer A Put J and S in the not-in-forest group, and every other bird in the in-forest group. Notice that I cross birds off the list as I put them in a group. G H J M S W

in-forest: G H M W not-in-forest: J S

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Now we go through the rules. When looking at "If… then…" rules, we only apply a rule when the "if" part is the case. Rule 1, for example, says "If H is in-forest…" H is in the forest, so we look at this rule. It goes on to say "…then G is not-in-forest." This contradicts what the answer tells us (it tells us that only J and S are not-in-forest), so this answer can't be right. Cross off this answer, because this can't be a complete list of birds not in the forest. Cross off the diagram, because it breaks a rule, and we don't want to use it accidentally later on. Before we go on, look at rule 3. We wouldn't do this on the LSAT, but I want to do it now to illustrate what I mean by "When looking at 'If… then…' rules, we only look at the rule if the 'if' part is the case." Rule 3 says "If J is in-forest…" In this answer J is not in the forest, so we ignore this rule. We don't assume the opposite of the rule (that H can't be in the forest), we just ignore the rule entirely. This is because "if" rules only tell us what has to be the case if the "if" part is true. So if the "if" part is not true, the rule has nothing to tell us. Answer B Again, put everyone in the answer – H and G – into the not-in-forest group, and everyone else into the in-forest group. G H J M S W

in-forest: J M S W not-in-forest: H G

Now let's go through the rules. Rule 1 says "If H is in-forest…", but H is not in the forest, so ignore this rule. Rule 2 says "If G is in-forest…", but G isn't in the forest, so ignore this rule. Rule 3 says "If J is inforest…" and J is in the forest, so we look at this one. H has to be in the forest as well, but it isn't. Thus, this answer breaks a rule, and we cross it off because it can't be an accurate list of birds not in the forest. Cross off the test diagram as well, because it is a rulebreaking diagram. Answer C Make your test diagram, putting G, J, and M into the not-in-forest group. G H J M S W

in-forest: H S W not-in-forest: G J M

Go through the rules. Rule 1 says "If H is in-forest…" and H is, so we look at this one. It tells us that G can't be in the forest. Well, G isn't in the forest, so that rule is being followed. On we go. Rule 2 says "If G is in-forest…", but G isn't, so we ignore this rule. Rule 3 says "If J is in-forest…", but J is not in the forest, so we ignore this. Rule 4 says "If M is in-forest…", but M isn't, so ignore this rule. Rule 5 says "If H is not-in-forest…", but H is in the forest, so we ignore this. Rule 6 says the same, so we ignore that one too. Rule 7 says "If W is in-forest…" W is in the forest, so look at this one. If W is in the forest, G has to be. But G isn't in the forest, so this rule is broken. Cross off this answer and cross off this diagram. Answer D Put G, M, S, and W in the not-in-forest group. G H J M S W

in-forest: H J not-in-forest: G M S W

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Rule 1 says "If H is in-forest…" H is in the forest, so we look at the "then" part. It says that G can't be in the forest, and, indeed, G isn't. So far so good. Rule 2 says "If G is inforest…", which isn't the case, so we ignore it. Rule 3 says "If J is in-forest…" and J is inforest, so we look at the "then" part. It says that H has to be in the forest, and H is. Another rule followed. Rule 4 says "If M is in-forest…", but M isn't, so ignore it. Rules 5 and 6 talk about H not being in-forest, so we ignore them. Rule 7 says "If W is in-forest…", but W isn't. Rule 8 says "If G is not-in-forest…", which is true, so look at the "then" part. W can't be in the forest, and W isn't, so this rule is followed. Rule 9 says "If J is not-inforest…", but J is, so we ignore this. Finally, rule 10 says "If S is not-in-forest…" S is not in the forest, so we have to have J in the forest, and it is. This diagram follows every rule. This (answer D) is the right answer. A couple of points about this question. First, you see how necessary it is to realize that everyone not listed in the answer is in the other group. If you hadn't listed the "in-forest" birds, you couldn't have gotten this right. Second, you should see that you need to develop the skill of skimming down lists of "If… then…" rules, looking only at the ones that are relevant to the situation you are working on. If you can't do this, you will be very slow. Third, you should see that it is important to realize that this is not a "Which is a complete and accurate list…" question, but really a "What can be true?" question. All of these are skills you can practice or ideas you can memorize, so start doing so. Question 7: An If-question – do it now We do If-questions first, along with "What can be true?" questions. The first step in every If-question is to redraw our original diagram. G H J M S W

in-forest: not-in-forest:

The second step is to write down the situation described in the question. In this case, we put M and H in-forest and cross them off our list. G H J M S W

in-forest: M H not-in-forest:

The third step is to go through our list of rules and see what has to be true. Remember, every time you figure out something new that has to be true, go back through the list of rules one more time. Also, when looking at "If… then…" rules, only pay attention if the "if" part matches what you have written down in your diagram. Rule 1 says "If H is in the forest…" Well, H is in the forest, so let's look at the "then" part. G can't be in the forest, so we put G in the not-in-forest group and cross G off our list. G H J M S W

in-forest: M H not-in-forest: G

Since we've learned something new, we have to go back through the rules. Not too hard when we've only looked at rule 1. Rule 2 says "If G is in-forest…", but we just learned that G isn't in-forest, so ignore this rule. Rule 3 says "If J is in-forest…", but we don't know if J is the forest or not. Ignore this rule. Ignore a rule if you don't know whether or not the "if" part is true. Rule 4 says "If M is in-forest…" and we do know that M is in forest. So we also know that the "then" part has to be true. This tells us that H is in-forest, which we already

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knew. Since we haven't learned anything new, we don't change our diagram, and we don't start going back through the rules. OK, on we go. Rules 5 and 6 say "If H is not-in-forest…", so we skip these. Rule 7 says "If W is in-forest…", but we don't know one way or the other, so we skip this. Rule 8 says "If G is not-in-forest…" Bingo, we know that G isn't in forest, so we look at the "then" here. W can't be in the forest. Add this to your diagram. G H J M S W

in-forest: M H not-in-forest: G W

Go back through the rules; nothing changes up to rule 8 (reread the previous two paragraphs to simulate going back through the rules if you'd like). So let's continue from there. Rule 9 says "If J is not in-forest…", but we don't know about J one way or the other. And rule 10 says "If S is not in-forest…", but we don't know about S either, so we skip this one too. We know the status of G, H, M, and W; J and S may or may not be in the forest. Let's look at the answers. This is a "What must be true?" question, so we can test the answers out by doing something different from what they say. Do you see how putting these rules together works? Not so hard, as long as you are methodical, and are comfortable with it. You need to practice the skill until you just automatically skim through lists of "if"s, ignoring those that aren't relevant to your situation. Once you can do this, going back through the list every time you learn something new doesn't take much time. Get used to this and you'll be able to figure out all sorts of exciting stuff on games like this one (and they are pretty common – about one in five games has three or more "If… then…" rules). Answer A Before we test this answer out, we have to understand what it means. What do they mean by "only other birds"? They mean "other than what we've just told you about." Specifically, other than M and H. This would be false if another bird was in the forest, or if S wasn't (see "If… then…" Rules and Negations). We test this answer out by doing something other than what it describes. In this case, let's not put shrikes in the forest, and put someone else in. Alternately, we could have both S and someone else in, or neither S nor anyone else. Who is another bird that we can put in? J's the only other one unassigned, so let's put J in the forest (and not S). G H J M S W

in-forest: M H J not-in-forest: G W S

Go through your rules and see if this works. The only rule that applies here that didn't apply before is rule 3. It says "If J is in-forest, then H is in-forest." That is followed here, so this is possible (we know that everything we already had follows the rules). We know that this answer doesn't have to be true, because something different than it can be true. Cross the answer off. Let's use this diagram and try to eliminate some other answers. We can eliminate an answer if the situation it describes is different from what this diagram shows. Answer B wants just J, M, and H to be in the forest, which is what we have here, so we can't eliminate it. It might have to be true. Answer C says that J and S should not be in the forest. Well, this diagram has J in the forest, so C doesn't have to be true. Cross it off. D says that there have to be two or more birds in-forest besides M and H. We know that doesn't have to be true because this diagram only has one other bird in-forest. We can cross off D. E

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says that there are no more than two birds besides M and H in-forest. That agrees with this diagram – only one other bird is in-forest, which is not more than two. We can't cross off E, because it might have to be true. So we have to test out either B or E. Answer B Again, "other" here means "other than what we've told you" (M and H, specifically). The answer says that J is the only bird other than M and H in the forest, so everyone else is notin-forest. We can't use the diagram for A because it has J in-forest, which is just what the answer says. So let's draw a new diagram, and try not putting J in the forest, while putting someone else in (who'd have to be S, since no one else is left). Again, we also could have tried putting both S and J in, or leaving both out. G H J M S W

in-forest: M H S not-in-forest: G W J

Look through our rules. The only one that applies here that didn't apply initially is 9, which says "If J is not-in-forest…", so I'm not going to rewrite the process of checking each of these (but you should go through it). Rule 9 is followed: S is in-forest. So this diagram follows all the rules. Cross off this answer. This leaves only E, so E is the answer. Question 8: An If-question – do it now Redraw your diagram and plug in what you are told. G H J M S W

in-forest: not-in-forest: J

Now we go through the rules. I'll remind you again, when you look at "If… then…" rules, only pay attention if the "if" part matches what you know to be true. Rules 1 and 2 talk about H and G, who we know nothing about so far, so we ignore them. Rule 3 says "If J is in-forest…", but that isn't the case, so we ignore it. Rules 4 through 8 are about birds other than J, so we ignore them too (yes, I know that rule 5 has J in the "then" part, but we aren't looking at the "then" parts, just at the "if"s). Rule 9 says "If J is not in the forest…", which is the case, so we know that the "then" part of this rule has to be true. S has to be in the forest. G H J M S W

in-forest: S not-in-forest: J

Since we've learned something new, go back through the rules. Go ahead, I'll wait. Did you see any rules saying "If S is in-forest…"? No? Then no rules are relevant here, so we end up ignoring them all. But you have to look at them, otherwise you might miss something. This is a "must be false" question, so the answer is something that can't be true. Any answer that is possible can be crossed off. Answer A Test this out by putting M in-forest. G H J M S W

in-forest: S M not-in-forest: J

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Go through the rules. Rule 4 is relevant. It tells us that H has to be in the forest. G H J M S W

in-forest: S M H not-in-forest: J

Since we just added something new, go back through the rules. Rule 1 is relevant; we can't have G in the forest. G H J M S W

in-forest: S M H not-in-forest: J G Keep going. Skip rules 2 and 3, because their "if" parts aren't the case here; we've already looked at 4; rules 5 and 6 aren't the case (because we have H in-forest); we don't know about W, so we skip 7; ahhh, rule 8. G is not-in-forest, so we can't have W in-forest. G H J M S W

in-forest: S M H not-in-forest: J G W

One more time through the rules. We've looked at everything relevant already except 9, and this diagram agrees with 9. This is a possible diagram. Cross off answer A. Now we have a diagram we can use on the other answers. The diagram tells us that H can be in-forest, so cross B off. Skip C because we can't use our previous diagram – it has both M and H in-forest, so it doesn't show us that M and H can be not-in-forest. When we get to D we are done; it can't be true. We know it can't be true because before we even looked at answer A, we learned that S has to be in the forest. So it isn't possible for neither M nor S to be in the forest. "Neither" means that both M and S are not-in-forest, but that can't happen if S has to be in-forest. So D is the answer. Question 9: A "What is the maximum number of … ?" question – do much later These questions are hard and time-consuming; we'll do it later, if at all (I'll explain a quick way to make a good guess at these questions later on). Question 10: A "What can't be true?" question – do it the second time through Question 11: An If-question – do it now Again, redraw your diagram and plug in what you are told. G H J M S W

in-forest: G not-in-forest:

Let's go through our rules and see if anything has to be true before we look at the answers. I'll say it for the millionth time (because it's so important): skip over "If… then…" rules when you don't know that the "if" part is true (i.e., when it contradicts what you have in your diagram, or talks about something you don't know about). Ignore rule 1 because we know nothing about H. Look at rule 2, because G is in-forest. We know that H can't be in the forest, so add this to our diagram and start over with the rules. G H J M S W

in-forest: G not-in-forest: H

Ignore 1 because H is not in the forest; ignore 2 because we just looked at it. Ignore 3 and 4 because we know nothing about J and M yet. Look at rules 5 and 6 because both start with "If H is not-in-forest…" We learn that J and M are not-in-forest.

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Game Three G H J M S W

in-forest: G not-in-forest: H J M

Start over with the rules. Rules 1 through 6 don't give us anything useful; they are either things we ignore, or thing we've already looked at. We ignore rule 7 because we don't know about W; we ignore rule 8 because G is not not-in-forest. Look at rule 9, because J is not-in-forest, so we know that S has to be in-forest. G H J M S W

in-forest: G S not-in-forest: H J M

Back through the rules one more time. Nothing new here, so we are done. The only bird we don't know about is W. I hear you saying to me, "Brian, why do you always make us go back through the rules? We've just looked at them, so you are wasting our time." Not so! Take a look at 8A. We go back to rule 1 after looking at rule 4, and doing so allows us to figure out many other things. Now, I'll admit, this doesn't happen every single time. But it happens often enough to be important. It doesn't take us very long to look back through the rules, does it? OK, well, it may seem like it takes a long time to you now, but that's just because you need to practice. Get good at it (and it's not that hard) and you'll find that it doesn't take too long. But if you don't do it, you'll miss things like question 8. This is a "What must be true?" question, so we are going to test the answers by doing something different than what they describe. Answer A Well, we don't even have to test this out. The work we've done so far tells us that S must be in-forest, because it's in our diagram, so there is no way this could not be true. We're done, this is the answer. Question 12: An If-question – do it now This doesn't look like an If-question at first glance – it has the word "suppose" at the very beginning. But the first sentence is just telling you "Imagine we had a new rule," which is just what If-questions do. This new rule just happens to be an "If… then…" rule. "Suppose" in a question makes it an If-question; see Common Equivalents for Each Question Type in the chapter The Fundamentals. Draw your diagram, and then write down our new rule (and its contrapositive, since it is an "If… then…" rule). G H J M S W

in-forest: not-in-forest:

If S in-forest, then H not-in-forest. If H in-forest, then S not-in-forest. This is a "What can be true?" question, so we'll just work through the answers until we find one that can be true.

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Answer A Let's test this out by putting J and S in-forest. G H J M S W

in-forest: J S not-in-forest:

Go through the rules. Look at the new rule (the one given by the question when it says "Suppose…") first. S is in the forest, so H can't be. G H J M S W

in-forest: J S not-in-forest: H

Now go through the regular rules. Ignore 1, because its "if" part isn't the case: H isn't in the forest. Ignore 2 because we don't know about G. Rule 3 says "If J is in-forest…" and J is in-forest, so we know that H has to be in-forest. But wait, H can't be in the forest (because we have it not-in-forest and we don't question our previous work). So this breaks a rule. Cross out the answer and cross out the diagram. Answer B Put W and S in-forest. G H J M S W

in-forest: S W not-in-forest:

Go through the new rules, the ones from this question, first. If S is in the forest, H is not. G H J M S W

in-forest: S W not-in-forest: H

Now go through the regular rules. Ignore 1, because H isn't in the forest. Ignore 2, 3 and 4 because we don't know about G or J or M. Look at 5 and 6, since we know that H can't be in the forest. This means that J and M can't be in the forest. G H J M S W

in-forest: S W not-in-forest: H J M

Go back through the rules. Nothing new until rule 7; if W is in-forest, G has to be. G H J M S W

in-forest: S W G not-in-forest: H J M

Back through the rules again. Rule 2 tells us that if G is in-forest, H is not-in-forest. This agrees with what we have. No other rules are relevant here. So this diagram works; it (answer B) is the correct answer. Question 9: A "What is the maximum number of…?" question – do much later Still skipping this one; we don't do "What is the maximum number of…?" questions until our fifth time through.

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Question 10: A "What can't be true?" question – we're doing it now, our second time through The right answer will be a pair of birds who can't both be in the forest; the wrong answers will be pairs who can both be in the forest. If they say "What pair (or what group, or what list) … can't have such and such a quality," they mean "at the same time." The same is true if they say "What pair/group/list can have such and such a quality;" they are looking for a pair/group/list that can all have the quality at the same time. We can (and should) use our previous diagrams on this question. We are looking for birds who can't both be in-forest, so eliminate any answer containing a pair of birds who show up together in-forest in a previous diagram. Answer A We don't have J and W both in-forest in any previous diagram, so skip it. Answer B J and S aren't both in-forest in any previous diagram; but, the diagram for 7 looks pretty close – we have both J and S as possibilities. Still, let's skip it for now. Answer C 12B has S and W in-forest. Answer D The diagram for 7A has J and M in-forest. Answer E Both 7B and 8A have S and M in-forest. At this point we have A and B left. Now, if we were pressed for time I'd just eliminate B; the diagram we made for 7 (before we tried out the answers) makes it look like we can have both J and S. But, since we have time, let's test out an answer; we'll test out A because I like to go in order. Put J and W in-forest and see what happens. G H J M S W

in-forest: J W not-in-forest:

Go through the rules. Rule 3 tells you that you have to have H in-forest (because we have J in-forest). G H J M S W

in-forest: J W H not-in-forest:

Go back through the rules again. Rule 1 tells us that we can't have G in-forest, because H is in-forest. G H J M S W

in-forest: J W H not-in-forest: G

Keep going through the rules. Rule 7 tells us that if we have W in-forest, we have to have G in-forest. But G is not-in-forest; this diagram breaks a rule, so A is the answer.

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Question 9: A "What is the maximum number of…?" question – our last question, so do it now A great question to skip if we are running out of time. There's a decent way, if you are running out of time, to make an educated guess on a "What is the maximum number of…?" question: look at your previous diagrams and find the maximum number of whatever the question talks about. Pick that as your answer (since you know that it is possible). Do the opposite for "What is the minimum number of…?" questions – find the diagram with the minimum number of whatever, and pick that. Here, the most we have in-forest at once are three birds (diagram 7A, for example). So we'd pick B. We'd be wrong, but that's not what guessing is for. Guessing is not supposed to get you the right answer reliably; otherwise we'd guess all the time. Guessing is supposed to get any answer fast, so that you can move on to questions you'd rather work on. If it happens to get you the right answer, well, that's just a bonus. But how do we do this question if we are not going to guess? We look at the biggest answer (the smallest one if this asked for the minimum) and try it out. Here we try to have six birds in-forest. Since there are only six birds, that means picking all of them. Answer E G H J M S W

in-forest: G H J M S W not-in-forest:

Now go through the rules. You immediately see that we can't have this – we can't have both H and G. Cross off the diagram, and cross off E. Go to the next biggest answer. Answer D We are going to have to get rid of one of the birds. Well, we know that we have to get rid of G or H, because we can't have both of them. We want to get rid of a bird who causes problems – one where having it in-forest forces many birds to go not-in-forest – and one where putting it not-in-forest doesn't make any other birds go not-in-forest. Go through the rules. If we put G not-in-forest, W has to go not-in-forest. But, if we put H not-inforest, J and M have to go not-in-forest. In either case, we are going to have to put more than one bird not-in-forest, and we have to move either G or H. So we can never have five birds in-forest. Answer C Let's move G, since putting G not-in-forest only makes us put W not-in-forest, while putting H not-in-forest forces J and M to be not-in-forest. Let's see if this works. G H J M S W

in-forest: H J M S not-in-forest: G W

Go through the rules. Rule 1 is followed; rule 2 is irrelevant, since G is not-in-forest. 3 is followed, 4 is followed, and we ignore 5 and 6. Ignore 7, and 8 is followed. Ignore 9 and 10. So all the rules are followed; we can have four birds in-forest. Thus, C is the answer. Whew, that's a lot of work. See why we skip these questions? Here's the way we do them, in summary: Try the biggest answer. If that doesn't work, move one down and see if you can make that work somehow. If not, move one more down, and so on. Try to make changes that cause the least trouble; that is, ones that force you to make the fewest changes. You want to change things that don't impact the rules much.

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Summary We have learned to make "not" groups when the game might leave some people out of the main group. We have learned the importance of understanding "If… then…" rules and their contrapositives. We would not have been able to do as well on these questions as we did without having the contrapositives of each rule written down. We have learned how to scan through lists of "If… then…" rules by ignoring those that aren't currently relevant. Make sure you understand these skills; from the year 2000 to the present, almost one in five games has had three or more "If… then…" rules (with one game having eight of them!). This means you are very likely to get a game with a list of these rules on your LSAT.

What Do I Do Next? Take some time before you go to look back at the questions on this game, and especially to practice skimming through lists of "If… then…" rules. At this point you have been exposed to all the fundamental concepts you need to do well on logic games. Now you need to practice some logic games. I provide a list of recommended games below. Work through these games, applying the studying skills I talk about in the Studying Guide. Once you feel comfortable doing these games, continue to Intermediate Techniques. I've also put a brief summary of the most important logic games skills in the next chapter, The Five Most Important Skills. Take a look at this before you start practicing games. Timewise, you want to move on to the intermediate techniques at least three weeks (and hopefully more) before the LSAT. This gives you a week to work through Intermediate Techniques and the ensuing five games, and to practice the techniques, and then gives you two weeks to work on timing (I'll talk more about this later).

Answer Key 6. 7. 8. 9. 10. 11. 12.

D E D C A A B

Recommended Games I have grouped the recommended games together by similarity to each other; while I believe, as I teach, that there is only one type of logic game, and that all games can be diagrammed by applying the same technique, some games are more alike than others. Try to divide your work somewhat evenly between the different groups listed below; this will ensure that you get practice with a variety of different types of rules and setups. "Game #" refers to the order in which the games are given in the specific LSAT; for example, game 3 is the third game in that LSAT. Again, you don't need to do all of these games before continuing on in this book. Do enough so that you become comfortable with the fundamental techniques – get to the point where you remember what to do when, and understand how to apply the techniques in most situations. I have excluded from this list games that you are better off doing after covering the next few chapters.

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If you have access to LSATs which are dated but not numbered, there is a chart (LSAT Number to Date Conversion Chart) which gives the date each number corresponds to at the end of the Introduction chapter. Group One LSAT 19 23 24 26 27 29 30 32 32 33 34 34 40 41 42 42 43 43 45 46 47 48 48

Game # 1 1 2 2 1 3 4 1 3 1 1 3 1 1 2 3 1 2 1 1 1 2 4

Group Two LSAT 19 19 24 26 27 29 29 34 35 37 42 43 45 46 47 47 48

Game # 3 4 1 3 3 1 2 4 2 3 4 4 4 2 2 3 3

LSAT 20 20 23 25 32 33 35 36 40 42 45 48

Group Three Game # 2 3 2 1 2 3 1 1 4 1 3 1

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The Five Most Important Skills

The Five Most Important Skills (In order of importance) You've read The Fundamentals. You've worked through three games with me. You are probably starting to get a sense of how to do games the right way, and you are about to embark on the great adventure of practicing games on your own. At this point I feel it is crucial to make sure that you know what the most important skills for you to practice are, and also to make sure you understand them. These skills are good candidates for putting on your short list when you study. If you don't know what a short list is, you need to reread Studying for the LSAT Logic Games Section. These are only the top five skills, and, of course, there are many more. One useful resource for you is the Glossary at the end of this book; there I define all the terminology you need to know, and give brief summaries of what to do when you see each term on the test. It may be helpful for you to read through that and make sure you understand each definition given. Here I will only touch on each skill, since I've gone through them in much more detail in previous chapters.

1. Know how to read LSAT sentences. If you can't understand what the LSAT is telling you, you won't do well on it. Reading on logic games is always an active process. You never just look at the words in front of you; instead, you are always looking for something, reading with a goal in mind. When reading the setup, you are trying to figure out what things you are matching together. When reading rules, you are trying to figure out what they mean. When reading a question, you are trying to figure out what type of question it is and how to test the answers. Make sure you read every word on the page, which means you need to read slowly and carefully; the easiest way to miss questions is to miss one crucial word in a rule or question. Always ask yourself what each sentence means. If you don't understand something, try to make it clearer using an example. For example, if a rule doesn't make sense, try applying it to a specific situation and see what happens; people think better about what is concrete, rather than abstract. You need to understand common LSAT vocabulary, such as "always," "only," "exactly," "neither," "except." If you don't know what these words mean yet (or how to negate them), make some flash cards and go through them every day. A more comprehensive list of these words is in the Glossary.

2. Know how to recognize the question types. This is a pretty straightforward skill, but it's absolutely crucial. If you aren't 100% on this, there is a list of common ways each question type is worded in The Fundamentals. If you don't have these memorized yet, start using flash cards (I explain a good way to make flash cards at the very end of The Fundamentals).

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3. Know how to determine if an answer to a question type is right or wrong. This includes knowing when and how to use previous diagrams, and how to draw test diagrams for each type of question. The Glossary has a brief summary for each question type, and The Fundamentals goes over this in more detail. If you find that you have to struggle to remember this when you do practice games, you need to make flash cards with this information and go through them every day.

4. Know how to make test diagrams. The process for making test diagrams is, briefly, to redraw your diagram, put in whatever you want to test, and then go through the rules and add to your diagram whatever the rules tell you. When you are finished going through the rules, fill any empty spaces with whoever is left, moving them around if the rules so require. If you can fill all the spaces without breaking a rule, the diagram works; if you can't, it doesn't. Here are all the steps, in order, in a little more detail: a) Recopy your original diagram (or, if this is an If-question, the diagram you drew when first setting up the question, which includes the rule the "If" gives you, and anything that causes to be true). b) Put in what the answer wants you to test (unless this is a "What must be true?" question, in which case you put in something other than what the answer says). c) Go through the rules – does this new information cause something else to happen? If so, write it down. d) If you wrote something new down, return to step (c) and go through the rules again (every time you learn something new, go through the rules and see if the new thing makes something else happen). e) Once you have gone through the rules and not added anything new, see if there are any empty spaces in the diagram. If so, fill them in from left to right in alphabetical order (to the extent the rules allow). As you put things into the diagram, mark them with a dot or a star. Every time you put someone in, go back through the rules again [step (c)]. f) Have you broken a rule? Try moving someone who is marked with a dot or a star (from left to right). If no one is marked with a dot or a star, or this doesn't help, the diagram won't work. g) Have you filled all the spaces? The diagram works.

5. Be comfortable going through the rules. When you go through the rules, start with the first rule you have written down and go through the rules in order. It is essential to be systematic, because this ensures accuracy and minimizes effort (which is important for speed and to reduce fatigue). Look at the rules you wrote, not back at the way the LSAT has them (these are harder to read). Recognize that sometimes rules don't tell you anything helpful about your current situation. For example, in general, rules that say two people or things are together, or next to each other, or not together or not next to each other, aren't worth thinking about if you don't know anything concrete about either person or thing. This isn't true if you have only a few spaces left in the diagram, though; at that point, there may be only one or two places to put these people, and every distinction counts.

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This is not a skill that can be learned in the abstract. It has to be practiced – the natural human tendency is to skip around, which leads to skipping rules and making mistakes. As you go through games, both in reading the explanations in this book and in practicing by yourself, pay attention to which rules are important when. Eventually, you will be able to go through lists of rules quickly and efficiently, putting them together with a minimum of fuss.

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Intermediate Techniques By now you should be starting to get comfortable putting together diagrams for games, writing down the rules, putting the questions in the right order, testing situations for answers, and using previous diagrams. There are a few other things you might try doing that will make your life a little bit easier. These aren't essential to your LSAT success, but they can help quite a bit. Some of these are things that you might be doing already, or are thinking of doing, but aren't sure if you should.

Diagramming with Columns You might have noticed that we redraw our diagrams often. This generally doesn't involve writing much – maybe just hastily scribbling down 1 2 3 4 5 6, or R S T Y, or the names of six birds. It doesn't take much time, but it does take some, and time is precious. There is a way to save yourself a couple of seconds here and there which may also make your diagrams easier to read. Instead of redrawing your diagrams from scratch every time, when you first draw your diagram, give yourself room and make columns underneath each space in your diagram. If you draw the diagrams vertically, make rows. For example, on Game One, it would look like this: 1

2

3

4

5

6

Your original diagram goes at the top of the columns, and you do the test diagrams for each answer underneath; this allows you to test diagrams quickly without doing any redrawing. We do all of our work in this chart, and, of course, cross off anything you put in there that breaks a rule. For example, after a few questions, our chart on Game One might look like this:

1 B 3 B 3 D

1

2

M M O

K L K

3 P P P P

4

5

6

L K L

N O M

O N N

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On Game Two, our chart might look like this (notice the first diagram breaks a rule, and is crossed out): R __

S __ __

T __ __

6C

H

H G

H L

6D

L*

G* H

H P*

Y __ __ __ L P __ L P H

This technique doesn't work that well for Game Three, mostly because that game doesn't really have anything we can put into columns. This technique is totally optional. It can save you a little time (not that much, but some), and being organized like this may be helpful as well. But it won't work on some games because you just don't have the room to do it. Try it out and see if you like it.

Remembering Rules After you've tested out anywhere from a couple of answers to a couple of questions, you might notice that certain rules stick in your mind. You know to use these rules before looking at the list of rules you have written down. For example, in Game One, the rule about L and K having one spot between them might have stuck in your mind; you might have wanted to fit L and K into the diagram before anyone else because you knew they had to have that relationship. In Game Two, you might have found it easy to remember that G couldn't be with L or P, so that anytime you put G in a spot you immediately knew without looking at the rules that you couldn't put L or P there. This is fine. Certain rules will stay in your head without you having to try to memorize them. Use them, and use them before you look back at the other rules. I often find that on games with relatively few rules, like Game One and Game Two, all the rules stick in my head after I do a couple of questions. Finally, don't try to memorize the rules – it's unnecessary, it's tough, and it wastes time. If you find that you do memorize some of them as you go, without trying, that's good. If you find that you have to look at the list every single time, that's fine too, just make sure you do it.

Making Deductions from Questions – Part 1 Once you've answered a "What can't be true?" question, you've discovered something that can't be true, in any diagram. That means you can use this knowledge to help you on other questions. You can write what you just learned as a new rule; often you can put it directly into your diagram. Look at Game One, question 3. The correct answer is E: O cannot be assigned to position 2. We can write this right into our diagram – put a little "no O" over position 2 – or we can just write down "O not in 2" as a new rule. That's sorta handy.

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This is likewise true about "What must be true?" questions. Their answers must be true always, so they give us new rules as well. However, you cannot get new rules from Ifquestions, even if they ask “What must be true?” or “What can’t be true?”; what must be true or can’t be true in an If-question must or can’t be true because of the new condition the question added, so won’t always be the case in other questions. You might be wondering: if this is true, why don't we do these questions earlier on in our process? That way we could have the benefit of these new rules for the other questions. That is a good question, and it has a good answer. There are two reasons. The first, and most important, is that these questions are generally harder and more time consuming. You've seen this. Saving them for later makes them easier, because it allows us to accumulate previous diagrams that we can use to eliminate answers. You've seen how handy that is – it saves us a huge amount of work, more than would be saved by doing the "What can't be true?" and "What must be true?" questions sooner. This leads us to the second reason why we don't do these questions sooner. The insights you get into the game by doing these "What can't be true?" and "What must be true?" questions are often not terribly useful. Look at Game One. How often in that game is knowing that O won't go 2nd useful? Never. We end up never even trying to put O 2nd, even without knowing this rule, because there is always someone else we want to put 2nd. For another example, look at question 4. Answer B, the correct answer, tells us that K or L has to be in position 4, which is something like a new rule. How useful is that? Only a tiny bit useful, because our application of the rules automatically forces us to put one of them there anyway. Again, we never (or almost never) even tried to put someone else there, so knowing that no one else could go there wouldn't have saved us a significant amount of time. Now look at Game Two, question 8. It is a "What can't be true?" question. Look at it and ask yourself how useful knowing the answer will be on later questions. It might be a little useful to know that no one can learn R and T, but not Y, but only a little. Compare that usefulness to how much time we save using previous diagrams to answer this question. We end up doing no work to solve this question because we use our previous diagrams. Now, once in a while, you may find that an answer to one of these types of questions is useful in answering other questions. That's why I'm telling you that you can use these answers as new rules. The great majority of the time, however, doing this won't save you more time than doing the questions in the order we've discussed. So we are going to play the good odds and continue to do the questions in the right order.

Making Deductions from Questions – Part 2 From time to time, you will come to realizations as you work through questions. For example, as you work through Game Two, you may realize that G will never go under R (because G has to go with H, and there is only one space under R). Or you might notice that G can't go under Y (because if it does, L or P can't go under Y, and then you can't fill all three of the spaces under Y – this might also show you that H, P, and L would have to go under Y, because you have to fill those three spaces with someone, and G can't be used). In each of these cases, you could write down what you've figured out as if it were a rule, so that you can use it to help out on future questions. Notice though, that in each of these cases you realize something has to be true, or can't be true, and you can give a reason for it. It's not enough to think something is true, or has to

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be true, or to be pretty sure. You must be sure, and to be sure you must be able to give a conclusive reason for it based on the rules. If you realize, while doing questions, that something must be true, based on the rules, write it down. If you are not sure, don't write it down.

Redrawing Diagrams – What Not to Copy Redrawing your diagrams is a wonderful, wonderful technique. It is easy, necessary, and extremely useful. But not every part of every diagram is equally necessary. I often find that writing down the names of all the variable things – the list of F G H I, etc., that we write down to the right of our main diagram – is not that useful, and it’s a little tedious. On most games where every thing is used once (such as Game One and Game Two), it's easier for me not to copy the names down. But you need to be able to figure out who the last person left is, so you can fill that last empty space; for this I just run through the main diagram, checking against each person on the list, until I find an unused one. With a bit of practice this is fast and easy. On the other hand, I have students who always make mistakes unless they write down all the names and cross them off as they go. If you find yourself leaving people out, using people twice, or just forgetting what to do next, err on the side of caution and copy everything down every time. It doesn't take that long. But I did want to let you know that, if you are careful, you can get away with not doing it. You do have to copy down the rest of your diagram, though. We're being efficient, not foolish.

Picking the Answer to Test In general, you should test the answers in order, from A to E. Anything else requires too much thought, and thought is the enemy of all good LSAT-takers. However, there is one (maybe two) situation(s) in which you might not want to test the answers in order. Here is the most important one. You have eliminated all but two answers, usually by using previous diagrams (which means you'll have at least glanced at both of the remaining answers). You'll only have to test one of the answers, since it will either be right, in which case you are done, or wrong, in which case the other is right, and you are still done. So it doesn't really matter which you test. If one of the answers seems either pretty obviously right or pretty obviously wrong, or really easy to test, then test that one. The other case where you might not want to test the answers in order is this: you are using previous diagrams to eliminate answers, and you come across an answer which you are pretty sure is right (but no previous diagram proves that it's right, otherwise you wouldn't even be considering testing it out). Try that one, you might save yourself some time; just be careful to remember which answer you are testing. Doing things out of order has a habit of confusing people, which is why I am usually against it, so you should be very confident that you are right; don't just do this on a whim, or it'll cost you at some point.

What Do I Do Next? Go through Game Four through Game Eight. These games will demonstrate some of these intermediate techniques. These games will also show you how to apply your fundamental techniques to games that people consider odd or difficult.

Game Four

119

120 Game omitted from electronic version of book.

Game Four

Game Four

121

Game Four (From LSAT 30) By this point you have learned and practiced the most important skills you will use on LSAT logic games. I've given you a series of techniques that you can memorize and apply to every logic game you come across. But sometimes the LSAT will throw something at you that seems extremely difficult, that seems not to fit into what you understand. In the next five games, I will demonstrate that even these seemingly different games are not, in fact, different at all. We don't need to learn anything new or approach the games in a way other than we have been. As long as we stick to our fundamentals and do what we have learned, these games will be as straightforward as anything else. Now that we've gone through a few games, I'm going to go a little more quickly through the explanations of the steps. We'll still do everything you should do, but I won't explain the fundamentals in quite as much detail. If something doesn't click, refer back to the previous chapters. Don't work through this game on your own yet; read along with me until you get the hang of how we are doing things, and then, if you want, finish the rest of the questions on your own before looking at the explanation.

Step 1: Read the Setup/Draw a Diagram Read the setup and see if you notice something different about this game. I've told you before that every game involves two or more types of things, and you are figuring out which of one type goes with which of the other. Up to this point, though, we have only seen games with two types of things – horses and positions, or researchers and languages. This game has three: cars, order (first, second, etc.), and types of washes. For each car we want to figure out where in the order it is washed, and what type of wash it receives; for each number in the order we want to figure out what car goes there and what type of wash it gets. This does not require any new way of thinking. We build our diagram in the exact same way. Which of the three types of things – order, cars, washes – do we know the most about? Which will change the least? The order; numbers never change the order they are in. So we will build our diagram around the order. Since there are five cars washed one at a time, there are five possible numbers (if more than one car could be washed at once, there could be fewer numbers): 1

2

3

4

5

One car will go with each number, and one type of wash. So we put a space under each number for the car, and a space for the wash; car names (O, V, etc.) go in the top spaces and the wash types they get in the bottom ones. 1 __ __

2 __ __

3 __ __

4 __ __

5 __ __

Finally, we put in the names of the cars and washes. 1 __ __

2 __ __

3 __ __

4 __ __

5 __ __

Cars: F M O T V Washes: r, s, p

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Game Four

You will see games like this, which involve more than two types of things, regularly on the LSAT. They are not harder than any of the games we have seen before, and they don't require any different kind of thinking. We just read what we are given and work through the rules exactly like before.

Step 2: Read the Rules Many of these rules are actually two rules disguised as one, like the first rule. It tells you not only that the first car washed doesn't get a super wash, it also tells you that there has to be at least one super wash. At least means there has to be one s and maybe more. You need to write both of these things down. 1 is not s At least one s The next rule contains the word exactly. This means that one, and only one, car gets a premium wash. Exactly one p The next rule is also simple: 2 and 3 same wash This next rule can be written as two rules, one about O and one about T; we break it down to make it easier to understand. We also translate it into a way we easily understand. If O isn't before V, then V must be before O. Usually we say that someone is before someone else, not "not before." Try to translate rules into a format you've used before and are comfortable with. V before O V before T This next rule should also be written as two rules. I translate "after" into "before." M before F O before M The last rule is more complicated; breaking it into two rules – one about M and one about the car before M – makes it easier to apply. M is r r before M (and next to) I put in the "and next to" to point out that the r comes immediately before M. You could write is somewhat differently (e.g., "r right before M," or "rM"), as long as you understand what you wrote.

Game Four

123

Here is our original diagram and list of rules: 1 __ __ 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

2 __ __

3 __ __

4 __ __

5 __ __

Cars: F M O T V Washes: r, s, p

1 is not s at least one s Exactly one p 2 and 3 same wash V before O V before T M before F O before M M is r r before M (and next to)

Step 3: Answer the Questions Before we go through the questions, I'm going to list them in the order we do them in. By this time you should understand that we do this by going through the questions in order, skipping the ones that we know we shouldn't do yet; thus, the game may take us two or three go-throughs to finish. This game actually takes several go-throughs: we do the "What can be true?" and If-questions first, but that leaves a "What must be true?", a "What is a complete and accurate list?", and an odd question. We end up skipping these three questions the first time through. Here is the order in which we should do the questions: Question Number 11 12 13 14 15 16

Question Type What can be true? If If What must be true? Which is a complete and accurate list? If (that changes the rules)

Question 11 Although the question says "accurate list," it asks for a list that "could be an accurate list," so this is a "What can be true?" question. For each answer, go through all the rules until you find a rule that it breaks. Answer A The first wash isn't s, it's p, so this follows rule 1. There is one s, so this follows rule 2. There is only one p, and the 2nd and 3rd washes are the same, so this follows rules 3 and 4. But this violates rule 5: V should be before O, not after.

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Game Four

Answer B This follows all the rules, so this is the answer. Write this diagram down, so that you recognize later on that it is a usable previous diagram. 1 V p

2 O r

3 T r

4 M r

5 F s

Question 12 This is a tough question, as we'll see. It tests our ability to draw sample diagrams to the limit. Are you ready? Are you LSAT-gamer enough? Let's do it! First, we are told that V doesn't get a premium wash. OK, write that down. V not p Glance through the rules and see if that tells us anything about V. Well, we know that V has to be before O and T, but we don't know much else about V. I don't see where it will go (although you might), since it could be 1, 2, or 3 and still be before O and T, and I'm not sure whether it will have an s or r wash. So let's work through the answers. This is a "What must be true?" question, so we test the answers by doing something other than what they describe. Now, where V goes and what wash V has are both things that it turns out we could figure out. But there's not really any way for us to know we could figure them out, so unless we somehow just see it, we shouldn't try to do so. Looking for nonexistent deductions is one of the biggest logic games time-wasters, so once you've looked through your rules, start looking at the answers. Answer A Since the answer says O and V have the same wash, we want to try and give O and V different washes. We don't know what wash V is going to get, so we don't know what wash to give O, either. Here is where some people will panic – we don't know anything definite about O or V, so what do we do? How do we test this out? OK, let's calm down. The best way to test things out is to make them definite – draw a diagram and test something. So let's draw our diagram and write down what we are trying to test – that O is not the same as V. 1 __ __

2 __ __

3 __ __

4 __ __

5 __ __

Cars: F M O T V Washes: r, s, p O not same as V

I feel better already. We want to test out O and V, so we want to put them in our diagram. We don't know quite where they will go, but we'll just try places until one works, or we realize that nothing will work. We know a whole lot about V, so we'll put her in first. Let's just put her in the first available spot, spot 1. That's an easy way to start. Then we'll try place 2, and so on. We put a little star next to V to remind ourselves that we could have put V someplace else – later on we might move V. 1 V* __

2 __ __

3 __ __

4 __ __

5 __ __

Cars: F M O T V Washes: r, s, p O not same as V

Game Four

125

Look through the rules before we go on. The question tells us that V can't have p; rule 1 tells us that position 1 can't have s. So V must have wash r, since that's the only wash left. We don't star r, because this has to happen (given that V is first). 1 V* r

2 __ __

3 __ __

4 __ __

5 __ __

Cars: F M O T V Washes: r, s, p O not same as V

OK, now we try to put O in. Let's try putting O in position 2, because that's the first position we have available. If that doesn't work, we'll try 3, and so on. We'll put a little star next to O to remind ourselves that this was a decision we made – we can try moving O if it doesn't work. 1 V* r

2 O* __

3 __ __

4 __ __

5 __ __

Cars: F M O T V Washes: r, s, p O not same as V

Look through our rules before we go on. Remember, any time you write something definite in the diagram, go through the rules. This works so far. Now we assign a wash to O. It is supposed to be different from V, so we don't want to assign it r. That leaves p and s. Can we give it p? Look through the rules. I'll wait. No, space 2 can't be p, because 2 and 3 must be the same, and p only gets used once (rules 3 and 4). We can actually write this as a rule, because we see that it must always be true. 11. 2 not p 12. 3 not p So O has to be s, which makes position 3 s (rule 4). Again, we don't star s because s has to be where it is. 1 V* r

2 O* s

3 __ s

4 __ __

5 __ __

Cars: F M O T V Washes: r, s, p O not same as V

Now we start putting in the others. Go through our rules. We've used at least one s, so rule 2 is happy. We don't have a p, so one of our last two slots has to be p. V is before O; that's fine. V is before T, so T will go in someplace after 2, but we don't know where. M is before F, so M has to be either 3 or 4 – if it were in place 5, there would be no room for F. Then we see that M has to be r (rule 9), so M can't be 3; this means that it has to be 4th. 1 V* r

2 O* s

3 __ s

4 M r

5 __ __

Cars: F M O T V Washes: r, s, p O not same as V

Keep going through the rules. This breaks rule 10 – the place before M is not r. So this won't work. Go back to the last place we made a decision and change it (look for the last place we marked). So let's move O (it's the last dot/star we put in, because M had to be 4, since she couldn't have s or be last). Put it in position 3 (and cross our the diagram we just made, since it breaks rules); remember, when you move people around, be consistent in moving them in the same direction (generally left to right) so that you don't lose track of where you have tried them.

126

Game Four 1 V* r

2 __ __

3 O* __

4 __ __

5 __ __

Cars: F M O T V Washes: r, s, p O not same as V

What wash is O going to get? It can't get r (we are testing answer A, so we want O and V to be different). We just figured out that 2 and 3 can't be p because there is only one p. So they have to be s. 1 V* r

2 __ s

3 O* s

4 __ __

5 __ __

Cars: F M O T V Washes: r, s, p O not same as V

M was a problem before; where can it go? Well, it has to go after O (rule 8), and it can't go in position 5 (rule 7). But we just saw that if it goes in position 4, then 3 has to be r, and 3 isn't r. So there is no place M can go. We can't move O over any more, because that would leave M even fewer places to go. So moving O isn't going to fix anything. Let's look at our other starred person, V. Let's try moving V around. Put V in position 2. 1 __ __

2 V* __

3 __ __

4 __ __

5 __ __

Cars: F M O T V Washes: r, s, p O not same as V

Now look through the rules. V is before O and T, so they have to go somewhere in 3 through 5; we know that they can't be in position 1. 1 2 __ V* __ __ no O no T

3 __ __

4 __ __

5 __ __

Cars: F M O T V Washes: r, s, p O not same as V

Look through the rules again (every time we figure out something new, we look back through the rules). O is going to be before M, so M also can't go in position 1 (if O is somewhere in 3 through 5, M has to be after it). 1 2 __ V* __ __ no O no T no M

3 __ __

4 __ __

5 __ __

Cars: F M O T V Washes: r, s, p O not same as V

Look through the rules again. Rule 7 tells us that M is before F, which means F can't go in position 1 either. But this means no one can go in position 1. This means that V can't be in position 2 ever. This is a deduction and we can write it down as a rule (see Intermediate Techniques). We should also put V in position 1 in our original diagram, so that we always put it 1st when we draw a new diagram. 13. V is 1

Game Four

127

Now, we've tried to move everything we can; we can't get a diagram that works. Since this is a "What must be true?" question, and we can't get a working diagram, this (answer A) must be the answer. Notice that, while we had no definite place to start on this question, just calmly working through it gave us the answer, and it gave us a lot of information about this game. Feel better? Be systematic and stick to the rules, and you can answer any question. Worst-case scenario, though, you realize that you just can't figure it out, so you skip the question and do another one. I also want to make another point. This seemed to take a long time. Perhaps you are thinking it would have been faster if we had figured out that V had to be 1st ahead of time. But how could we have figured out where V goes without doing most of what we just did? We couldn't, so doing it sooner wouldn't take less time, it would just mean we spent that time earlier. We still would have had to work out where O could or couldn't go. By waiting to think about V until the answers force us to, we only do what we have to. If we had thought about V sooner, it might have turned out not to be useful. But now, since the question talks about V, we know thinking about V will be useful. Question 13 We are told that position 4 and 5 have the same wash. Write this down. 4 and 5 same wash Look through the rules and see if any tell you what wash this will be. It can't be p, because we can only have one p. I don't see anything else jump out at me – no rules tell us anything about positions 4 and 5 – so let's look at the answers. This is a "What can be true?" question, so we just try out the scenario the answer describes. Answer A Let's test it out. Put O 3rd (and V 1st, which we figured out in question 12). By the way, even if we hadn't figured out that V has to be first, we'd approach the next few questions in a similar way. Since V has to be before a lot of people, when testing the answers it is safe to put V 1st. We wouldn't know that it has to be there, but we know that it works there. 1 V __

2 __ __

3 O __

4 __ __

5 __ __

Cars: F M O T V Washes: r, s, p

Go through the rules. Rule 7 tells you that O has to be before M, so M will be 4th or 5th. Last question, we saw that M can't be 5th. If you had forgotten that, when you looked at the rules again, you would see rule 7 says that M must be before F, which means M can't be 5th, since F would have no place to go. Anyway, we put M 4th. Since M has to go there, we don't mark it with a dot or star. Since we are on rule 7, we know that F has to go after M, which puts F 5th. There is only one spot left (2), so T has to go there. 1 V __

2 T __

3 O __

4 M __

5 F __

Cars: F M O T V Washes: r, s, p

128

Game Four

Now, rules 9 and 10 tell us that 3 and 4 must get wash r. The question tells us that 4 and 5 will have the same wash, so 5 is r as well. Write this down, and then go back through the rules. Rule 4 tells us that 2 is the same as 3, so it is r also. 1 V __

2 T r

3 O r

4 M r

5 F r

Cars: F M O T V Washes: r, s, p

Go through the rules again. We have to have at least one s and at least one p. This is impossible, so this diagram won't work. Cross off the diagram and cross off answer A. Answer B Put T 5th. 1 V __

2 __ __

3 __ __

4 __ __

5 T __

Cars: F M O T V Washes: r, s, p

Let's go through the rules. V is before O, and O is before M, so let's put them in someplace; put them in as early as possible, and we'll move them if we have to. Mark O because we chose to put it 2nd (although it will end up that it had to go 2nd). 1 V __

2 O* __

3 M __

4 __ __

5 T __

Cars: F M O T V Washes: r, s, p

There is only one spot for F – 4 – and rule 7 tells us that F has to go after M, so space 4 is fine. Rules 9 and 10 tell us that 2 and 3 are going to be r. 1 V __

2 O* r

3 M r

4 F __

5 T __

Cars: F M O T V Washes: r, s, p

Go through the rules one more time. 4 and 5 have to be the same according to the "If" part of this question, and rule 3 tells us that we can only have one p. This means that 4 and 5 can't be p, so make them s (because we need at least one s). Make 1 p, since we need a p. 1 V p

2 O* r

3 M r

4 F s

5 T s

Cars: F M O T V Washes: r, s, p

This works, so this (answer B) is the answer. See, not much harder than any other game. Question 14 Since this is a "What must be true?" question, use your previous diagrams first (we have diagrams from 11B and 13B). We look for diagrams which have situations different than what the answer describes. Answer A Every previous diagram has V getting a p, so we don't know if it can be false or not. We skip this one.

Game Four

129

Answer B The negation of "exactly" is "fewer" or "greater"; this doesn't have to be true if we have a previous diagram where there are fewer than two s, or one in which there are more. The diagram for 11B shows that we can have just one s, so this doesn't have to happen (see why I make you recopy the answers to these questions – it is so easy to overlook that as a previous diagram because it just looks like an answer choice). Eliminate this answer. Answer C Every previous diagram has 5 getting an s, so skip this. Answer D 11B shows that 4 doesn't have to get an s, so this doesn't have to be true. Eliminate this answer. Answer E 2 gets an r in each previous diagram, so we can't eliminate this. OK, so we have to go back and test some of A, B, and E. Let's test A first. Don't give V a premium wash. Since she is 1st, she can't have a super wash (rule 1), so give her a regular. We don't mark r, because we have to use an r to test this answer. 1 V r

2 __ __

3 __ __

4 __ __

5 __ __

Cars: F M O T V Washes: r, s, p

Now go through the rules. V is before O, and O has to be before M, so let's just put O and M in 2 and 3, like we did before. Rules 9 and 10 tell us that both will get r washes. Mark O and M because they don't have to go 2 and 3, but don't mark the r's because they do have to go with O and M. 1 V r

2 O* r

3 M* r

4 __ __

5 __ __

Cars: F M O T V Washes: r, s, p

Now we have to put in T and F; it doesn't seem to matter where they go. We also have to put in one p and one s; it doesn't seem to matter where they go, either, so use alphabetical order. 1 V r

2 O* r

3 M r

4 T p

5 F s

Cars: F M O T V Washes: r, s, p

I could have switched T and F, and the s and p, if I wanted. This works, so A is wrong. This also shows us that C is wrong; we didn't have to put the s in spot 5. The p could have gone there as well. E is the answer. Question 15 Use your previous diagrams before you do anything else. The question asks for people who must have r washes. Any person who doesn't have to have a regular wash should not be in the answer. If we see a previous diagram where a person doesn't have an r, we know they don't have to have r, so shouldn't be in an answer.

130

Game Four

Answer A F doesn't have to have a regular wash – the diagrams for 11, 13, and 14 give him a super wash. Answer B Both M and O have r in every previous diagram. Skip this. Answer C T has an s in 13 and a p in 14, so eliminate this. Answer D We just saw that T doesn't have to have r, so eliminate this. Answer E V has a p in the diagrams for 11 and 13. Eliminate this. B is the answer. Question 16 This gives us an additional fact, so it seems like a regular If-question, but it is really changing the rules by adding a car. We have to expand our diagram – we only have room for 5 cars now, not 6. The additional space may complicate things. We don't know how it affects the deductions we have made – for example, perhaps V doesn't have to be 1st (maybe it could go after J?). This makes this question difficult, and so we save it for last. It also means that we couldn't use diagrams from this question on other questions, another reason to do it at the end. We always save questions that change the rules for last – not those that add new information, like regular If-questions, but those that alter the basic rules of the game. These questions always explicitly tell you that they are altering the rules, so don't worry about not spotting them. Let's draw a new diagram with six spaces, and put J in with the cars. 1 __ __

2 __ __

3 __ __

4 __ __

5 __ __

6 __ __

Cars: F M O T V J Washes: r, s, p

Now let's test out the answers, just like normal. This is a "What can't be true?" question, so we try each answer out and eliminate those that are possible. We can't use previous diagrams because we've added a new rule. Answer A We can't give O a premium wash until we know where he goes. We want to put O in the first available spot. We know that O can't be first, because he still must be after V. Try putting O 2nd, and mark him. 1 __ __

2 O* p

3 __ __

4 __ __

5 __ __

6 __ __

Cars: F M O T V J Washes: r, s, p

Now go through the rules. They tell us that 2 and 3 must get the same type of wash. However, there is only one p. This can't work, nor can O go 3rd, for the same reasons. Put O 4th.

Game Four 1 __ __

131 2 __ __

3 __ __

4 O* p

5 __ __

6 __ __

Cars: F M O T V J Washes: r, s, p

Now let's put in everyone else. V has to be before O, so V will be in 1, 2, or 3 (most likely 1). Let's put V 1st and mark it. 1 V* __

2 __ __

3 __ __

4 O* p

5 __ __

6 __ __

Cars: F M O T V J Washes: r, s, p

M has to be after O, so M will have to be 5 or 6. We've already seen that M can't be last, since F has to be after her, so M has to be 5th. 1 V* __

2 __ __

3 __ __

4 O* p

5 M __

6 __ __

Cars: F M O T V J Washes: r, s, p

But this won't work. Rule 10 tells us that the car before M has to get an r wash. Cross off this diagram and move O one over. 1 __ __

2 __ __

3 __ __

4 __ __

5 O* p

6 __ __

Cars: F M O T V J Washes: r, s, p

Go through the rules again. M has to be after O, but that makes M last. This won't work, since F won't have anyplace to go. If we move O any more, M will not fit at all. So this will never work. This (answer A) is our answer.

Summary This game didn't involve any new skills. We still had to draw diagrams in the same way and test answers out by trying to put them in diagrams that work. Games like this, which involve more than two types of things, can be difficult, because sometimes it's hard to know definitely where to put people or things. But that is not a serious obstacle for us; we try them someplace, and if that doesn't work, move them to the next available place. As long as we are consistent in the way we do this, and always look at the rules, we can do as well on these games as on any others.

What Do I Do Next? Take a break. Then look over your notes and think about how we applied the fundamental skills to this game. Then, when you feel ready, maybe today, maybe tomorrow, maybe in a day or two, go back and do this game with no notes. By this stage you should have memorized the fundamental skills. By that I mean you should know the techniques for diagramming and how to do every kind of question, including when and how to use previous diagrams and how to eliminate answers on every type of question. If you haven't, you need to make up some flash cards and be working on them.

132

Game Four

Answer Key 11. 12. 13. 14. 15. 16.

B A B E B A

Game Five

133

134 Game omitted from electronic version of book.

Game Five

Game Five

135

Game Five (From LSAT 40)

Step 1: Read the Setup / Draw a Diagram Let's go through this setup piece by piece, as we would on the LSAT. The first sentence tells us that five of seven medications are being tested. Immediately we ask ourselves the question we ask about every logic game: what things are being matched up? Here we have medications; what are we doing with these medications? We are testing them, but not all of them, just some of them. So we have the "test" group, and the "not-tested" group. This game should remind you a bit of Game Three. Keep reading the first sentence. It then tells you that the medications that are tested (those in the "test" group) are being ranked from 1 to 5. So we're doing two things here: figuring out which medications are being tested, and then ranking those medications. We have three types of things floating around: the "tested" / "not-tested" groups, the numbers 1 through 5 (which occur in the tested group), and the medications. Which type of thing do we know the most about? We know the most about the numbers, as always, so we'll base our diagram around these numbers. These numbers are the tested group, so we'll label them as such: test:

1

2

3

4

5

Each number gets one medication assigned to it, so we'll put one blank under each number. test:

1 __

2 __

3 __

4 __

5 __

Now, we also have a not-tested group, which we should also write down. Whenever we have two or more groups, you should give space to both. And whenever only some things/people/medications are selected, some are not selected, which means that you have both a "selected" and a "not-selected" group (or, in this case, a tested and not-tested group). How many medications go in the not-tested group? Well, we have seven medications to start with, and we are testing five of them, so we are not testing two (seven minus five equals two). test:

1 __

2 __

3 __

4 __

5 __

not:

__

__

FGHIKLM

Step 2: Read the Rules The first rule is relatively simple: it tells us that L is 2nd. If L is 2nd, it must be tested, since the "not" group is not ranked. So we can put L in position 2 in the test group in our diagram, and write down the rule as well. L is 2 The next rule is also simple: F or G is in position 1. Now, if F is 1, where is G? I don't know – we aren't told. G might be 3rd or 4th, and so forth, or not picked. Be careful not to assume that one is 1st and the other is not picked.

136

Game Five F or G is 1

The next rule tells us that I is tested, so it will go in the "test" group, but we don't know in which position. I is tested The next rule is an "If… then…" rule. Don't be confused by the placing of the "if" towards the end of the sentence – a rule with an "if" in it is still an "If… then…" rule, regardless of where the "if" falls in the sentence. We should write it as an "If… then…" rule (moving the "if" part to the beginning of the sentence so it looks more normal): If H and G tested, then H before G. Notice that we can't break this into two rules because it says "H and G," so we need both for the "if" to be true, not just one. What's the contrapositive? If H is not before G, then H and G aren't both tested. It's worth taking a minute to see what this means. Let's look at the first part of the contrapositive, the "if" clause. How would we know that H is not before G? Imagine a situation in which you knew that H couldn't be before G. Go ahead, do it. What is it? Well, one way for us to know this is if a rule told us this, but that's too easy. Imagine a situation in which the question doesn't tell you explicitly about both H and G, but you know that H is not before G. Think hard, think very hard. How might this happen? OK, here's my answer. If you knew, for example, that G was 1st, then H couldn't be before it. Or, if you knew that G was 3rd, let's say, and there was no room in front of G for H to go, then H couldn't be before G. This is an important thing to understand – when you look at an "If… then…" rule, you need to be able to know when what the "if" part describes is the case; otherwise, you won't know whether or not to use the rule in a situation. The next rule is very similar: If K and F are tested, then K is before F. If K is not before F, then both K and F are not tested. Here, if we knew that K couldn't go before F (for example, if F was 4th but there was no room in 1 through 3 for K) then you would know that you couldn't have both the medicines. The last rule is really two rules, since M being tested tells us something about F, and also something about H. We'll break it up (see "If… then…" Rules and Negations). If If If If

M tested, then F tested. M tested, then H tested. not F, then not M. not H, then not M.

Game Five

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Here is how our original diagram and list of rules end up looking: test:

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

1 __

2 L

3 __

4 __

5 __

not:

__

__

FGHIKLM

L is 2. F or G is 1. I is tested. If both H and G tested, then H before G. If H is not before G, then H and G aren't both tested. If K and F are tested, then K is before F. If K is not before F, then both K and F are not tested. If M tested, then F tested. If M tested, then H tested. If not F, then not M. If not H, then not M.

Step 3: Answer the Questions Here is the order in which you should do the questions: Question Number 6 7 10 8 9

Question Type What can be true? What can be true? If What must be true? Which is a complete and accurate list?

Question 6 Since this is a "What can be true?" question, let's go through the answers, seeing if they break the rules or not. Each answer lists all the medicines in the "test" group, so the other two are not tested. Answer A This breaks rule 1: L is not 2nd. Answer B This follows rule 1 and rule 2. It breaks rule 3, though, because I is not on the test list. Answer C This follows rules 1, 2, and 3. We don't worry about rule 4 because H and G aren't both tested, so the situation the "if" part of the rule describes isn't the case here. Rule 5 is followed – H isn't before G, because H and G aren't both selected (H can't be before G if there is no G in the tested group). We don't have both K and F, so we ignore rule 6, and rule 7 is followed. Rule 8 is followed, but rule 9 is not: we have M but no H. This is wrong. Answer D This follows 1, 2, and 3. We don't have both H and G, so rule 4 is irrelevant, and rule 5 is followed. We don't have both K and F, so we ignore rule 6 (and rule 7 is followed). Rules 8 and 9 are followed, because we have M, H, and F. Rules 10 and 11 are irrelevant, because

138

Game Five

their "if" parts say "not F" and "not H," but we test F and H. So this follows all the rules, and it is the answer. Since it is the answer, it is a possible diagram; copy it down and we'll use it for later questions. I'm also going to take the time to fill out the "not" section; this may or may not come in handy later on, and it isn't hard to do. test:

1 F

2 L

3 I

4 H

5 M

not:

G

K

Question 7 This is a "What can be true?" question, so we'll go through each answer and see if we can make it work. Answer A If G ranks better than M, both have to be tested (after all, you can't be ranked higher than someone if one or both of you isn't ranked at all). Now, we don't know where G will go, so we'll try G 1st; if this doesn't work, we'll try him someplace else. Let's put a * next to G, so we know that we can move him if we have to. I'm not going to put M in a spot because I haven't looked at the rules yet, so I don't know where M can or can't go. So as not to forget M, though, I put it floating around near the "test" group. test: M

1 G*

2 L

3 __

4 __

5 __

not:

__

__

FGHIKLM

Now let's go through the rules. We've got 1 and 2 covered – L is already in our original diagram, and we've just put G 1st. Rule 3 tells us that we also have to test I, but I don't know where that's going to go, so I'll just sort of put it near M. test: M I

1 G*

2 L

3 __

4 __

5 __

not:

__

__

FGHIKLM

Looking at rule 4, I don't know if both H and G are tested, so I ignore it. Now we look at rule 5. It says "If H is not before G"; here, there is no room before G, so H isn't before G. Thus, we can't test both H and G. What does this mean? It means that we can't test H, since we've already got G tested. Put H in the "not" area. test: M I

1 G*

2 L

3 __

4 __

5 __

not:

H

__

FGHIKLM

Let's keep going through the rules. We can't test both K and F because we only have three spaces left and we have to have M and I, so we ignore rules 6 and 7. We know that M has to be tested, so we have to test F and H (rules 7 and 8). But wait… we can't test H (it's in the "not" area), so this won't work. Cross out the diagram. We don't know if this answer will work or not, because we haven't tried all the possibilities. Since G is starred, it could go someplace else, so we have to move it. G can't go 2nd (L has to go there), so put G 3rd. Again, I'm putting M floating around near the test group, because the answer wants us to put G before M, but I'm not sure exactly where to put M. test: M

1 __

2 L

3 G*

4 __

5 __

not:

__

__

FGHIKLM

Game Five

139

Rule 2 tells us that F or G is 1st, so put F 1st, since G is 3rd. test: M

1 F

2 L

3 G*

4 __

5 __

not:

__

__

FGHIKLM

Rule 3 tells us that I is picked, so put that in our diagram someplace; this means that the two empty spaces will have I and M in them. Put H and K in the "not" area. test: MI

1 F

2 L

3 G*

4 __

5 __

not:

H

K

FGHIKLM

Keep going through the rules; we can't have both G and H, so ignore rule 4. Rule 5 confirms that H can't be tested. We ignore 6 because K isn't tested. Rule 8 is violated, because we have M tested but not H. Cross off the diagram and move G over one more. test: M

1 __

2 L

3 __

4 G*

5 __

not:

__

__

FGHIKLM

We probably remember that F or G goes 1st, so put F in 1. The answer says M is after G, so put M 5th. test: M

1 F

2 L

3 __

4 G*

5 M

not:

__

__

FGHIKLM

Rule 3 says I has to be tested, so I will go 3rd. Now, you're probably seeing that we're going to have a similar problem here as before – M is tested, so H has to be, but there is no room for H. Moving G over one more won't help us, because then G couldn't be before M. This won't ever work – cross off the diagram and cross off the answer. Answer B This is going to be a similar drill to the previous answer. We want H to be before F, but we don't know where either one goes. We could try H 1st, but having worked through the previous answer, we probably remember that either F or G has to go 1st (rule 2) So let's put H 3rd (since rule 1 says that L is 2nd), and put F someplace as a reminder not to forget it. I'll put G 1st (since F sure can't go there – the answer wants F after H). I don't put a star next to G because G has to go 1st. test: F

1 G

2 L

3 H*

4 __

5 __

not:

__

__

FGHIKLM

Skim through the rules until you see one that is broken. Which is it? That's right, it's rule 4. We're testing both H and G, but H is not before G. Is there any way to remedy this situation? The only medicine we have starred is H, so that's the only one we can move around. We already know that it can't be in 1 or 2, which means that it can only be moved to the right (this is the virtue of consistently starting with the left-most position and moving things to the right). But this would still mean that H is after G, which it shouldn't be, so moving H further to the right won't help. This will never work. Cross off the diagram and cross off the answer.

140

Game Five

Answer C Same drill – try I wherever you can until it works. We start by putting I 3rd, since we know that F or G is 1st and L is 2nd. test: F

1 __

2 L

3 I*

4 __

5 __

not:

__

__

FGHIKLM

We want I to be before F, so F can't go 1st. This means that G goes 1st (rule 2). test: F

1 G

2 L

3 I*

4 __

5 __

not:

__

__

FGHIKLM

Let's go through the rules. 1, 2, and 3 are fine. Since we don't know if H is tested, we ignore rule 4. We do know that H can't be before G (since G is 1st), so we look at rule 5. It tells us that we can't test both H and G; since we have G, we can't test H (or we'd be testing both). Put H in the "not" area. test: F

1 G

2 L

3 I*

4 __

5 __

not:

H

__

FGHIKLM

We ignore rules 6 and 7 because we don't know if K is tested, and we don't know where F goes (which means we don't know if K could go before F or not). We also don't know if M is tested, so ignore rules 8 and 9. Ignore 10 because F is tested. Look at rule 11, because H is not tested. This means that M can't be tested. Put M in our "not" area. test: F

1 G

2 L

3 I*

4 __

5 __

not:

H

M

FGHIKLM

Our "not" area is full; all the remaining medicines must be tested. Only K remains, so it must be tested. And I happen to remember rule 6 says something about K… We know that K must be before F, so the order must be: test: F

1 G

2 L

3 I*

4 K

5 F

not:

H

M

FGHIKLM

This (answer C) is the answer, since it works. Notice that the question started a little slowly – we had to do a lot of testing. However, as we got the hang of the game, things sped up. We start to remember the rules and understand how they work, which means we spent less time looking at our list and trying to figure things out, and just whip through our diagrams. One of the big time-wasters on the LSAT is anxiety. You start working on a question, or a game, and it feels like it is going to take too long. It hasn't actually taken you much time yet, but you feel like it is going to. So you worry, and you fret, and you start looking for a different way to do things, some kind of magic inspiration that will make the question so much easier. But usually you don't find it, and you end up not only taking too long, you also don't even answer the question. If you had just stuck to your program, you would have answered the question quickly enough. The moral of the story is to use what you know, not to look for some unique way of solving this question. Now, that is not to say that you shouldn't skip a question if you know it will take you too long (for example, if you have already spent too much time on it). But there is a difference between worrying that what you are doing is too slow and it actually being too slow. You have to have the confidence that you know what you are doing and that it will work. How do you build this confidence? Practice and honesty. You have to practice enough times to know what you are doing and to see that it works. And you have to be honest with yourself when it does work. Too often students want to deny that they know what they are doing, or

Game Five

141

long (for example, if you have already spent too much time on it). But there is a difference between worrying that what you are doing is too slow and it actually being too slow. You have to have the confidence that you know what you are doing and that it will work. How do you build this confidence? Practice and honesty. You have to practice enough times to know what you are doing and to see that it works. And you have to be honest with yourself when it does work. Too often students want to deny that they know what they are doing, or that they can get questions right, when the evidence that they can is staring them right in the face. Question 10 Since this is an If-question, we have to redraw our diagram and put the information we are given into it. test:

1 __

2 L

3 I

4 __

5 __

not:

__

__

FGHIKLM

Now we go through the rules. Go ahead… Anything else have to happen here? None of the rules (except rule 3) is about I, or about position 3, so we don't know what else is going to happen here. Let's look at the answers. This is a "What can't be true?" question (the EXCEPT means that the wrong answers can be true, so the right answer can't be), so we'll test out each answer to see if we can make it work. Answer A Let's put M before H. I happen to remember that F or G is 1st, so M can't go there, which means that M and H have to go 4th and 5th (no other spaces available). test:

1 __

2 L

3 I

4 M

5 H

not:

__

__

FGHIKLM

Now we go through the rules. L is 2, so rule 1 is happy. Rule 2 tells us that F or G will be 1st, but we don't know which. We've obeyed rule 3 because I is tested. We ignore rule 4 because we don't know if we have both H and G, so we don't know if the "if" part of the rule is true. Rule 5 is worth a look – we know that H can't be before G. Why? Because H is last, so there is no room after H for G to go. So we can't have both H and G, which means that we can't have G, since we already have H. Put G in the "not" zone. test:

1 __

2 L

3 I

4 M

5 H

not:

G

__

FGHIKLM

Now, since the rule about F or G being 1st sticks in my head so much, I start thinking about it. G isn't picked, so F has to go 1st. This fills up the entire "test" area, so everyone else goes in the "not" area (only K is left). test:

1 F

2 L

3 I

4 M

5 H

not:

G

K

FGHIKLM

Go through the rules again, since we've added a lot of stuff. Every rule is obeyed – since we don't have both F and K or both G and H we ignore 4 through 7 – so this answer works. This makes it wrong (we're looking for something that can't be true). Since this is a "What can't be true?" question, let's use this diagram to eliminate other answers if we can. Does this diagram show that any of the other answers are possible?

142

Game Five

Unfortunately not. None of the situations described in the other answers occurs in this diagram. Answer B Recopy our diagram for this question. Remember, on an If-question we recopy the diagram we create for the specific question, where we put in what the question tells us (here, that I is 3rd), not our original diagram. test:

1 __

2 L

3 I

4 __

5 __

not:

__

__

FGHIKLM

The answer wants us to put K before G. Again, only F or G can be 1st, so we have to put K 4th. That makes G 5th (since we are trying to put K before G) and it forces F to be 1st (rule 1), since G can't be. test:

1 F

2 L

3 I

4 K

5 G

not:

__

__

FGHIKLM

There is no room left in the "test" area, so everyone else (H and M) goes in the "not" area. test:

1 F

2 L

3 I

4 K

5 G

not:

H

M

FGHIKLM

Let's go through our rules. Rule 1? Check. Rule 2? Check. Rule 3? Check. Rule 4? Ignore, because we don't have both H and G. Rule 5? Check (we don't have both H and G). Rule 6? Broken – we've got both K and F, but K is not before F. This diagram doesn't work. Can we fix it? Well, nothing is marked with a star, so everything we have in the diagram is mandatory. Since there is nothing we can change here, there is no way of fixing the diagram (so cross the diagram out). This (answer B) is the right answer. Question 8 Since this is a "What must be true?" question, we can use our previous diagrams to eliminate answers that don't have to be true. We are looking for a medicine that must be tested, so if a medicine can be in the "not" area in a previous diagram, it is not the answer. We have previous diagrams from 6D, 7C, and 10A. Answer A F doesn't appear in the "not" area of any previous diagram. Skip this answer. Answer B G appears in the "not" area of 6D and 10A, so it doesn't have to be tested. Cross off this answer. Answer C H appears in the "not" area of 7C, so it doesn't have to be tested. Cross off this answer. Answer D K appears in the "not" area of 6D and 10A, so it doesn't have to be tested. Cross off this answer (you know, I really like saying that). Answer E M appears in the "not" area of 7C, so … you know…

Game Five

143

The answer is A. Question 9 The question asks us for a complete and accurate list of the medicines that can be 5th. The right answer will include all medicines that could be 5th, leaving none out; the wrong answers will either leave one out or have one that can't be 5th. We can use our previous diagrams to see which medicines we already know can be 5th, and eliminate any answer that leaves one out. The diagram for 6D has M 5th; the diagram for 7C has F 5th; and the diagram for 10A has H 5th. So we can eliminate any answer that doesn't include F, M, or H. This eliminates B, C, and D. We are left with A and E. We only want to test medicines that are not on both lists, and the only one that is not in both answers is I. We will see if I can be 5th; if it can, E is the answer. If not, A is the answer. Let's go! Actually, why don't you go ahead and try it out? I'll wait. OK, here's how to do it – we put I 5th. test:

1 __

2 L

3 __

4 __

5 I

not:

__

__

FGHIKLM

Now we go through the rules. No rule tells us much about I; this is a good indication that I can go 5th (if an item is not limited much by the rules, it can usually do lots of things). But this isn't good enough for me – I need to know that I can go 5th. So I want to try some things out. Let's start putting things in. First I'll put F in position 1. Why? Well, someone has to go there, and I have seen that F works pretty well in my previous diagrams. I'll star F so I can try someone else if it doesn't work. test:

1 F*

2 L

3 __

4 __

5 I

not:

__

__

FGHIKLM

Now I go through the rules. Rule 7 tells me that K can't be picked (because it can't be before F). test:

1 F*

2 L

3 __

4 __

5 I

not:

K

__

FGHIKLM

That's all the rules tell me. But I have two spaces left. Whom shall I put in? Well, I've got G, H, and M left. I remember that H goes before G (rule 4), so I'll pick them. test:

1 F*

2 L

3 H

4 G

5 I

not:

K

M

FGHIKLM

This follows all the rules, so this works. Thus, E is the answer. By the way, you could have arrived here in many different ways. If you had put G in position 1, you would have known that H couldn't be picked (rule 5), which in turn means that M couldn't be picked (rule 11). This leaves K and F, which have to go in that order. This would work. Alternately, if you started by putting F 1st, but you didn’t know who to put in 3 and 4, you could have put H and M in as well.

144

Game Five

could have put H and M in as well. What's the lesson to be learned? Try things out, don't hesitate and worry that you'll try the wrong things. In the absence of information guiding you as to what to try, just try something. If that doesn't work, try something else; usually, working out one thing will give you an idea of what to try next, or you'll have some hunch based on your previous work on the game, but there is nothing wrong with just going through the rules one by one and trying what they suggest (e.g., putting F or G 1st because the rules say so, and going from there).

Summary Another odd game, where you had to deal with several different issues – who gets tested and who is not tested, and in what order. But it wasn't that hard, you just had to work through the rules carefully. Notice how crucial it was for us to do the contrapositives of the rules about G and H, and K and F. If we hadn't done those contrapositives, and hadn't understood what they meant, the game would have been much harder. Go back and look at the rules again, and think about how we knew what the contrapositives meant. You are likely to see rules like this on the LSAT, and understanding them now means that you will be more likely to understand them then.

What Do I Do Next? Take a break. Then look over your notes and think about how we applied both the fundamentals and the intermediate techniques to this game. Then, when you feel ready, go back and do this game with no notes. By this stage you should have memorized the fundamental skills. By that I mean you should know the techniques for diagramming and how to do every kind of question, including when and how to use previous diagrams and how to eliminate answers on every type of question. If you haven't, you need to make up some flash cards and be working on them. Once you've done this game on your own and feel comfortable with it, go on to Game Six.

Answer Key 6. 7. 8. 9. 10.

D C A E B

Game Six

145

146 Game omitted from electronic version of book.

Game Six

Game Six

147

Game Six (From LSAT 39)

Step 1: Read the Setup/Draw a Diagram Let's go through the setup piece by piece. The first sentence tells us that three people attend a three-day conference. So far we have two types of things – people and days. The next sentence gives us a third type of thing – sessions on different topics. So now we have three types of things to think about – topics, days, and people. We have to ask which of the three types of things we know the most about. Generally we know more about days than we do other types of things – specifically, days have to come in a certain order. Here, though, I'm not yet sure if we are concerned with the order of the days. If they had told us that the days were numbered 1, 2, and 3, or that they were Monday, Tuesday, and Wednesday, I'd know that order mattered, since numbers and days of the week have order built right in. So far, however, they have told us no such thing. What do we do when the setup doesn't give us enough information? Where do we look for more information? That's right, we look at the rules or the questions. Glance quickly through the rules and see if the order of the days is important. Do any of the rules tell us that we should think about the order the days come in? Yes, one does. The third rule tells us that Tate doesn't attend on the third day. The word "third" means that there has to be a first and a second day, and words like "first," "second," and "third" have the concept of order built in. In fact, words like these are called ordinal numbers (as opposed to "one," "two," and "three," which are cardinal numbers), which name even contains the word "order". You don't have to know the words "ordinal" or "cardinal" for the LSAT, but you should understand the idea that words like these tell us that order matters in the game. Rules containing words like "before" or "after" or "earlier" or "later" would have told us that the order of the days was important. For example, "Tate can't be assigned to a day earlier than Maria." If a rule had said, "Tate can't be assigned to a session earlier than Maria," we would have known that the order of the sessions was an issue. This might just mean that the order of the days was an issue (maybe the sessions on each day are simultaneous), so that a session on the first day is before a session on the second, or it might mean that the sessions on each day are in a certain order. We would need more information to tell us which. Never assume anything on the LSAT – just rely on the definite literal meaning of words. Now that we know that the order of the days is important, we know that we know something about the days – their order. One of the days is first, another is second, and another is third. We can name the days 1, 2, and 3. Since we know something about the days, and not much about the people or sessions, we'll build our diagram around the days. We write them down in order: 1

2

3

148

Game Six

Now, the next question we ask is, how do the other things – session and people – get matched up with the days? You tell me; it says right in the setup. "Each day, there are three sessions…" OK, that's pretty clear, but what are the sessions? The sentence goes on to tell us that they are "one on hiring, one on investing, and one on regulations." So each day gets one of each kind of session. Let's write that out. We can write the three sessions under each day, or just sort of make a chart, with each session getting a row: 1

2

3

H I R Now, how will the people get matched up with the sessions and days? Is it one person per session per day? One person per day? Something else? I don't know – the setup doesn't tell us. We've got enough of a diagram so far (well, we should add in the names of the people – write them down off to the side), so we can proceed on to the rules.

Step 2: Read the Rules The first rule answers the question we raised at the end of the previous step – how we match up the people to sessions and days. Each person will attend two sessions; no one attends multiple sessions on the same topic, or on the same day. What does this mean? To better understand it, give yourself a concrete example of something that could happen or something that could not happen. M, for example, couldn't attend two sessions on day 1, or attend a session on I twice. Now, we have three people, each of whom will be used twice; so it seems that we'll fill up six of the nine sessions, leaving three empty ones. This is useful to know – when not every space in a diagram will be filled, try and figure out how many empty spaces there are. Here, we have three empty spaces. This last point, about the empty spaces, is actually false, but it is an easy mistake to make. I'll talk more about why it is false, and how to avoid making the mistake, later. I'm going to write this down in two different ways. Since we will use each person twice, I am going to write each of their names twice. That way, each time I put a person into a specific session, I can cross off one of the names; once I have crossed off both, I won't try to put that person in the diagram any more. This is a useful technique: when you will use one of the variable things (the ones that aren't built right into our diagram) more than once, write its name as many times as you will use it. (See The Fundamentals for more on variable things; here, the people are variable because we don't have them built right into our diagram.) We are also going to write down Xs for each empty space. A rule might tell us, for example, that no one attends I on day 3, and we'll put one of our Xs there. We have three empty spaces, so we have three Xs. 1 H I R

2

3

M S T X M S T X X

I'm also going to write this rule down as a rule, so that I don't miss it by accident. I'm going to break it into pieces to make it easier to understand. You might abbreviate these rules a little more than I do (but don't abbreviate to the point of incomprehensibility); I'm

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writing them out more explicitly because I don't want to force you to learn my own idiosyncratic form of abbreviation. Each person goes to 2 sessions. No one goes twice on same day. No one goes to same kind of session twice. If you are curious, here's how I abbreviated the rules for myself: everyone 2 times no 2 times same day no one I H R twice Everyone abbreviates slightly differently, based on how they think. I want you to abbreviate in a way that you find comfortable, and not to have to learn the way that I think, which may not ever be comfortable for you. You don't even have to abbreviate at all – it saves very little time, as long as you write the rules in a clear, easy-to-understand way. You've probably noticed that there are certain areas of the logic games where I just give you guidelines and let you do things your own way – diagramming is one of these, to a certain extent, as is writing the rules. Writing these things down is supposed to help you, which means you have to do it in a way that you are comfortable with, and that depends a lot on your personal history. There is little to be gained by learning a very specific way of doing these tasks (although you can make things somewhat easier by diagramming better, which is why I spend more time talking about it). On the other hand, there are other tasks which will give huge benefits if you do them a certain way, such as answering the questions, and I am very dogmatic about doing these the right way, no matter how weird the right way makes you feel. In these areas, the benefits of doing these tasks right far outweigh the costs of having to learn the methods. I'm going to break the next rule into two rules, one about Maria and one about Suki. M doesn't go to I. S doesn't go to I. I abbreviated these as: M not I S not I The next rule is quite simple. T not on 3 The last rule is somewhat surprising. It tells us that we can't have more than two employees per session. The word "given" means the same as "specific," and it tells us that we can't have more than two employees in a specific instance of the session (such as H on day 2), as opposed to "type of session" or "topic," which would be about all the Hs or all the Is. But I (honestly) never even thought that we could have more than one employee per session, much less more than two. Let's write this rule down and then we'll think about what it tells us. Not more than 2 people per session

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If we can't have more than two people per session, that means that we could have just two (or one or none). This means we can double up employees in a single session. Earlier we thought we'd have to fill six sessions, since we have three people and are using them twice each. This meant that we'd have three empty spaces, which we signified using Xs. Now we can double up people, which means we could have a lot more empty spaces (if everyone went to a session with someone else we'd only use three sessions, so we'd have six empty spaces), although we don't have to, because we don't have to double up. Let's erase those Xs, because we don't know how many we have to have, and I don't want to confuse myself later on. Now, what lesson do we learn here? Never assume anything that you weren't told, but we already knew that. More specifically, never assume that a space has to be filled unless you are told. Now, how could we be told that a space has to be filled? One way would be for the game to tell us that we were going to put things in spaces, one per space (see Game One). Another would be for the game to tell us that things were going to get matched a certain number of times. For example, in Game Two, we are told that each language is learned a certain number of times, so we create that number of spaces for each language. A game could also tell us that we couldn't have ties, or couldn't have more than one thing per area (unlike this game), which would tell us how many spaces were needed – if there are five people, and no ties, then five spaces are needed. A game could also tell us that we are going to order a certain number of things, and that the number of ordered spaces was equal to the number of objects. For example, the game before this one in LSAT 39 says "Eight files will be ordered from first to eighth." You couldn't have an eighth file if you didn't have seven files in order in front of it. One last point. We use the blank "__" to signify a space that has to be filled. Here we haven't put any blanks in our diagram, because we don't know which spaces will be filled and which won't (also, we'd have to put in nine blanks, which would take too long, so we wouldn't use blanks even if we were filling all the spaces – we only use blanks to help us, not because we have to). Let's summarize: the rules here told us that we were going to match people to sessions on specific days. The rules reminded us that we might put people together. So the rules really help to determine how we diagram this game. When in doubt on how to diagram, look at the rules. So, here is our original diagram (in its final form) and our list of rules: 1 H I R 1. 2. 3. 4. 5. 6. 7.

2

3

M S T M S T

Each person goes to 2 sessions. No one goes twice on same day. No one goes to same kind of session twice. M doesn't go to I. S doesn't go to I. T not on 3 Not more than 2 people per session

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Step 3: Answer the Questions Here is the order in which you should do the questions: Question Number 8 10 11 7 9 6

Question Type If If If What can't be true? What can't be true? What is the maximum number of…?

Question 8 The question tells us that two (no more, no less, that's what exactly means) sessions on day 3 are attended. Since we don't know which sessions they are, let's make a note of that, something like 2 sessions on 3 Be careful that you don't write "2 people on 3," because that might be false. Two sessions are attended, but they can each be attended by more than one person. Now let's look at the rules, and see if this tells us anything. We're looking for rules about day 3, since that's what we have information on. Rule 6 tells us that T doesn't go on day 3, so the sessions that are attended have to be attended by M and S. Now that we've learned something new, we go back and look through the rules again (remember, every time you learn something new, go back through the rules and see if that leads to more information). We want to see what we know about M and S – we're always looking to use our new information. Rules 3 and 4 tell us that M and S can't attend a session on I. Since M and S, and not T, are attending on day 3, and M and S can't attend I, I can't be attended on day 3. But this question tells us that two sessions have to be attended on day 3; what will they be? They can't be I, so they have to be H and R (the only two sessions left). So we can put this in our diagram by drawing blanks in those spots, to tell us that we have to put someone there, and put an X in the spot where no one can go. I'm also going to jot down M and S under day 3, to remind me that they will be the ones to fill those spots. We don't put the M or S in either spot – at the beginning of an If-question, before we look at the answers, we only write what has to be true. This is because we will use this diagram for every answer, so we don't want to prematurely eliminate situations that might be possible. 1 H I R

2

3 M S T __ M S T X __ M, S

Go through the rules again; nothing much more jumps out at me. Now we want to look at the answers. This is a "What must be true?" question, so we'll test the answers out by trying to do something other than what the answer describes.

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Answer A Now, what is something other than "exactly two"? (See "If… then…" Rules and Negations.) More than two or fewer than two is different from "exactly two." Let's try to have fewer than two sessions attended on the first day. If this doesn't work, we can try more than two. To have fewer than two sessions attended on the first day, we want to put as many people as we can in the second day, since they have to go somewhere and the third day is filled. Let's start by putting in our second M (the one not under day 3). Look at the rules and see where this M can go. Rule 2 tells us that M can't go on day 3 twice, and rule 3 says that it can't go to the same session twice. Well, we don't know where M went on day 3, so we don't know where it can't go on the other day. Let's just put M in H and S under R to make things easier on us conceptually (it's so hard to think about them without putting them someplace specific); I'll put a star next to them because they don't have to go in these places. 1

2

H I R

3 M* X S*

M S T M S T

OK, now we know that M can't go under H again. We also know that M can't go under I (rule 4). So let's put M under R on the 2nd day because we are trying not to put people on day 1 (with a star because I could have put M someplace else). 1 H I R

2 M*

3 M* X S*

M S T M S T

Now on to S. Where do we put the second S? Well, checking the rules, similar rules apply to S as to M. So let's put S on the 2nd day, under H, since we can't put it under R again. 1 H I R

2 S* M*

3 M* X S*

M S T M S T

Now let's think about T. Looking at the rules, the only rule about T is that it can't go on the 3rd day. Let's put a T on the 2nd day, since we are trying not to put many people on the 1st day (so as to test this answer). We could put it anywhere on the 2nd day, but why not put it under I, since the space is empty (with a star as well, since this was a pretty arbitrary decision). 1 H I R

2 S* T* M*

3 M* X S*

M S T M S T

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Now for the last T. It can't go on the same day as the other T (rule 2), and day 3 is booked up, so we put it on day 1. Check the rules to see where it could go; as long as it doesn't go on I again, we can put it anywhere. H is the first open space, so I'll put it there. H I R

1 T

2 S* T* M*

3 M* X S*

M S T M S T

This all works, so what does this tell us about the answer? It's a "What must be true?" question, so… that's right, since this works, the answer is wrong (because something other than what the answer says can be true, which means that the answer doesn't have to be true). Cross off answer A. Let's see if this diagram allows us to eliminate any other answers. Does it give a situation different from that described by any other answer? We don't have exactly two sessions attended on day 2, we have more, so B doesn't have to be true. Cross off B. C looks like it might have to be true, since we don't have M and S together in this diagram. D and E look fine as well, since M and T are not together, and T does indeed attend an I session. We are going to have to test these out ourselves. By the way, in the course of doing this diagram, you may have noticed some deductions. First, T has to attend sessions on days 1 and 2 (since he can't go on day 3). Second, the I session on day 3 will never be attended (the rules say only M or S go on day 3 (rule 6) and M and S don't attend I (rule 4 and 5), and these are general rules, not specific to this question). However, we don't know that M and S have to go on day 3 – that information was specific to this question. If you think that M and S have to go on day 3, I'll bet you that you can draw a good diagram in which they don't – try it out. Here's one that works (and it isn't the only way to do it): H I R

1 SM T

2 T

3

M S T M S T

SM

Now, you shouldn't actually have tried that out on the LSAT – it takes too long. The point is that if you want to make deductions while you do the questions, you should be careful not to use information that comes from the "if" parts of If-questions. If you noticed these deductions, feel free to write them into your diagram, or in your list of rules. If you didn't, don't worry too much. Answer C We test this out by making M and S attend a session together. We already know they both go on day 3; can they be together on day 3? Well, according to the diagram we drew when we started this question, we have to fill two sessions on day 3, and M and S both have to be used. We can't double them up if we want to fill these two spaces (otherwise we'd have to use one of them twice, and we can't use someone twice on the same day, according to rule 2). So we have to try and put them together on a different day. It'll be helpful to know which sessions M and S attend on day 3, so, as we did before, we just put them in sessions, and put stars next to them, since we don't know which exact sessions they have to attend.

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Game Six 1

2

H I R

3 M* X S*

M S T M S T

Now, we want to put M and S together. We already know they can't go together on day 3, so let's try to put them together on day 1. Let's put them both in H on day 1 (we'll put a star next to them so that we can move them if we have to). Now that we've put M and S into definite places, go through the rules. Rule 3 tells us that M can't go in H again, and S can't go in R again. We want to put M and S together. Where could they both go? They can't both be in H or R, so they'd both have to be in I. Put them in I and check the rules. This breaks rules 4 and 5. There is no place to move the pair that will make this work. Cross off this diagram and the last one, since they break the rules. What have we just learned about this answer? It must be the right one, since we can't make anything different from what the answer says work. Answer C is the answer. Question 10 Another If-question. It tells us that all the sessions on the first day are attended. It doesn't tell us by how many people, so we should ask if they can be attended by more than one person. Well, can they? How many people are there? Three. And there are three sessions on that day. By this point we probably remember rule 2 by ourselves, which tells us that people can't attend more than one session per day. So each person only attends one session, at the most, on day 1; since all three sessions are attended, everyone must attend only one. Let's put that in our diagram; again, we use blanks to say "Someone goes here": H I R

1 2 __ __ __ MST

3

M S T M S T

Now let's go through the rules and see what we can learn. We've already considered rules 1, 2, and 3. Rules 4 and 5 tell us that M and S don't attend I; this leaves only T to attend I, which we should note in our diagram. H I R

1 __ T __ MS

2

3

M S T M S T

Rule 6 tells us that T doesn't go on day 3; this means that the second T has to go on day 2 (but we don't know where). H I R

1 __ T __ MS

2

3

M S T M S T

T

Go through the rules one more time; there is at least one more small thing you can figure out, but I'm not going to tell you what it is. It isn't crucial, and it isn't the sort of thing that

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you have to be able to catch, so let's practice how we do LSAT questions when we can't quite figure everything out. This question asks "What must be false?" which is the same as "What can't be true?" We'll try out each answer and see if it will work; if so, we cross it off. Answer A Let's try to put them together on day 3 and see if we can make this work. We don't know quite where they should go on day 3, so where do we put them? What do we do when we want to put someone someplace, but we don't know where? Put them in the first available space and mark them with a star. H I R

1 __ T __ MS

2

3 M S T MS* M S T

T

Now we try to make the diagram work. We have to put in one more M and one more S. Our diagram tells us that they have to go in day 1. Where can we put them? Look through the rules. According to rule 3, neither M nor S can go in H on day 1, since they are already in H on day 3. This leaves no one to go in H on day 1, but we have to have someone there. How do we know? We have a space there, which means "Put someone here," and we trust our notes. This won't work. Since M and S are starred, we have to see if we can move them someplace else. Rule 4 and 5 tells us they can't go in I; can we put them in R? If you aren't sure, try it out. You should see that they can't go there, for the same reasons that they couldn't go together in H (we wouldn't be able to put anyone in R on day 1, and we have to). This will never work, so this (answer A) is the answer. Cross off the diagram. By the way, you could have gotten this question right without figuring out that T goes in I on day 1. We know only that all three sessions have to be filled on day 1. So we put M and S in H on day 3. This means they can't go in H on day 1, so we put T there. But then no one can go in I on day 1, so this doesn't work. The point? Don't despair if you start doing an If-question and can't figure much out – work through the answers and you still should be able to get it right, just a tiny bit slower. By the way, the other small thing you could have figured out before looking at the answers is that I on day 2 and I on day 3 are going to be empty. Totally useless, but you could have figured it out just by looking at the rules.

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Question 11 The question tells us that M and T are on day 1, and that they are the only people on day 1 (which means S isn't on day 1). Let's write that down and look at the rules to see if we can figure out where on day 1 they go. 1

2

3

H I R

M S T M S T

MT no S Rules 1 through 3 don't tell us much, except that M and T will only attend one session each on day 1. Rule 4 tells us that M won't attend I (T certainly could, but doesn't have to – there's no reason anyone attends I on day 1). Rules 5, 6, and 7 are likewise not very helpful. So let's look at the answers. The question says "could be true EXCEPT," so we know that the wrong answers can be true, which means that the right answer can't be true. Answer A M and S can't attend 2 sessions together. We don't even have to diagram this. M and S only attend two sessions each. One of the sessions M attends is on day 1, and S doesn't attend a session on day 1. So one of the Ms won't be with an S. That leaves only one other M, which might go with an S. One is not exactly two, so this is not possible. This is the answer. Question 7 "Must be false" means the same as "What can't be true?" This means that the wrong answers can be true. We'll test the answers out one by one, but we can use our previous diagrams to eliminate answers. We only have one previous diagram that didn't break a rule, which is the diagram for 8A. This diagram allows us to eliminate answer B, since the diagram for 8A shows S on only the last two days. If you made the deduction I talked about in question 8 (see the boxed text in question 8, answer A), that session I on day 3 can't be attended, as you went through the answers you would have noticed that E can't occur, so E is the answer. However, for those of us that didn't make this deduction, let's work through the other answers. Answer A Let's try to put M on just the first two days. By this point you might remember that M can't go in I; if not, skim the rules to see what we know about M, and you'll see that rule 4 says M can't go in I. So we'll put M in H and R; it doesn't seem to matter which session goes on which day, but I'll put a star next to M just to be cautious. H I R

1 M*

2 M*

3

M S T M S T

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Now let's put in the Ss. We can put them anywhere we want, but it's easiest to put them in the first available spaces. Here those are in H and R, with M (since two people can go together, spaces with one person in them are still available). H I R

1 2 M*S*

3

M S T M S T

M*S*

Now let's put in the Ts. The first available spaces are in I on day 1 and H on day 2. H I R

1 2 3 M*S* T* T* M*S*

M S T M S T

This works, so we can eliminate this answer. We can also use this diagram to try and eliminate other answers. Fortunately, it helps us eliminate C (we have two people, M and S, attending a session together on day 2). If it didn't, we could test out C, which would be easy to eliminate. This doesn't eliminate D, because we have two sessions attended on day 2. We've eliminated B from previous diagrams, so let's look at D. Alternately, we could have put S on days 1 and 2, in R and H. H I R

1 M*

2 S*

S*

M*

3

M S T M S T

Now let's put in the Ts. Rule 6 tells us that T can't go on day 3, so I'm going to have to put T on days 1 and 2. Let's just double up T with M on each day (T is going to have to double up on at least one of the days, since it can't go in I both times). H I R

1 2 MT* S* S*

3

M S T M S T

MT*

This would also have eliminated answer C for us. I'm just showing you this to remind you not to get hung up looking for the "perfect" place to put people when drawing test diagrams. Answer D Let's try to have only one session attended on the 2nd day. That means we'll try to put all but one person on days 1 and 3, so we want to avoid day 2 if possible. Let's start with M, because she is our first person in alphabetical order. Can we avoid putting Ms on day 2? Sure; we'll put M on days 1 and 3. Look at the rules to see where we can put M; rule 4 tells us that M can't go in I. So put M in H and R (since we can't put M in H twice, or R twice), in whatever order you like (since there are no rules specifying).

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H I R

1 M*

2

3

M S T M S T

M*

Now let's put in the Ss. The rules for S are much the same as for M; we could double up the Ms and Ss if we wanted, or we could put them separately, as long as we avoid day 2. Let's put them with M, since these are the first available spaces. H I R

1 2 M*S*

3

M S T M S T

M*S*

Now we just have the Ts left. Look at the rules and see what we know about T. We know that T can't go on day 3 (rule 6), and we can't put the Ts on the same day (rule 2). This means that the two Ts go on days 1 and 2. Put them wherever you want, other than H on day 1 (which already has two people in it). H I R

1 2 M*S* T*

3 T*

M S T M S T

M*S*

This works, so we can eliminate this answer. The answer has to be E. Question 9 The question is an EXCEPT question, so it is explicitly describing the wrong answer to us. The wrong answers are possible, which means that the right answer is impossible. This is a "What can't be true?" question. Let's use our previous diagrams to test it. We now have diagrams from 7A, 7D, and 8A. Answer A What does this mean? It means that every session with people in it (since there will be a few not attended at all) has exactly one person at it, not two. If it said "Every session is attended by exactly one Capital employee," it couldn't be true, since we don't have enough people to fill all the spots; to avoid being so easy, it specifies that it is only concerned with the sessions that are attended at all. Is it possible to have no spots with two people in them? Sure, we see this in 8A. Eliminate this answer. Answer B What does this mean? It means that there are no sessions with just one person in them. Well, do we see this in a previous diagram? No, so skip the answer. Answer C We can eliminate this using the diagram for 7A or 7D. Answer D We don't see this in a previous diagram, so skip the answer.

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Answer E We don't see this in previous diagrams (unless you'd diagrammed 7A differently; see the boxed text in 7A). We have to skip this answer. Notice, by the way, that dumb luck factors in a little in eliminating answers. Some of our choices in diagramming are a little arbitrary, and if we are lucky then these will give us diagrams that eliminate a lot of answers. If we had diagrammed 7A differently, we might have been able to eliminate E, or maybe we'd be able to eliminate D, or some other answer on another question. This is nothing to worry about; there is no way to predict the kind of diagrams that will be helpful later on, so don't even bother thinking about this when you have to make a random decision in trying things out. Now we have to go back and test out answer B. We want to make a diagram in which everyone is paired with someone else. Let's try it out. I have no idea who I should be pairing up, so I'll just start pairing people up in order. Let's start by pairing up M and S; we'll put them in the first possible position. Since this is totally arbitrary, I'll mark it with a star. H I R

1 2 MS*

3

M S T M S T

Skim the rules. We now know that M and S can't be picked on day 1 again. We can put them together on day 2. H I R

1 2 MS*

3

M S T M S T

MS*

Now there's no one to pair with T, and T can't pair up with himself (rules 2 and 3). Hmm… so we don't want to pair up S and M twice. Let's pair M with T instead. They have to be paired on day 2, since M can't go on day 1 twice, and T can't go on day 3; and they have to go under R, since M is already in H once, and can't go in I. So they have to go in R under 2, and they don't get a star (poor them). H I R

1 2 MS*

3

M S T M S T

MT

Cool, now we can pair S and T. But where would they go? S is already on day 1, and T is on day 2; T can't go on day 3, so there is no place to put them. Hmm… go back to the last place we have starred. Maybe we shouldn't have paired M and S on day 1? I don't see that it would matter where on day 1 they went, and I don't see how it would help to put them on day 2, so let's put them on day 3. 1 H I R

2

3 M S T MS* M S T

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Alright, now we know we can't pair M and S again and make this work (because no one will go with T, as we saw above), so we'll pair M and T. They have to go in R, since M can't go in H again and also can't go in I. Let's put them in day 1 (day 1 or 2 won't make a difference). 1 H I R

2

3 M S T MS* M S T

MT

Now we can pair S and T. But where do they go? S can't go in H again, or in I, so it would have to go in R. But M is already in R. This won't work either. By this point, and maybe before it, you should have realized that this answer won't ever work. There is still one change we can make, which is not pairing M and S at all, but that just means we'll have to pair only S and T, which leaves no one for M. As long as we pair M and S once, we see that we can't make the diagram work, no matter where we put M and S. Putting them under R, rather than H, won't make a difference; the same rules govern both H and R, so if it won't work in one place, there is no reason why it would work in the other. Since this won't work, it (answer B) is the answer. This may have seemed like a lot of work, and I agree that it was. Once in a while you'll eliminate all but two answers. We really should have tested out D, which would have been much easier (see Picking the Answer to Test under Intermediate Techniques), but I thought it would be a good learning experience to test B. Question 6 A maximum number question; look at your previous diagrams and see what is the largest number of sessions attended in any of them. The diagram for 8A has 6 sessions attended. We can eliminate A through C, since we know that these aren't the largest possible number of sessions attended. The only question is if we can have seven sessions attended. Think about it. Well, we only have three people, who attend two sessions each, and two times three is six. A session has to be attended by someone, so I don't see how we can have seven sessions attended. E can't be right, so D is the answer. This is the sort of thing they throw in to a) confuse people who don't understand the rules, or b) waste the time of people who don't have the confidence in themselves to eliminate ridiculous answers, and have to test out things they already know to be true or false.

Summary This game seems odd on its face, but I think it just reinforces the importance of taking the setup apart piece by piece and applying the skills we have already learned to construct a diagram. Once you have a diagram, you have to understand the rules; that requires making the rules concrete – thinking about how they apply to the specific people in the game – but not adding anything of your own. Review the rules to this game and think about why we shouldn't assume that each person attends a session by themselves (before we see the last rule), and when on other games you should or shouldn't assume this.

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The questions on this game test your ability to make test diagrams; the questions don't give you a lot of guidance, which means that you have to be confident enough in yourself to just make arbitrary decisions, and that you have to know how to modify your diagrams when these decisions don't work out. The questions also test your understanding of LSAT phrases like "exactly," and "or more." If you feel comfortable with this game, you are in pretty good shape for the LSAT – the game is challenging, and draws upon almost every skill we have learned so far. Since the game and its questions are so open-ended, it really tests your ability to be methodical and not jump to conclusions.

What Do I Do Next? Same as at the end of the previous chapter: take a break. Then look over your notes and think about how we applied both the fundamental and the intermediate techniques to this game. Then, when you feel ready, go back and do this game with no notes. By this stage you should have memorized the fundamental skills. By that I mean you should know the techniques for diagramming and how to do every kind of question, including when and how to use previous diagrams and how to eliminate answers on every type of question. If you haven't memorized these things, you need to make up some flash cards and be working on them. Once you've done this game on your own and feel comfortable with it, go on to Game Seven.

Answer Key 6. 7. 8. 9. 10. 11.

D E C B A A

162 Game omitted from electronic version of book.

Game Seven

Game Seven

163

Game Seven (From LSAT 40) Now let's take a look at a game that doesn't seem at first to fit what I've told you, and see how we apply our fundamental skills to it.

Step 1: Read the Setup/Draw a Diagram Before you take a look at the setup paragraph for this game, I want you to think about how we diagram games. What do we look for in every game when we want to diagram it? Once you've remembered and thought about this, read the setup paragraph and think about how you might diagram this game. I've told you that every game involves two or more types of things or characteristics that you match together. What are the two types of things in this game? Well, we have cities. What else do we have to think about? We have connections: we are trying to assign connections to pairs of cities (a connection can't be with just one city, right?). So here are our two types of things: connections and cities. Which do we know more about? At this point I don't think we know much about either, so I'm just going to write down that these two things exist: Connections

Cities: H M P T V

Not a very exciting diagram, but what else is there to write down? A couple of things to remember: connections are between two cities, and every city gets connected to some other city. Notice also that the setup doesn't say that there is a difference between H being connected with M and M being connected with H; in fact, it tells you that cities are connected with each other if there is a flight between them, so if there is a flight between H and M, in either direction, these two are connected. There's another way to diagram this game (well, there are probably a few other ways to diagram this game, but there's at least one other good way to do it). Many people find this easier to use, so I'll put it out for you to look at. I'll also illustrate how to work with this diagram alongside our other diagram as we go through the questions. The game involves connecting cities, which you would normally do on a map. So we'll draw a little map, and connect the cities on that. Since we don't really have any guidelines as to how the cities are arranged, we'll just arrange them roughly in a circle. H

M

V

P T

As the cities get connected, we'll draw lines between them. If a city can't be connected anymore, we will cross it out. Now, should you go out of your way to memorize this type of diagram? No, because this sort of game is pretty rare: there haven't been any other games like it on LSATs 31 through 42 (the LSATs released from 2000 to the time this book was written), although the fourth game on LSAT 33 has a slightly map like diagram as well. But you should learn this lesson: if you see a way to diagram a game that seems easier to you, use it. But don't spend a lot of time looking for alternate diagrams, because it isn't worth it.

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Game Seven

lesson: if you see a way to diagram a game that seems easier to you, use it. But don't spend a lot of time looking for alternate diagrams, because it isn't worth it.

Step 2: Read the Rules Before we read the rules we have been given, I'm going to write down something we were told in the setup, because it seems like a rule. I want to write down that every city needs to be connected to at least one other city. Every city connected at least once Now let's go through the rules. You should know how to do this by now, so I'm only going to go into detail in places where we see something new and/or difficult. M connected only one other city The word "exactly" in that rule tells me that M is connected once and only once. H not connected with T This next rule has the word "any" in it, which means that it is an "If… then…" rule; so we have to write it and its contrapositive. If a city connected with H, then that city is connected with T If not connected with T, then not connected with H The next rule is also an "If… then…" rule: If P connected with T then P not connected with V If P connected with V then P not connected with T And here is our original diagram with the complete list of rules: Connections 1. 2. 3. 4. 5. 6. 7.

Cities: H M P T V

Every city connected at least once M connected only one other city H not connected with T If a city connected with H, then that city is connected with T If not connected with T, then not connected with H If P connected with T, then P not connected with V If P connected with V, then P not connected with T

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Step 3: Answer the Questions Here are the questions, and their types, in the order we should do them in: Question number 11 12 14 15 17 13 16

Question Type What can be true? If What can be true? If If What can't be true? What is the maximum number of…?

As we go through the questions, you will have to look through the rules over and over again. I am going to assume that you know how to do this by now; instead of walking you through every rule every time, I will just point out rules that are relevant (and some that are irrelevant in interesting ways). I do this here to make these explanations easier to read and follow. Understand, though, that each time I do this, it is because I looked through each of the rules one by one, and I'm just skipping the ones that obviously don't apply. Question 11 Although the question contains the words "complete and accurate list," it says "Which… could be a complete and accurate list…" which makes it a "What can be true?" question. The words "complete and accurate list" tell us that each answer is supposed to list all the connections; if one of the connections in the list won't work, or if another connection is required, the list is bad and the answer is wrong. We go through the answers one by one, trying to see if they follow all the rules. Answer A Rule 1 says that all the cities must be connected at least once; well, this list includes all the cities, so that is fine. Rule 2 tells us that M can only be connected once, and it is. Rule 3 says that H can't be with T, and it isn't. Rule 4 says that if a city is connected with H, it must be connected with T as well. H and V are connected, and V is also connected with T, so that's good. No one else is connected with H. Rule 5 says if someone is not connected with T, they can't be connected with H, and that is fine – only P is not connected with T, and it isn't connected with H either. Rule 6 is irrelevant, because P is not connected with T (remember, ignore "If… then…" rules when the situation described in the "if" part doesn't occur). Finally, we have rule 7. P and V are connected, and P is not connected with T. So this is the answer. We should copy this diagram down in our own writing so we will remember that it is a potential situation, and we can use it on later questions. Here it is using both diagrams (although you should only use one or the other): Connections H and V M and T P and V T and V

H

M

V

P T

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Question 12 Copy down our original diagram and plug in what we have been told. Here we are told that P will be connected three times (exactly), so I'm going to put three Ps in the "connected" section of my diagram and cross P out, so that I won't try to use it again. In the alternate diagram, I'll just make a note next to P that it has to be connected three times. Connections P P P

Cities: H M P T V

H

M

V

P(3) T

Look through the rules. As you skim through them, nothing much should catch your eye until you get to rules 6 and 7 (because rules 1 through 5 are about cities other than P, but we only know about P here). We are told that if P is connected with V, it can't be connected with T; and, if P is connected with T, it can't be connected with V. So P can't be connected to both of these. Why does that matter? P has to be connected to three cities. What does this tell us? I'll let you think about that for a bit, and go on to look at the answers. There is a deduction to be made here, but it might not jump out at you. I'm going to answer the question without making the deduction, and then with making the deduction. There will be a lesson learned, I hope. Before we look at the answers, we need to know what the question is asking. It is asking for a pair of cities that can be connected. So we'll try each answer out and see if it can work. Answer A Try connecting H and M. Connections P P P H and M

Cities: H M P T V

H

M

V

P(3) T

Go through the rules. M can only be used once, so we can cross M off. Keep on looking. Rule 4 tells us that any city connected to H must also be connected to T. So M must be connected to T. But we crossed M off; it can't be connected again. This isn't possible, so we can eliminate this answer (and cross off the diagram too). By the way, we might notice from this that H and M can never be connected. Answer B Try connecting H and V. Connections P P P H and V

Cities: H M P T V

H

M

V

P(3) T

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Go through the rules again. Rule 4 tells us that V must be connected with T. Connections P P P H and V V and T

Cities: H M P T V H

M

V

P(3) T

Look through the rules again. No other rules obviously apply. We still need to figure out the three cities to which P is connected. Let's try putting cities in and see if we can make it work. We need to use each city (rule 1), so let's make sure we use cities that haven't been used yet. Only M hasn't been used, so connect it to P. I put a star next to this to mark that this is a decision I made, which wasn't forced on me by the rules. I'll use a dotted line instead of a star in our alternate diagram to show a line that was optional. Connections *P and M P P H and V V and T

Cities: H M P T V

H

M

V

P(3) T

I crossed M off because it can only be used once. Who else can we connect P with? Well, how about H and T, since they are the first cities in alphabetical order that are still available? This doesn't break any rules – P is connected to both H and T, in accordance with rule 4, and we know that P can't be connected to V if it is connected to T, but it isn't, so we're OK. Connections *P and M P and H P and T H and V V and T

Cities: H M P T V H

M

V

P(3) T

This works, so this (answer B) is the answer. OK, now what was the deduction we could have made? It was that P will have to be with M, H, and T – it has to be connected with three cities, and it can't be connected with V; if it is connected with V, it can't be connected with T (rule 7), and thus it can't be connected with H either (rule 5). This wouldn't fill all of P's spaces, so V is out, which only leaves M, H and T. Now, how much easier does that make this question? Not much – you arrive at the same place by just working through the answers. Often times you will look at an If-question and feel that there is a deduction in there someplace; but if it doesn't come to you, just work through the answers. That may not feel like the fastest way to answer the question, but it sure beats staring at the page hoping for inspiration. I never noticed this deduction when I first did the game; it wasn't until I started typing up this chapter that I realized a deduction could be made here. Lesson? Even the best LSAT takers often don't see or use deductions.

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Game Seven

takers often don't see or use deductions. Question 14 It's a "What can be true?" question, so try each answer out until one works. Answer A Let's test it out: connect M and P in a diagram and see if it works. Also, note that no one else is connected with M and P. Connections M and P no more M and P

Cities: H M P T V

H

M

V

P T

Notice that not only did I cross off M and P in my list of cities, I scrawled a little note to myself in the connections column that I can't use M and P any more; I know that I sometimes don't notice that I've crossed things off, so I make sure I can't forget what the answer tells me to do (in the alternate diagram, I just crossed off both cities to note that I couldn't connect them any more because it's harder to miss). Let's see if we can make this work. Rule 1 tells us that every city must be connected at least once (this, by the way, is the type of rule you are likely to remember without looking at it when you do a game; see Intermediate Techniques). So we need to connect H, T, and V with someone. We can't connect H and T (rule 3), nor H with M or P (because they are crossed out), and H has got to be connected to something, so H and V have to be connected. This tell us that T and V must be connected (rule 4). Connections M and P no more M and P H and V T and V

Cities: H M P T V H

M

V

P T

Look through the rules again; we're following all of them. This works, so this (answer A) is the answer. Notice – this started as a difficult-seeming game, but we've just had three easy questions in a row. Question 15 Draw a new diagram and plug in what we've been told. Connections T and P no more P

Cities: H M P T V

H

M

V

P T

Notice that I wrote "no more P"; question 15 tells us that P is connected only with T, but it doesn't tell us that T isn't connected to anyone else (it doesn't say "P is the only city

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169

connected to T."). Look through the rules and see if any of them apply. Well, we've got to connect H, M, and V to other cities (rule 1). Rule 7 also applies, because P and T are connected, but it doesn't tell us anything we haven't already written down – we already know that P won't be connected with V. See if we can find an answer that can be true. Answer A This answer means we don't get to connect T with anyone other than P. See if we can connect up the cities that are left (H, M, and V). Connect H first (because it is first in the alphabet). If H connects with M, M has to connect with T (rule 4), but only P connects to T according to the answer. H can't connect with P because P is crossed out. H and T can't connect (rule 3). And H and V can't connect because then V could have to connect with T, but only P is connected with T here. H can't connect with anyone, so this answer is impossible and we don't have to think about the other cities at all. Answer B This means V is only connected once. Note that in your diagram. Connections one V V and

Cities: H M P T V

H V (1)

M P T

Let's try this out. Who is going to be connected with V? Work it out; I'll wait. OK, H won't work, because if H is connected with V, V also has to be connected with T (rule 4), but we want V to be connected only once. Try connecting V with M. Mark M with a dot or star (or use a dotted line) because this is something we are trying out, which we don't know has to happen. If the diagram doesn't work, we can try to change this. Connections one V V and *M T and P no more P

Cities: H M P T V H V (1)

M P T

Go through the rules. M is connected only once (rule 2), so cross M out. Now we have to connect H with someone. H can't be with M because M is crossed out. Can it be with P? No, because we wrote down "no more P." H can't be with T (rule 3). So if V is connected with M, there is no one to connect H to. Cross off this diagram.

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Since the diagram didn't work, let's go back and change what we have starred. Who else can we connect V with? H didn't work, M didn't work. P is out ("no more P"). Try V and T. Don't star T, because this is the last person left – it is forced on us by the rules (it's OK if you do put a star there, because then you'll say, "Who can I try next?" and realize that no one is left, so you'll arrive at the same conclusion). Connections one V V and T T and P no more P

Cities: H M P T V H V (1)

M P T

Who goes with H? No one except M. Will that work? If M goes with H, M has to go with T (rule 4), but M can only be used once (rule 2). This won't work. There is no one else to try to connect V to. V can't be connected with just one city, so this answer is wrong. Notice that we had to do a couple of diagrams to test out this answer. That happens, and it can be slightly confusing, as you might lose track of what it is that you are trying to figure out. That's why we put stars next to things we are trying out that we think may or may not work. It lets us know what we can try to change. It's important to make these changes systematically, in a certain order. Notice that I tried M before T – it's easiest to try things out alphabetically, or in numerical order. Once we have gone through the numbers or the people, and none of them work, there is nothing else to try and we know that what we are trying won't work. It's OK to glance back at the answer you are testing out to refresh your memory. Just think of how much more confusing this would be if you were trying to do it all in your head. Another thing: by this point you've probably noticed that M will never go with H – you've seen concrete examples of M not being able to go with H, and you understand the rules well enough to see why it is impossible. So this is a useful deduction, and you can write it down as a rule. See the section on Intermediate Techniques. Answer C Make a note that H is connected twice: Connections T and P no more P H and H and

Cities: H M P T V H(2) V

M P

T

The question is, who are these two cities going to be? By this time we know that M can't be one of them. P can't be one of them – that limitation is built into this question. So they have to be T and V. But, going through the rules, we see H can't be connected with T (rule 3). This is clearly impossible. Cross out the answer and the diagram and move on.

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Answer D T is already connected once, so note that it has to be connected again. Connections T and P no more P T and

Cities: H M P T V H

M

V

P T(2)

So, what is this mystery city that is connected with T? It can't be H (rule 3). Can it be M? Try it out. OK, finished? You should have seen that it won't work. Whoever you connect to H will have to be connected to T, which will give T too many connections. So T can't be connected with M. Let's try someone else; only V is left. Connections T and P no more P T and V

Cities: H M P T V

H

M

V

P T(2)

Now we need to connect someone to H. It can't be M, P, or T (we're only using T twice, remember?), so it must be V. I don't dot or star this connection, because this is forced upon us by the rules. Go through the rules – this seems OK so far, because V is already connected to T. Connections T and P no more P T and V H and V

Cities: H M P T V

H

M

V

P T(2)

Now we just need to connect M to a city. It won't be H, P, or T. But M and V can be connected. V is doing a lot of work for us, but there is no rule against it. Connections T and P no more P T and V H and V M and V

Cities: H M P T V

This follows all the rules, so this (answer D) is the answer.

H

M

V

P T(2)

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Question 17 Here we are told that one city is connected to four other cities. This means that the city in question is connected to all the other cities. What city could this be? You work it out, and work it out by looking at each city in turn. OK, here's how I did it. We already know that H can't connect to everyone, because it can't connect to either M or T. M clearly can't connect to more than one city, so M is out also. Could it be P? Look through our rules. We can't have P connected to both T and V (rules 6 and 7), so P can't connect to all four others. T can't connect to H. So the only city left is V; V must be connected to all four cities. This is one of those questions that seems really difficult, but isn't. At first you panic – you say, "I don't know what city this could be!" But there are only five cities, and there is nothing wrong with considering each of them in turn. If that seems like it is going to take too long, then work through the answers. But here, if we are calm and systematic, it all clicks. This is our diagram so far: Connections V and H V and M V and P V and T

Cities: H M P T V

H

M

V

P T

Notice that every city is connected to another city, so I don't need any more connections. There might be others, but they don't have to be here. This is a "What must be true?" question; we can eliminate any answer that doesn't have to be the case. Answer A Well, we can't connect H and M, so this is wrong. Answer B We don't need to connect any more cities than we already have; the diagram that we've created could be the final diagram. So we don't have to connect H and P. Answer C Ahh, a connection between H and V is right in this diagram, so it has to happen. C is the answer. We are done. Question 13 Let's use our previous diagrams to eliminate any cities that we know can be connected. Answer A Well, we don't have to look any further. By this point in the game, having done as much work as we have, we know that H and M cannot be connected. This (answer A) is the answer. Just to satisfy your curiosity, here's how to eliminate the other answers using previous diagrams. Eliminate B with the diagram from 12B. Eliminate C with 12B or 14A. Eliminate D with 15D or 17. Eliminate E with 15D.

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Question 16 This is a "What is the maximum number…?" question. Look at our previous diagrams and see what is the largest number of connections we have so far. The diagram for 12B has five connections, so we know that A is wrong. At this point on the LSAT, you really need to look at the clock. This is the last question in the game, and it's a hard one to answer. I would be very tempted to skip this question, even if I had over a minute left on this game. Just think of what you could do with that time on a different game; it could be much more fruitfully employed elsewhere – you might not even finish this question in a minute, which would mean that that time will be wasted when you move on. In many cases it's better to move on early than to start a hard question that you know you are likely to end up skipping halfway through for time reasons. On this actual LSAT, this would be the last game you did (you'll understand why when you read the Timing section), so skipping this question would be something of a non-issue. Still, the point is relevant to other games. If you did skip this question, you would pick B, since five is the largest number of connections you know is possible. Well, let's try this out. Start with answer E, since it is the largest number of connections you are given. Answer E We need to generate eight connections. We probably don't have any idea what they would be, so let's go through our cities one by one and try to connect them as many times as possible. Start with H – who can it connect with? H can only connect with P and V, so connect them (and cross H off because it can't connect any more). Connections H and P H and V

Cities: H M P T V

H

M

V

P T

Looking at the rules, we see that P and V will have to connect with T as well as H (from rule 4). Connections H and P H and V P and T V and T

Cities: H M P T V

H

M

V

P T

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Now let's move on to M. It can only connect to one city, so connect it to whomever you like (as long as it isn't M). I like P. Since it doesn't matter who I connect M to, I don't bother to mark this with a star; there's no reason to change this later on. Cross M off because it is done. Connections H and P H and V P and T V and T M and P

Cities: H M P T V

H

M

V

P T

Now on to P. We want to connect it as much as possible. It's already connected with H, T, and M. Can we connect it to V as well. Nope (rule 7). Now on to T. It's already connected to P and V. It can't connect to H, and M is done, so there is no one else for T to connect with. How about V? Anyone else for it to connect with? It's already connected to H and T, M has been used, and it can't connect to P because of rule 7. So this is it, we've got all of our connections, and there are only five. We tried to get eight, but we couldn’t make it, and there's nothing here we can change. The answer is B.

Summary What lessons have you learned from this game? Well, the lesson I want you to learn is that no matter how odd they first seem, all games are really the same on the inside. It is impossible for a game not to be a case of matching two or more types of things together. All you have to do is spot the two types of things that the game is interested in and you are in business. Our diagram wasn't terribly fancy or exciting, but it did the job and that is all that matters. I also want to point out a possible variation on this game. We can imagine a case where H being connected to M is different from M being connected to H (e.g., one-way flights). This doesn't make the game any easier or harder; it would just be something that we would need to be aware of. Any other lessons to be learned from this game? No, and that is the most important lesson of all. You already had all the tools you needed to get these questions right. When students do poorly on a game like this it is because they lack the confidence in themselves to just work through the questions. Don't be afraid of games; don't try to approach different games differently. You know how to answer questions on any game you might see on the LSAT; all you have to do is actually apply your skills.

What Do I Do Next? Take a break and then redo the game without notes. Do the game twice, once with each type of diagram, and see how you like them. Make sure you are working through the rules systematically – one by one, in order. Once you've done this game on your own and feel comfortable with it, go on to Game Eight.

Game Seven

Answer Key 11. A 12. B 13. A 14. A 15. D 16. B 17. C

175

176 Game omitted from electronic version of book.

Game Eight

Game Eight

177

Game Eight (From LSAT 41) This is one of the rare games where I want you to do something sort of special for the diagram. I generally dislike teaching students new techniques – if the techniques you already know are capable of dealing with a situation on the test, why learn more? It just makes things more complicated, and crowds your brain. But this is a case where a somewhat unique diagram makes the game noticeably easier, the diagram is not hard to learn, and it is very obvious when you should apply it. So here we go!

Step 1: Read the Setup/Draw a Diagram Read through this game's setup. What makes this game different from other games we have done? Well, the people are sitting in a circle; usually they are in a straight line. Circles have the odd property that they don't have beginnings or ends, so everyone is next to two people. Lines aren't like that. We want to build the properties of circles into our diagram. We could just diagram this in a line, like we usually do, and remember that the people on the ends are next to each other, but making circle diagrams is fun and easy. There is one other thing we want to remember – people sitting in circles sit across from each other. The game tells us that two people are across from each other if they have three people between them on either side. This isn't so shocking; there are eight people, so if I'm sitting exactly opposite from you, half of the other six people should be on my left, and half on my right. We also want to build this aspect of the circle into our diagram. To remember who is across from whom, our diagram is going to have lines connecting each pair of people across from each other. There are four pairs of people across from each other, so we draw four connecting lines.

At the end of each line will sit a person. Now we write down the names of the people, and our diagram is done. FGHIKMOP

One thing to notice is that we have no reason to number the seats – the setup doesn't talk about numbers at all. Should we put numbers in anyway? When in doubt about the setup, look at the rules. They don't mention numbers either (for example, by talking about "the fourth seat," or "the first seat"), so we won't add numbers to our diagram. This means that no seat is any different from any other seat until we start putting people in.

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Game Eight

Step 2: Read the Rules "Across" in the first rule means that there are three people between F and G, on either side, so we include that when we write the rule. F across from G (three between them) The second rule is a little more complicated. It tells us about H's relation to both F and K. It relates H to two different people, so I think we should break it into two rules to make it simpler. One rule tells us that H is not next to F, and the other rule tells us that H is not next to K. Notice that the order is not specified, so, for example, H can't be on F's right or left. We can write these rules about H, F, and K one of two ways: H not next to F H not next to K or no no no no

HF FH HK KH

I prefer the second way – it spells out in a very easy to read way what will never happen. The last rule tells us that I will be next to O, clockwise. We could write this in words, but we would have to put in enough words to make sure we don't misunderstand it later: I immediately clockwise from O I grew up looking at digital watches, so it takes me a moment to visualize what clockwise means. It is easier for me to write this rule in a way that visually represents what I will see in the game. Remember, it is best if the way in which you write rules mimics the way the people will appear in the diagram. I like to write this rule in this way: OI or IO

The little arrows tell me that it will look one way on one side of the circle, and another way on the other side. You don't need to write the rule in exactly this way, because you may not need help thinking about clockwise in the same way I do; the point is that you should find a way of writing rules that you find easy to understand, and that is responsive to how you think.

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Here is how our original diagram and list of rules looks: FGHIKMOP

1. 2. 3. 4. 5. 6.

F across from G (three between them) no HF no FH no HK no KH OI or IO

Step 3: Answer the Questions Here is order in which you should do the questions: Question Number 18 19 20 21 23 24 22

Question Type What can be true? If If If If If What is the minimum number…?

Question 18 Each answer gives us the seating arrangement of half of the table – four people next to each other, in order. We have to test them out and see if they follow the rules. Since these don't give us the seating arrangement of the entire table, we may have to draw a diagram to test them; however, we should first check that the four they tell us about don't obviously break any rules. Answer A This breaks rule 1 – there are only two people between G and F. Answer B This doesn't explicitly break any of the rules, so we have to put this into a diagram and test it out. Since none of the seats are different from any other seats (because they aren't numbered), it doesn't matter where we put the people we are given, as long as we put them in the right order. When two blanks in a game are identical to each other – that is, there are no given differences between them – it doesn't matter if you put someone in one or the other. For example, in Game Two, language Y has three spaces under it. They are all the same – all are under Y – so it wouldn't matter if we put a researcher in the top,

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middle, or bottom one. Here, all the seats are seats, so we can put these people in any four next to each other (keeping this order, of course). This is not a case of not knowing where to put someone, so we don't need to put a little dot or star next to them. In this case, we know any position will work – they are all the same – so there would be no point in putting them someplace else later on. I put H on top and the rest clockwise after H. H

FGHIKMOP

O I K

Now let's go through the rules. Rule 1 tells us F has to be across from G. But this is impossible; none of the remaining seats are across from each other. This answer is wrong. Answer C This doesn't explicitly break any of the rules (it doesn't put O in, but there is room before I for her to fit). Let's draw a diagram and test it out. Again, it doesn't matter where we put anyone, as long as they are in the right order and next to each other, as the question tells us. I

FGHIKMOP

F P M

Now let's go through the rules. Rule 1 tells us that F and G are across from each other. We know where F is, so put G across from her. I

FGHIKMOP

F P

G

M

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Rules 2 and 3 tell us that H can't be next to F, but since F has no open spaces next to her, we don't need to worry about that. 3 and 4 tell us that H can't be next to K, but we don't know where K is yet, so we won't sweat that either. Rule 6 tells us that O will have to be in that spot next to I. That leaves K and H in the last two spots. We don't know which goes where, so put them in and mark them. O

I

K* G

FGHIKMOP

F P

H*

M

Since this follows all the rules, it (answer C) is the answer. Question 19 The question tells us that H and O are next to G. But who is on what side? Look at the rules and tell me. You are right, it has to be H, then G, then O (and then I, from rule 6), in that order clockwise. This is because O has to be on I's right. If O was on G's right, there would be no room for I. We saw in the last question that we can just drop them anywhere in our diagram, so let's do that. H

G

FGHIKMOP

O F

I

I also put F across from G, since that is what rule 1 tells us. Let's go through the rest of the rules. I know K can't be next to H, so I'll write that in too. no K

H

G

FGHIKMOP

O F

I

The question asks me which two people can both sit next to Peter. (I know that both of them have to be next to Peter because it says "Each of whom." If it said "Either of whom," it would be asking for two people who can sit next to Peter, but not necessarily at the same time; remember, its crucial to make sure you understand what the question is talking about before you try to answer it. See the Glossary for a definition of "each" and "either.") I don't know where P goes, but I know he'll have to go in one of the three blank spots. Let's look at the answers.

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Answer A Can P be next to both F and K? Well, we know where F is. There are blank spots on both sides, but if P goes on the right, he'll be next to F and I, not K; if he goes on the left, K can't be on his other side, as we have written in the diagram. So P won't be between F and K. Answer B Can P be next to both F and O? They are too far apart for P to be next to both of them. This is wrong. Answer C This is also wrong; H and I are too far apart for P to be next to both of them. Answer D Well, I know where H is. Could P be between H and K? It looks possible, but let's try it out to make sure. Put P next to H, and then put K next to P. P

H

G

K

FGHIKMOP

O F

M

I

Since M is the only person left, I put him in the last space. Look through the rules; this follows all of them. This (answer D) is the answer. By this point I feel pretty confident that you can handle this game. You've seen how we diagram it, and how we test the answers. Go ahead and try to answer the rest of the questions. Once you've done that, work through the explanations that follow. Question 20 We are told that G is not next to H. We don't know where G is, or where H is, so we can't draw a diagram yet. Just write this down so we are ready to plug it in when we do test this out. no GH no HG This is similar to the last question; we are looking for two people who can be next to M. So to test each answer, we put both people next to M and see if we can make the diagram work.

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Answer A Can F and H be next to M? I don't know what order they are supposed to go in, so I'll try them in one order (mark them with dots or stars), and if that doesn't work I'll try them in the other order (that is, I'll try FMH then HMF). F*

M

FGHIKMOP

H*

Now we go through the rules and see what we can discover. Rule 1 tells us where G goes. F*

FGHIKMOP

M H*

G The question tells us that G and H can't be next to each other, but that isn't a problem here. Go through the rest of the rules. Rules 2 and 3 aren't an issue because F and H can't possibly be next to each other. We know that K can't be next to H, so write that in. F*

M

FGHIKMOP

H* G

no K

We know that O and I have to be next to each other. Put them in someplace. I

F*

O*

M

FGHIKMOP

H* G

no K

I didn't have to put O and I exactly there – I could have put them one space over, counterclockwise. But I have to put them someplace; if this ends up causing problems, I'll move them over. That's why I put the star next to O – to tell me that if the diagram doesn't work out, this is someone I can move.

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P and K are left; there is only one space where K can go, so we put him there, and P goes in the last space. I

F*

M

O*

FGHIKMOP

H* K

G

P

Look through the rules. This follows all of them, so this (answer A) is the answer. Notice that the diagram would still have worked if we'd put O one space over. Question 21 We are told that M and O are next to each other. In what order are they? Look at the rules and figure it out. They have to be MO (then I), in that order, clockwise, because of rule 6. As I mentioned in Intermediate Techniques, some rules stick in your head, and the OI rule sticks in my head. So I know that I'll have MOI. We can put these right into our diagram. M

O

FGHIKMOP

I

The question asks who must be next to F. We don't know where F goes, but the fact that the question asks about her should make us check and see if there are any rules about her. She has to be across from G, and there are only two spots left that are across from each other – the ones next to M and I. So F will have to go in one of those. With that hint, I'm going to let you take a stab at this question. Look at my explanation when you are done. This is a "What must be true?" question, so we test the answers by doing something other than what they say. That is, we don't put the person in the answer next to F. Of course, if an answer obviously can't be true, we can cross it off without testing it. Answer A Well, we know that H can't be next to F from rules 2 and 3, so we don't bother testing this out. Something that can't be true isn't something that must be true.

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Answer B We want to see if F could be someplace other than next to I. Well, we know that F and G have to be across from each other, and there are only two open spots. Put G, rather than F, next to I, and F across from him. F

M

O

FGHIKMOP

I G Now let's go through the rules and see if we can make this work. H can't be next to F, so put her someplace else. Mark her with a dot or star so we know that we can try her someplace else if this doesn't work. F

M

O

FGHIKMOP

I H*

G

Go through the rules again. Rules 4 and 5 tell us that K can't be next to H. But there are no open spots that are not next to H. Does this mean that our diagram is totally wrong? No – go back and move the person we have starred (that's what the star tells us). The last thing we did was to put H where she was. Can we put her someplace else? Not next to F (rules 2 and 3), and not where she is, so how about next to G? That gives K room to go next to F, and P plops in the middle. F

M

K P

O

FGHIKMOP

I H

G

Some of you may have been slapping your foreheads when I put H where I did before, saying "Come on, Brian! She can't go there!" But I wanted to illustrate that sometimes you try things and they don't work. That doesn't mean that your diagram is impossible; sometimes you can change one thing and make it work. So, when a diagram breaks a rule, go back to the last time when you had a choice of where to put something (which you marked) and put it someplace else. If you run out of choices and the diagram still doesn't work, then you know it breaks a rule. I know I've told you this many times before, but it's so important that I'm going to keep on saying it. Back to the question. This diagram works; this is a "What must be true?" question, so what do we know? We know that the answer is wrong. See if you can use this diagram to eliminate any other answers. The diagram has F next to K and M, which isn't different from what C or D says, so we can't eliminate them, but it does show us that F doesn't have to be

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next to P. We can eliminate E, which leaves C and D. We only have to test out one more answer and we'll have found the right one, either directly or by elimination. Answer C We got the previous diagram by putting F next to M, and we saw that K has to be next to F in that situation; there's no reason to keep testing F there because we'll keep getting the same result. Let's put F someplace else and try to not put K next to her. Where else can F go? She can only go next to I (because she has to be across from G). G

M

O

FGHIKMOP

I F OK, now we don't want to put K next to F. G

M

O

FGHIKMOP

I no K

F

So where do we put K? Try putting him next to G. But then H can't go anywhere, because H can't be next to K or F. Try putting him in the middle spot. But then H still can't go anywhere. So this won't work. On a "What must be true?" question, when your diagram won't work, the answer is correct. C is the answer. Question 23 K is across from I; let's put that in the diagram someplace. K

I

FGHIKMOP

O

We put O in as well, since we probably remember she's on I's right. Now let's go through the rules. F has to be across from G. There are a couple of spots F and G could go, so I'm not going to put them anyplace. When you first set up the diagram on an If-question, you only put in what has to be true (because you are setting up something that has to work for every answer); when you test the answers, you can put things anyplace that they can go (because you are only testing that particular answer). H can't be next to K, so I'll put that in.

Game Eight

no H

187

K

I

no H

FGHIKMOP

O

Let's try out the answers. This is a "What can't be true?" question, so we can eliminate any answer that turns out to be possible. We test each answer by putting that person next to O, as the question asks us to. Answer A Put F next to O, and put G across from her. no H

K

no H

G

FGHIKMOP

F I

O

Notice that there is only one space where H can go (the only empty one that doesn't say "no H" in it – see how handy writing "no-such-and-such" can be?), so put her there. no H

K

no H

G H

FGHIKMOP

F I

O

M and P are all that are left, and we don't have any rules about them, so drop them in wherever. M

K

G H

FGHIKMOP

P F

I

O

This works, so this is the wrong answer. Unfortunately, it doesn't help us eliminate any other answers, since Ingrid (who is next to O) is not one of the answer choices. On we go.

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Answer B Try putting G next to O. no H

K

F

no H

FGHIKMOP

G I

O

Go through the rules. H can't be next to F (rules 2 and 3). But that leaves no space for H. H has to go someplace, so this won't work. We can't change anything in this diagram – we've made no decisions so far, just followed rules – so this is the right answer. Cross off this diagram and circle answer B. Question 24 Put K directly across from H, as the question tells us to, and go through the rules. H FGHIKMOP

K Rules 2 and 3 tell us that F can't be next to H (rules 4 and 5 tell us that K can't be next to H either, but that is not a possible issue here). no F

H

no F

FGHIKMOP

K So there are a few spaces F can go in. The rules don't tell us anything else useful, so let's look at the answers. The question wants the minimum number of spaces between G and K (with K clockwise from G). So we try the smallest answer first (A), and work our way up from there. Answer A Our smallest answer is zero. Having zero spaces between G and K means that G and K are next to each other. Putting G right next to K (with K clockwise from G) would put F right across from G, next to H, and that won't do. This is wrong.

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Answer B Let's move G one space over counter-clockwise and see if we can have one space between G and K. Now there is one space, clockwise, between G and K. no F

H

no F

F

FGHIKMOP

G K

Now go through the rules. We have to put OI in someplace. But there are no two spaces next to each other left. This won't work. Answer C Put two spaces between G and K (K on G's left). no F

F

H

G

FGHIKMOP

K

Now let's put in O and I. There are two spots where they can go – in the two empty spaces on the left (between F and H) or on the right (between G and K). Try them wherever you want. Then put P and M in the other two spaces. P*

H

G

FGHIKMOP

O*

M * F

K

I

This works, so we are done. C is the answer. Question 22 We want the smallest number of spaces between I and M (with M clockwise from I). Look at your previous diagrams. The diagram from 19D has M directly to the left of I; there are zero spaces between them, and M is clockwise from I. Since there is no number smaller than zero in the answers, this is the minimum number. A is the answer. We are done.

Summary This game teaches us how to deal with people sitting around in a circle. From time to time you will be presented with other situations that you can't represent by putting things in a

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straight line. For example, you might have houses facing each other along a street, or people sitting in rows. In these cases you will have to draw a diagram that helps you visualize the situation; draw something that is like a map of the situation, or a birds-eye (overhead) view of the area. If people are sitting in rows, make rows in your diagram; if houses are facing each other along a street, draw blanks across from each other. These games are not difficult once you have seen one – just make sure you understand the situation they are describing, then draw a diagram that looks like it.

What Do I Do Next? Take a break. Then look over your notes from this game and think about how we applied the fundamental skills to it. When you feel like you understand the game, take another break, and then do the game without notes. By this stage you should have the fundamentals memorized so well that you can recall them without having to think much. If you still struggle to recall the fundamental skills – how to do questions, or what order to do them in, or how to make diagrams – you need to make up some flash cards and be working on them. Once you've done all that, here is what you will have accomplished: you will be conversant with all the techniques that are most important to your logic games score. In addition, you will be ready to handle the toughest, weirdest games on the test. At this point you will now need to practice what you have learned and turn these skills into habits. Practice games from the recommended list at the end of Game Three, and from the recommended list at the end of this chapter (coming up in a second); do about an equal number from each list. Make sure that when you practice you go through the steps I talk about in the Study Guide – make a short list of the techniques you want to practice, refer to it as you practice, and review every game you do, trying to spot things you might want to do differently in the future. If you don't remember what these techniques are (and you probably don't), go back and reread that chapter. You can only ensure progress by studying properly, and the Study Guide tells you how. Once you feel comfortable with the techniques and the games, go on to Advanced Techniques. You will then start working on timing. You need at least two weeks to work on timing. If you are not comfortable with all these techniques, but you have only two weeks left to work on games (either because the LSAT is in two weeks, or you need to work on other aspects of the test), move on to Game Nine (skip Advanced Techniques). Game Nine through Game Twelve come from the same LSAT, LSAT 38. They are difficult games. I use them to illustrate some of the advanced techniques, but I also show you how to do the games with just the fundamental techniques. Work through those chapters and read the chapter on Timing; follow the instructions therein.

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Recommended Games List I have grouped the games by similarity to each other. You won't be able to distribute the games you do evenly between the two groups, since group 2 contains so many more games, but you should at least do a few from group 1. I also recommend that if you are doing games untimed, try to do games in LSATs from which you have already done games. Once you start working on timing, you will want to be able to do complete LSAT games sections and work on managing your timing through the entire section. When doing this it is important to do games from the same section. Some games have many more questions than others, and each section generally has a balance of long and short questions. Thus, you'll want to have available for practice many games sections that you've never looked at. If you have access to LSATs which are dated but not numbered, there is a chart (LSAT Number to Date Conversion Chart) which gives the date each number corresponds to at the end of the Introduction chapter. Group One LSAT 20 22 33 35 36

Game # 1 3 4 3 3

Answer Key 18. 19. 20. 21. 22. 23. 24.

Group Two

C D A C A B C

LSAT 20 21 21 22 22 23 23 24 25 27 28 30 30 31 31 32

Game # 4 1 4 1 2 3 4 3 3 2 3 1 2 1 4 4

More Group Two LSAT 35 36 37 39 39 39 40 41 43 44 44 44 46 46 47

Game # 4 2 4 1 3 4 2 2 3 1 3 4 3 4 4

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Advanced Techniques Who Should Learn These Techniques? The following techniques can be helpful in many circumstances, but they are not necessary to do well on the LSAT, and there are some people who should not bother learning them. If you are still having trouble with the fundamental techniques I discuss in The Fundamentals – that is, if you often forget steps, or don't always feel comfortable going through the steps – don't bother reading this section; mastery of the basic techniques is crucial for LSAT logic games success, and spending time acquiring that mastery will get you more questions right than spending time learning these advanced techniques. Let's say that you have mastered the fundamental skills I cover in The Fundamentals, but your test date is a week or less away. Don't read this chapter. These skills take some time to learn; if you get to the LSAT and have only half learned them, they may do you more harm than good. What if you have mastered the fundamentals, and have plenty of time before the LSAT, but haven't mastered what I cover in Intermediate Techniques? Spend at least a few practice sessions practicing the intermediate techniques. You don't need to feel completely comfortable with them, but you need to be aware of what they are and how they work. Learning several skills at once makes you slower at learning any of the skills. Once you remember and feel comfortable applying all the fundamental skills, and are familiar with the intermediate techniques, and if you have a couple of weeks before the test, ask yourself if you have reached your logic games score goal (or are very close). If you are already doing as well as you want to on the games, you may not need to learn any more techniques. But, if you have ambitions that you have not yet met, read this chapter and add these skills to your short list. Learn not just how to use these skills, but also when.

Reusing Previous Diagrams – Equivalence Now, raise your hand if you like to use previous diagrams. All of you? Great. Now, there are only two problems that I know of with using previous diagrams: first, that we can't use them on every question, and second, that they don't always eliminate as many answers as we'd like. Well, this technique addresses that second issue. We'd like to eliminate more answers using previous diagrams if we can. Sometimes, when we look back at previous diagrams, we find that the situation we are looking for isn't in any of them. Yet, when we test the situation out, we find that it could have happened, meaning that it could have appeared in a diagram. So why didn't it? Why?! Well, I'm not going to answer that question. But I am going to tell you how to get more use out of the previous diagrams that you have. That'll be nice, right? Here's how it works: some games have certain variable people/things that are equivalent. Remember, the variable things are the ones we didn't build our diagram around; we write them off to the side and put them in blanks when we can. In Game One, the horses are variable. In Game Two, the researchers are variable. In Game Three, the birds are variable. In Game Four, the cars and washes are variable. In Game Five, the medications are variable. In Game Six, the employees are variable. In Game Seven, the cities are variable. In Game Eight, the people are variable.

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193

are variable. In Game Six, the employees are variable. In Game Seven, the cities are variable. In Game Eight, the people are variable. When two things are equivalent, anyplace one can go, the other can go as well. Let's imagine that X and Y are equivalent in some game. We know (because we have a previous diagram) that X can go 1st. That tells us that Y can go 1st too, since the two are equivalent. Or let's say that we have a previous diagram where X is 3rd and Y is 5th. Well, then we know that X could be 5th and Y 3rd – we can just switch them. This potentially doubles the number of diagrams that we have (because you can switch the two in every diagram). Not only can variable things be equivalent, definite things in a game can be equivalent. The definite things are the ones you build the game around. In Game One, the numbers are fixed. In Game Two, the languages are fixed. In Game Three, the in-forest and notin-forest groups are fixed. In Game Four through Game Six, the numbers are fixed. In Game Seven, the connection group is fixed. In Game Eight, the table is fixed. For example, if I have three fixed groups, A, B, and C, two of them might be equivalent. Let's say A and B are equivalent; anyone who goes in A, then, could go in B, and vice versa. I can look at any previous diagram and switch everyone in A and B, and that's a good diagram too. When switching between equivalent fixed things in a diagram, you have to switch every variable thing that goes in that fixed place with everyone in the other fixed place. Why? Because you may have rules about one of the variable things; if you switch only one of them, you are assuming that those variable things are equivalent. If they are not, just switching one of them may break a rule. But you know that the entire collection of them in that place works, so making the switch to an equivalent place all at once will work as well. Now, how do we know that two people or things or places are equivalent? If two people/things/places don't have any rules about them, they are equivalent. If two people/things/places have exactly the same rules about them, they are equivalent. In the first case, neither person/thing/place is limited in any way, so there is no reason not to be able to switch them. In the second case, the two people/things/places are limited in all the same ways, so any way that works for one will work for the other (because the rules that govern the two are the same). Now, this means that spots in the diagram are rarely equivalent. Take a game where we are putting things in order, from 1 to 5. Each spot is different from every other spot; 2 is the only spot next to both 1 and 3, 3 is the only spot next to 2 and 4, and so on. So no two of these spots are equivalent. Let's look at some of our previous games and see where we can find equivalence. Look at Game Two. We have researchers and languages. Are any of the researchers equivalent? Sure – L and P are equivalent. Neither can learn the same language as G, and that is the only rule that governs either. G and H aren't equivalent because G can't learn the same languages as L or P, but H could (we have no rule against it). Are any of the languages equivalent? You tell me… S and T are equivalent, because two researchers learn each, and no other rules govern either of them. So any place L can go, P can go, and any group of researchers who can learn S can learn T. Now, does this actually help us on this game? Yes, on question 9. On question 9, we want to see who can learn both S and Y at the same time. We look at previous diagrams, and

194

Advanced Techniques

switch the people in S with the people with T (because S and T are fixed, we have to switch everyone at once). Here, for example, is the diagram from question 6, answer D: R L*

S H G*

T H P*

Y H L P

researchers: G H L P

We can switch everyone in S with everyone in T. R L*

S H P

T H G

Y H L P

researchers: G H L P

This tells us that we can have H and P in both S and Y; this eliminates one of the answers. We can also switch P and L. R P

S H L

T H G

Y H L P

researchers: G H L P

This gives us H and L in both S and Y, eliminating another answer. See how this works? In Game Three, none of the birds are equivalent – they are all subject to different rules. The two groups – in-forest and not-in-forest – aren't equivalent, because they are subject to different rules as well (for example, rule 1 tells us about H being in-forest, but we don't have an identical rule about H being not-in-forest). In Game Four, none of the people (Frank, Marquitta, and so forth) are equivalent. Everyone has to be before or after different people. For example, F is the only person who has to be after M; O and T both have to be after V, but O is also before M, so O and T aren't equivalent. The washes aren't equivalent, because there can be only one p, whereas there has to be at least one s, and there have to be at least two r's (since M is r and the car before M is r). The positions aren't equivalent because each is before and after a different number of positions. In Game Five, none of the medicines are equivalent because each appears in different rules. For example, F and G look equivalent, because one of them has to be 1st, but then F is in rule 6 with K and rule 8 with M, and G isn't. The positions aren't equivalent because they are numbered, and the groups aren't equivalent because there will be five medicines in the "test" group but only two in the "not" group. In Game Six, M and S look equivalent, but they aren't. You can't have an M or S attending two of the same type of session – if you switch an M with an S, you might inadvertently switch them into sessions they already attend. The sessions aren't equivalent for the same reasons that the employees aren't: if you switch the people in H and R, you might make the same person attend two of the same kind of session. Of the days, days 1 and 2 are equivalent because there are no rules about either. If you switch everyone on day 1 with everyone on day 2, you will always get a good diagram (provided that the diagram you started with was good).

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In Game Seven, no cities are equivalent because they are each subject to different rules. In Game Eight, M and P are equivalent because there are no rules about either. We can switch the two whenever we want. That ends up not helping too much because almost all of the questions are If-questions, so we don't use previous diagrams (except as I talk about below). One thing to point out: If-questions say that people have to go in certain places, so this might make equivalent people temporarily not equivalent. For example, question 21 puts M in a certain place. Any diagram you make for that question has to have M in that place, so you can't switch M and P in diagrams for this question. For example, let's say you made a diagram for answer A, and you wanted to just switch M and P to make a diagram for answer B. You couldn't do it, because it would violate what the If told you. On Ifquestions, the condition laid down in the If, if it is about one of two equivalent things, will make those equivalent things not equivalent for that question. You can see that equivalence can get a little complicated. The key idea is that if two things are governed by all the same rules (or by no rules), switch them (or everything associated with them) at will, unless otherwise specified by the question you are doing. Here is my recommendation on how to master this. Go back through games you have already done and spot any equivalent things. Then go through your questions and previous diagrams and see where you can use equivalence to answer questions. Make sure it gives you the right answer; if it doesn't, you did something wrong, and you should go back and check. Once you are comfortable using this concept on games you have already done, you are ready to try it on a new game. It is only something to be thinking about in the later part of the game, when you've answered all the If and "What can be true?" questions, and are working with previous diagrams. It won't help you on every question, and it won't eliminate the need to make test diagrams in general. But it can save you time here and there. Some cautions: if you find that you spend more time thinking about what is equivalent, and trying to rearrange previous diagrams, than you do making test diagrams, you are hurting yourself. Students often spend a lot of time trying to take a previous diagram and totally rearrange it to make it useful for an answer. This is often more complex than just creating a diagram from scratch, and there is no guarantee that it will actually work. Making a test diagram always gives you a diagram that is relevant to the answer you are testing. Don't try to make multiple changes on a single previous diagram. If you can't get a helpful diagram by making a single switch, you are probably wasting time looking at it. Move on to another diagram, or test the answer out yourself. One more time – making test diagrams from scratch guarantees a useful diagram. Using previous diagrams is supposed to save time, but if you are trying to make too many changes using equivalence, that defeats the purpose.

Reusing Previous Diagrams on If-questions I told you that you couldn't use previous diagrams to test answers on If-questions. Well, I wasn't being entirely honest. The skill is a little complicated, and often not that useful, but once in a while you can do it. Any previous diagram that matches the situation described in the If part of the question can be used on that question. This includes diagrams from other If-questions. For an example, take a look at Game Five. Question 10 has as its "if" condition that I ranks third. We've done two questions before this, 6 and 7. In the diagram for 6D, I is third, and in the diagram for 7C, I ranks third. We can use these diagrams to help us on question 10.

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Use the diagrams as you would for a question that didn't have an "if." For example, if the question says "If blah blah, what can't be true?", you can eliminate any answer that gives a situation you see in the previous diagram. If the question says "If yadda yadda, what must be true?", you can eliminate an answer if the previous diagram gives you a situation different from what the answer describes. And if the question says "If such and such, what can be true?", the previous diagram probably won't be helpful. Let's see how this would work on Game Five, question 10. This is a "What can't be true?" question, so we can eliminate any answer that appears in our previous diagrams. Neither of our previous diagrams has M before H, so we can't eliminate A. Neither has K before G, so we can't eliminate B. But the diagram for 7C has I before F, so we can eliminate C. The diagram for 6D has H before M, so we can eliminate D. And 7C has G before K, so we can eliminate E. Now, why can we use these diagrams? Well, the "if" condition can be treated as a temporary rule – it is something that you have to obey when testing the answers to that question. We still have to obey all the regular rules as well. If we find a previous diagram that matches the situation described in the "if," we know that it conforms to this temporary rule and all the regular rules (since every diagram follows all the given rules). Thus, it is relevant to this If-question. There are usually very few previous diagrams that can be used for a given If-question, because most diagrams won't match the "if" condition. It's typically a waste of time to look for these previous diagrams unless you've already done several questions. If you decide to use previous diagrams, look for ones you can use on that question (ones that match the situation described in the "if") before doing any other work for the question. Once you find a diagram that you can use, look at all the answers and see if it eliminates any of them. Then look for another diagram that you can use. If you run out of diagrams, make your own diagram, plug in the "if" rule, go through the regular rules, and then test out the remaining answers as normal.

Making Deductions Before You Look at the Questions – Useful and Easy Deductions Sometimes two rules that you are given can be combined to make a third rule. That is, you are told two things have to be true, and on the basis of that you can figure out that something else, something you weren't told, also has to be true. This new thing that you figured out is called a deduction. If you can figure some of these out before you look at the questions, you can save yourself a bit of time. Making deductions can be a difficult and time-consuming process. The time it takes is typically wasted; I find that deductions rarely save more time in answering questions than it takes to make them, and they almost never save more mental energy than they cost. Everyone knows that you have very little time on the LSAT, but it is equally true that you have very little mental energy to spare; a big part of getting a good LSAT score is minimizing the energy you use on the test. That said, there is one type of deduction that is easy to make (thus requiring a minimum expenditure of thought and energy), can be made quickly, and is often very useful. So I am going to teach you to make it.

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Here is what to look out for: rules that tell you one person/thing is before another. These are the kinds of rules we write using the word "before." Let's say we had the following rule: X before Y From this we know that X can't go in the last spot. Why not? You tell me. That's right, because then there would be no place for Y (because Y goes after X). What else do we know? We know that Y can't go 1st, because then there would be no place for X. These two things are worth writing down. But there is more. Games often contain several of this kind of rule, and often more than one of them is about the same person. Count up the number of people who will go after X; for each of them, we know X can't go in one more spot at the end. For example, if we know that X before Y X before W X before Z Three people go after X. So X can't go last, can't go 2nd to last, and can't go 3rd to last. If there were seven spots, X couldn't go 7th, 6th, or 5th. Why not? Because if X went 7th, there would be no room for W, Y, or Z. If X went 6th, there would be room for one of these three, but not for all of them. If X went 5th, there would be spaces for two of them, but not for all three. Likewise, we know that W, Y, and Z can't go 1st, because X has to be before each of them. But one of them could go 2nd, because then we would have room for X. Here's how we could put it in our original diagram: 1 no Y no W no Z

2

3

4

5 no X

6 no X

7 no X

Now, it can get a little more complicated. Imagine the following set of rules: A before B B before C This tells us that two people have to go after A; A is before B, who is before C. A must be before C as well. We also know that C has to go after two people – A and B; thus, it can't be 1st or 2nd. Once you've figured out that there are multiple people before or after someone, it is good to write this down. If you know the order they have to go in (like in the A, B, C example), write this down as a sequence of "before"s. If you don't know the exact order they will go in (in the W, X, Y, Z example, W, Y, and Z are after X, but we don't know what order they go in; W might be before X or after X, etc.), write it down in a way that tells you that you don't know the exact order. So you might write something like: A before B before C

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(I will often just add the C rule to where I wrote down the A rule, so as not to write a bunch of similar rules) X before W Y Z (what order?) Now let's see how we could use this in games. In Game One, we know that M is before N. So M can't be 6th and N can't be 1st. Not that useful. We don't know anything about K and L, for example, because we don't know which is before the other (they can go in either order). But look at Game Four. Here are the relevant rules: V before O V before T M before F O before M Well, we've got V before O and T, but we don't know what order they go in, so just add in the T to the O rule, like so: V before O, T (what order?) Now we've got O before M, so add this in; they are in a definite order, so we want to include that in our rule. However, with the T in there, it all gets confusing. I'm not going to include the order in the rule, because I still have the "O before M" rule to remind me of the order. I know I'll confuse myself if I put it together, and I have all the information written down someplace, so it doesn't have to be written in the most efficient way possible. Remember, our goal is to make the rules clear and complete. V before O, T, M (what order?) O before M But now we know that M is before F, so we have to put that in. I also combine it with the O before M rule. V before O, T, M, F (what order?) O before M before F There are only five spaces in this game. V has to have four people after her, so she can't be, let's see, 5th, 4th, 3rd, or 2nd. That makes her 1st. O can't be 5th or 4th, so he has to be 2nd or 3rd. M can't be 5th. F can't be 1st or 2nd or 3rd (because V, O, and M are before him). M can't be 1st or 2nd (because V and O are before her). See how useful that was? Let's see this in a diagram: 1 V __

2 __ __ no F no M

3 __ __ no F

4 __ __ no O

5 __ __ no O no M

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Sometimes when people can only be in a couple of slots, it's better to show where they can go, rather than where they can't go. Based on our above diagram, O can only go 2nd or 3rd, F can only go 4th or 5th, and M can only go 3rd or 4th. It might be easier to write that than to write all the "no this" and "no that." I like to use brackets, like this: M 1 V __

2 __ __

3 __ __ O

4 __ __

5 __ __ F

We don't have to draw these brackets when we draw diagrams to test answers. These brackets are here for our reference, like new rules. We can see them when we look back at the rules so we don't have to draw them in every time, just like we don't rewrite the rules. Notice, though, that we did the game previously without making these deductions. We made some of them (about V and M) as we went through the questions, and totally missed the deduction about O (I never made that deduction myself until I was writing this book). The point is that, while these deductions can be quite handy, you don't need to make them initially. If they are important, the questions will force them on you. That said, if you can get good at making them, and these deductions are straightforward and quick, you can often save yourself some time. So let me summarize. Look for rules that tell you who is before whom. If someone is before or after multiple people, figure out who they are before and after and write this down. Count the number of people before someone. For every person before them, they can't go in one of the first spots (moving left to right). Count the number of people after them. For every person after them, they can't go in one of the last spots (moving right to left). Write all this down. Get used to this and it is quick, quick, quick. It is totally memorizable and totally mechanical, just the way logic games should be.

Making Deductions Before You Look at the Questions – General Theory We've just discussed one type of deduction you can make before you look at the questions, but there are others. I was very tempted not to include anything further in this book about making deductions, but I knew that someone out there reading this book would hunt me down if I didn't. So here you are. Before I talk about how to make these deductions, I want to give one last warning. You may think that I have belabored this point about how bad deductions can be, but I don't think I have. Among the brightest and most ambitious students, a focus on making deductions before answering the questions is the number one cause of bad LSAT scores. This is because these students tend to be perfectionists – they want to figure out everything possible about the game before they do any questions. This is a waste of time, for all the reasons I have already talked about: deductions rarely save you much time, and most games either have few deductions or the deductions are very difficult to find, meaning that the time spent looking for deductions often results in finding nothing. Even when a deduction is made, the costs are often not worth the benefits. Among students who think logic games are difficult and confusing, one of the primary causes of that confusion is trying to make deductions without the help of the questions. The process of making deductions

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requires more thought and decision-making on the part of the test-taker than any other aspect of the game, and it is hard to know where to start looking. Thinking and making decisions with little guidance, under time pressure and in the presence of huge amounts of information, results in confusion and possible mistakes. When you do questions, on the other hand, the answers give you guidance as to what to test out, making things much easier. Plus, thinking when doing questions is guaranteed to help you get questions right, whereas thinking before doing the questions is not. My concern is that students want to spend the most time learning what they find challenging, rather than what will improve their scores the most. Making deductions before looking at the questions is a challenge, and thus students overemphasize it, and don't learn more important skills. So here is my first warning: don't try the following unless you have mastered everything else in this book. OK, if you are still reading, I'll assume that you have mastered everything else in this book. If you haven't, shame on you for trying to sneak past me. Now, here's the second warning: the most important part of making deductions is knowing when to stop. The deductionmaking process is a potentially vast pit of time wasting. If you know when not to make deductions, then you won't go wrong. Here is how to make deductions. Start by looking at the first rule. This rule will be about at least one thing. Now, put your finger on this first rule, so you remember where you are. Keeping your finger where it is (marking the first rule), skim down the list of rules and see if there are any other rules about that thing, or any other aspect of this rule. Once you have looked at every thing in that first rule, go to the second rule, and do the same thing. Only look at rules under the rule you have your finger on (because you already tried to put together the rule you're looking at with the rules above it when you had your finger on them earlier). Now, what if you find that you have more than one rule about the same thing? What do you do? First, make sure that you are aware of all the rules about that thing. Are you? Good. If you are working with a variable thing, use another finger, and point at each empty spot in your diagram. Ask yourself, "Can this thing go here?" If it looks like it, look at the next spot. If it would clearly break a rule (and you have no doubts about it), write down that it can't go there. Go through every spot in this way. Once you have done this, go to the next thing/rule. If the thing you are thinking about is a fixed entity, meaning that it can't move (it is written in one place in your diagram), then try to put every variable entity with it. Write down any that can't go under it. It is very important that you don't get too complicated when working out your deductions. You shouldn't have to make an entire test diagram to see if a thing can go in a given place; it should either be obvious, or figure outable in one or two steps. I'll give you an example soon. If you think that you might have a deduction, but you start getting confused, or if it seems to take a lot of work to figure out, skip it and move on. If you are not sure about a deduction – you don't know if it has to be true or not – don't write it down. Oh, that's important, let me say it again: If you are not sure about a deduction, don't write it down. And don't worry about it; move on. You lose points by having false deductions, not by missing deductions. So what it boils down to is this: you are looking through all the rules, one by one, for things that are the subjects of multiple rules. We make sure to go through the rules in order so that we don't miss anything, or get confused. If something is the subject of multiple rules, try it in every spot in the diagram. If a position in the diagram is the subject

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of multiple rules, try to put every different thing in it. If something ends up not being possible, write it down. With some practice, you can get quite good at this. One more thing: when you look at "If… then…" rules to see who they are about, only look at the "if" part. For example, let's say you have a rule that says "If X, then Y." You have another rule that says "If A, then Y." These rules are not about the same person (Y), because Y is not in the "if" part, so we don't try to put them together. For an explanation of why this is, see Game Three. Now, when do you not do this? If a game has a lot of rules, especially a lot of "If… then…" rules, don't try to make deductions. It will take forever. Look at Game Three; there are quite a few deductions to be made in this game, but making them takes longer than answering all the questions. If figuring out the setup and the rules took you too long, don't try to make deductions. Remember, answering the question takes the most time, and is the most important step. A good rule of thumb is that you shouldn't spend more than two minutes (maybe two and a half minutes) before answering the questions. If steps 1 and 2 take you two minutes, don't make deductions. If you don't understand the rules well, don't make deductions. You are likely to confuse yourself; working through the questions is a much easier way of understanding the game, because the questions will give you something to work with – either If conditions, or answers to test out. If you have looked at each of the rules once, stop trying to make deductions. If you have looked at each of the rules, you have made all the deductions that you are capable of making. Maybe you've missed something, but you've missed it for a reason – you aren't able to see it. If you were able to see it, you would have. OK, let's do an example. Look at Game Two. This is full of deductions. Here is our diagram and the rules: R __

1. 2. 3. 4. 5. 6. 7.

S __ __

T __ __

Y __ __ __

researchers: G H L P

Each researcher can learn 1 to 3 languages. If L learns a language, then G can't (learn that language). If P learns a language, then G can't (learn that language). If G learns a language, then L can't (learn that language). If G learns a language, then P can't (learn that language). If G learns a language, then H learns it (the same language). If H doesn't learn a language, then G doesn't learn it (the same language).

Let's go through the rules. Rule 1 doesn't mention any particular researcher or language, so we skip it. Rule 2 mentions L in the "if," but we don't have any other rule that has L in the "if" part. Rule 2 mentions P in the "if" part, but no other rule does. Rule 4 is about G, and so are 5 and 6. Bingo! We know that G has to go with H, but not with L or P. We are aware of all the rules about G, so let's try to put G in all the spots. Look at R first (be systematic). Can G go with R? No, because G has to go with H, but there isn't any room under R. Can G go with S? Looks like it (there's room for H), so we don't worry about it. Same for T. How about Y? Well, if G went with Y, then L and P couldn't go there. But then there wouldn't be enough people to fill the three spaces. So G can't go under Y. And, since there are only three people left (H, L, and P), they have to go under Y.

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R __ no G

S __ __

T __ __

Y H L P

researchers: G H L P

So how useful was that? We didn't make any of those deductions when we did the game, and we didn't find the game that hard. In fact, I went through every games section since LSAT 19, not letting myself make a single deduction of any kind prior to doing the questions, and I found the sections do-able under normal LSAT time limits (35 minutes per section). In only a couple of cases did I think that a game would have been easier with deductions, and all of these cases were ones where the deductions were the easy kind I talked about prior to this. But, if you want to try it out, here it is. To practice these deductions, go back to games you have done before and work through this process. Don't be sloppy – go through the rules one at a time, like I say, and don't go through them more than once. See how many deductions you find; if you find any, go through the questions and see how they impact what you do. If you find the process not worth the effort, forget it. But, if you find it worthwhile, and get comfortable with it, start applying it to games in the future. Be careful to watch your time, though, and don't get caught up in the deductions to the detriment of the questions.

What Do I Do Next? We are going to do the entire games section from LSAT 38. I consider this games section one of the most difficult I've ever seen. Every game in the section is challenging. We'll employ all the techniques we've learned in this book, except the more complex type of deductions. This will reinforce how the fundamentals help to make tough games easier, and show us how to use these advanced techniques. Once you've seen how the new techniques work, you can then start applying them, first to games you've done before, and then to new games.

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204 Game omitted from electronic version of book.

Game Nine

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Game Nine (From LSAT 38) You should try to do this game on your own. When you are finished, read through my explanation and see if there is anything you should have done differently.

Step 1: Read the Setup/Draw a Diagram Based just on the setup, the game seems pretty straightforward. We are trying to figure out what order the clowns come out of the car, so we are matching clowns to positions in the order. We know more about the order than we do the clowns – the order of the numbers is unchanging (one is always before two) – so we will build our diagram around this ordering. The game doesn't tell us how many positions there are. However, there are eight clowns, and we are putting them in order. The game tells us that the clowns will get out one at a time, so we know that there are eight positions, one clown per position. Since the clowns are getting out in order, we assign a number to each position. That is, a clown will be first, a clown will be second, and so forth. Our diagram ends up looking like this: 1 __

2 __

3 __

4 __

5 __

6 __

7 __

8 __

Clowns: Q R S T V W Y Z

Step 2: Read the Rules Each rule talks about the order of the clowns. Some of the rules, such as the first one, should be written as two rules for the sake of simplicity. Notice also that some rules say "after" instead of "before." We translate "after" into "before" (if someone is after so-and-so, you know that so-and-so is before them). We prefer "before" for two reasons: 1) we are used to it, and 2) it mimics the order of the diagrams. If X is before Y, then X will be to the left of Y in the diagram; X is also to the left of Y in "X is before Y," which makes for easy reading. 1. 2. 3. 4. 5. 6. 7.

V before Y V before Q Z before Q T before V R before T V before S R before W

The Deductions Since we have all these "before"s, we can put them together as I discuss in Advanced Techniques (the section on Useful and Easy Deductions). This assumes that we haven't spent too much time writing down the setup and rules. If we had, we'd skip the deductions, no matter how promising and helpful they looked. Let's go through this step by step. As we work through the questions, I will put commentary in boxes on how you could have answered the question without having made these deductions.

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Look at rule 1 first. It is about V, and we have many other rules about V. We know that V has to be before Y, and also before Q and S, so we add this to the first rule. We don't know which will come first, Y, Q, or S (because there isn't a rule about it), so we note that. 1. V before Y & Q & S (what order?) No rules tell us that Y or Q or S will be before anyone, so we have nothing more to add to this rule. We know now that V can't be 8th, 7th, or 6th; remember, for every person that comes after someone, that someone can't go in one of the last spots. Since three people come after V, V can't go in any of the last three spots. We also know that Y, Q, and S can't go 1st, because V has to be before them. But we aren't done with the first rule. We still have more rules about V. Rule 4 tells us that T has to be before V, and rule 5 tells us that R must be before T. Two people come before V, so V can't be 1st or 2nd. We can write all of this in our diagram, like so: 1 __ no no no no

2 3 __ __ Y no V Q S V

4 __

5 __

6 7 8 Clowns: Q R S T V W Y Z __ __ __ no V no V no V

Sometimes writing several "no so-and-so"s for the same person can make our diagram hard to read. Instead, it may be easier to put a bracket around everyplace someone can't go (e.g., put a bracket around 6, 7 and 8 and write "no V" under it), or to put a bracket around the places they can go, if there are only a few of them. V can only go 3rd, 4th, or 5th, so it'll be easier to write that than all these "no"s. 1 2 __ __ no Y no Q no S

3 __

4 __

5 __

6 __

7 __

8 Clowns: Q R S T V W Y Z __ no Z

V

Now we move on. Rule 2 is about V, but we've already looked at V. It is also about Q. Do we have any other rules about Q? Sure, we see that Z is before Q also. So Q can't be 1st or 2nd, because two people (V and Z) have to be before it, and Z can't be last. 1 2 3 __ __ __ no Y no Q no Q no S

4 __

5 __

6 __

7 __

8 Clowns: Q R S T V W Y Z __ no Z

V

The next rule is about Z. We don't have any rules about Z below this, so we move on (we already combined this rule with any previous ones when we originally looked at those previous ones). The next rule is about T. T is before V. We already know that V has three people after it, so T has to have these three plus V, which makes four. So T can't go in the last four

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spaces. Also, T is after R (rule 5), so it can't go 1st. This means that T can only go 2nd, 3rd, or 4th. We write all this down; we add it to rule 4 (about T) 4. T before V before Y & Q & S (what order?) and we put it in our diagram. T 1 2 3 __ __ __ no Y no Q no Q no S

4 __

5 __

6 __

7 __

8 Clowns: Q R S T V W Y Z __ no Z

V

The next rule is about R. R is before T, who is before all these other people. R is also before W (rule 7), but I don't know exactly where W will go in that list (it might be before T, or after V, or anyplace). Since I already have rule 7, and I don't know where W goes after R, it'll be too confusing to add it to rule 5. Here is what I do write down: 5. R before T before V before Y & Q & S (what order?) R is before six people, including W, so it can't go in any of the last five spaces. This means that it can only go in space 1 or 2. Put this in the diagram. We're running out of room below the spaces, so I'll write it above. R T 1 2 3 4 5 6 7 8 Clowns: Q R S T V W Y Z __ __ __ __ __ __ __ __ no Y no Q no Z no Q V no S The last two rules don't tell us anything new. But we've figured out quite a bit. And it didn't take us too long; all we did was see how many people come before and after each clown in the rules, and then quickly calculate where that clown could not go. If you go through that process once more on your own, you'll see that it's faster to do than to describe.

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Here is the final state of our original diagram and rules (note that we don't have to recopy all the brackets and "no"s when we make diagrams to test answers; we have all the brackets and "no"s in this diagram, so we can just refer back to it as we refer back to the rules): R T 1 2 3 __ __ __ no Y no Q no Q no S 1. 2. 3. 4. 5. 6. 7.

4 __

5 __

6 __

7 __

8 Clowns: Q R S T V W Y Z __ no Z

V

V before Y & Q & S (what order?) V before Q Z before Q T before V before Y & Q & S (what order?) R before T before V before Y & Q & S (what order?) V before S R before W

Step 3: Answer the Questions Here's the order in which we do the questions: Question Number 1 2 3 4 5 6 7

Question Type What can be true? What can be true? If If If If If

Question 1 Eliminate any answer whose list breaks a rule. Answer A This doesn't have R in spot 1 or 2, so this can't be right. This answer also breaks the R before T rule (rule 5), in case you are curious as to how we'd do this question if we hadn't made the deduction. Answer B This doesn't have T in spot 2, 3 or 4. The answer breaks the V before Q rule (rule 2). Answer C This has R, T, and V in the right areas. But it breaks the Z before Q rule (rule 3). This breaks a rule, but doesn't violate our deductions.

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Answer D This has R in spot 3. This answer breaks the R before W rule (rule 7). Answer E is the answer. Copy this answer down as a possible diagram: 1 R

2 W

3 T

4 V

5 Z

6 S

7 Y

8 Q

Notice that we could have done question 1 without any deductions. Question 2 This is a "What can be true?" question. Let's test the answers out. Answer A Draw a diagram; as I said above, you don't need to copy all the brackets and "no so-andso"s from the original diagram, since you have it all in the original diagram to refer to. When you create new diagrams to test answers, you don't have to recopy all the deductions from the original diagram; just make sure that you actually look back at that diagram when you look back at the rules. It's easy to forget to look at your original diagram and end up not using the deductions you made. Put Y 2nd as the answer calls for: 1 __

2 Y

3 __

4 __

5 __

6 __

7 __

8 __

Clowns: Q R S T V W Y Z

Go through the rules, looking at our original diagram (with all the brackets and "no"s) first. I see that R has to be 1st or 2nd in our original diagram. Since Y is 2, R has to be 1. 1 R

2 Y

3 __

4 __

5 __

6 __

7 __

8 __

Clowns: Q R S T V W Y Z

Now we look through the rules. Rule 1 says that V has to be before Y, but there is no room for V. So this isn't possible. Cross out the diagram and cross off the answer. Plus, we just learned that Y can't ever go 2nd, so we can write that in our original diagram. Here's how you do it without deductions. Put Y second. Rule 1 tells you that V is before Y, so V goes first. Rule 4 tells you that T is before Y, but there is no room. This teaches us that Y can't go 2nd or 1st (for similar reasons), which is something we can write down. Answer B This violates the deduction we made originally, that R has to be 1st or 2nd, so we don't bother even diagramming it. Here's how you do it without deductions. Put R third. Rule 5 tells you that R is before T, so put T 4th, and mark it with a dot or star, because it might have gone later; rule 7 tells us that R is before W, so put W 5th and mark it. Remember, every time you write something down in a diagram, you go back through the rules, so go through the rules again. Rule 4 tells us that T is before V, so put V 6th and star it. Rule 1 tells you that V is before Y, so put Y 7th; rule 2 tells you that V is before Q, so put Q 8th. But then rule 6 says V is before S, and we are out of room. Can we move anyone around to make this work? No, the problem is with the number of people, not their position. We are trying to fit six people in five spaces, and this won't work.

210

Game Nine

and we are out of room. Can we move anyone around to make this work? No, the problem is with the number of people, not their position. We are trying to fit six people in five spaces, and this won't work. Working through this answer teaches us that R can't go 3rd or later. Answer C Put Q fourth. 1 __

2 __

3 __

4 Q

5 __

6 __

7 __

8 __

Clowns: Q R S T V W Y Z

Look at our diagram. We have multiple places V, T, and R can go (V can still go 3rd or 5th, T can still go 2nd or 3rd, and R 1st or 2nd). Now go through the rules. Rules 2 and 3 tell you that Z and V must be before Q. Put them in someplace, and mark them, since we decided where to put them (note that I still prefer alphabetical order for V and Z). 1 __

2 V*

3 Z*

4 Q*

5 __

6 __

7 __

8 __

Clowns: Q R S T V W Y Z

But wait, that gives us no room for R and T. If we move V or Z (our marked people) to make room for R and T, we'll break rule 2 or 3. This won't work, so cross it off. We now know that Q must be later than 4th. You might have been able to do this in your head, but I like to see things in front of me; it makes it easier for me to think. Do this without deductions: put Q fourth. As above, put Z and V in before it. Then you see that T has to go before V, and R before T. But there is no room. Answer D Put S 5th. 1 __

2 __

3 __

4 __

5 S

6 __

7 __

8 __

Clowns: Q R S T V W Y Z

We know from the brackets in our original diagram that V, T, and R will go before S (the latest V could go is 5th, and S is sitting right there). So put them in. I like to put them in spots 1, 2, and 3; not only are they the first available spots, but I also know that lots of people will go after these three, so this gives them as much room as possible. There are certain people in your game, the ones that have a lot of rules about them, to whom you want to give as much leeway as possible. I put a star next to V, because I could have put it someplace else (I don't star R and T, because my placement of V forced them to go 1 and 2). 1 R

2 T

3 V*

4 __

5 S

6 __

7 __

8 __

Clowns: Q R S T V W Y Z

Now we go through the rules. V is before Y, Q, and S, in no particular order. S is already in, so put Y and Q in (mark them, since the order we choose is optional). 1 R

2 T

3 V*

4 Q*

5 S

6 Y*

7 __

8 __

Clowns: Q R S T V W Y Z

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211

Uh oh, I see that Z has to be before Q (rule 3). So I move Q to the next available spot (7) and put Z before it. Z has to go there (it's the only spot before Q), so I don't mark it. 1 R

2 T

3 V*

4 Z

5 S

6 Y*

7 Q*

8 __

Clowns: Q R S T V W Y Z

7 Q*

8 W

Clowns: Q R S T V W Y Z

W is left, so put it in the last spot. 1 R

2 T

3 V*

4 Z

5 S

6 Y*

This works, so this (answer D) is the answer. The process for doing this without deductions is almost exactly what we just did, since we didn't use our deductions much. Y goes 4th. V goes someplace before it. By this stage in the game, we've already tested out seven answers; the main rules are probably starting to stick in your head. You probably remember that R and T go towards the front, so you automatically stick them before V; if you didn't remember that, your rules would quickly force you to do it. Then you just start dropping people in where you can; the only rule that you really have to watch out for is Z before Q (rule 3). Here are the deductions we could have made while doing this question that we can add to our original diagram: Y can't go 2nd, and Q can only go 5th, 6th, 7th, or 8th (so bracket these spots). Doing this question would have helped us make some of the deductions even if we hadn't made any initially. The wrong answers tell us stuff that can't be true (see Intermediate Techniques, the section on Making Deductions from Questions – Part 1). From answer A we learn that Y can't go 1st or 2nd. From B we learn that R is 1st or 2nd. From C we learn that Q is 5th, 6th, 7th, or 8th. Question 3 Before we make a diagram, let's consider if we should use our previous diagrams. In the Advanced Techniques I told you that you can use previous diagrams on If-questions, and this is an If-question. However, it is also a "What can be true?" question, and we don't use previous diagrams on these. Sorry, but we are going to have to work this out. Make a diagram and put Z seventh. 1 __

2 __

3 __

4 __

5 __

6 __

7 Z

8 __

Clowns: Q R S T V W Y Z

Go through the rules. Rule 3 is about Z; it tells you that Z is before Q. So put Q 8th. No other rule comes into play, because no other rule mentions Z. 1 __

2 __

3 __

4 __

5 __

6 __

7 Z

8 Q

Clowns: Q R S T V W Y Z

This is a "What can be true?" question, so we test each answer out and see if we can make it work.

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Game Nine

Answer A This is the sort of answer students are likely to jump on. They say to themselves, "Hey, I've got a deduction that says R can be first or second, so of course R can be the second clown. This is the answer." That's wrong. We've got a deduction that says R can be 2nd, given the rules we have. This If-question has limited the game even more; all the rules are going to apply, but R may be forced to go someplace definite (other than spot 2) by Z being where it is. Don't jump to conclusions – work the answers out. 1 __

2 R

3 __

4 __

5 __

6 __

7 Z

8 Q

Clowns: Q R S T V W Y Z

Our version of rule 5 tells us that R has to be followed by T and V (in that order) and then Y, Q, and S (in no particular order). So put these in, marking Y and S because, whatever order we put them in, they might go in another order. 1 __

2 R

3 T

4 V

5 Y*

6 S*

7 Z

8 Q

Clowns: Q R S T V W Y Z

So far, so good, right? But we still have to look through the rules one more time. And the last rule says that R is before W. But there is no place after R for W to go. This diagram breaks the rules. Cross it off, and cross off this answer. Here's how we do this without deductions. We put R 2nd. Then we go through the rules. We know that R is before T, but we don't know where, after R, T will go. We put T 3rd and mark it with a dot or a star, so we can move it later on if we have to. We put W after R as well, and mark it. We go through the rules again. We put V after T, and then go through the rules again. Eventually we realize that we are trying to fit five clowns (T, V, Y, S, and W) into four spaces, and we can't do it. There is no point in moving the clowns that we marked; the only direction we can move them is right, and that gives us even less room. Answer B Draw a new diagram based on the diagram for this question (with Z 7th and Q 8th), and put T 4th. 1 __

2 __

3 __

4 T

5 __

6 __

7 Z

8 Q

Clowns: Q R S T V W Y Z

Now go through the rules. Rule 4 tells you that T is before V, Y, Q, and S. But there isn't enough room for all of these clowns. This won't work. Read the boxed explanation for answer A above; the procedure is essentially the same. Answer C Draw a new diagram (remember to put Z and Q 7th and 8th; on If-questions, keep the diagram that you drew at the start of the question and recopy it for each answer). 1 __

2 __

3 __

4 __

5 W

6 __

7 Z

8 Q

Clowns: Q R S T V W Y Z

We have only one rule about W, that R has to be before it (rule 7). We want R to be first or second (and we saw in answer A that it can't be 2nd), so put R 1st (spot 1 is generally a safe

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213

bet for R, because he has to be followed by so many clowns). Then put V and T in, putting them 2nd and 3rd since they are the first empty spaces (putting them in low-numbered spaces is also more likely to work since they have to be followed by so many clowns). 1 R

2 T*

3 V*

4 __

5 W

6 __

7 Z

8 Q

Clowns: Q R S T V W Y Z

Now we go through the rules. V has to be before Y, Q, and S. Q is already after it, so put in Y and S; the order doesn't matter (as we noted when we wrote down the rule), so I don't mark them because there will be no point in switching them. 1 R

2 T*

3 V*

4 Y

5 W

6 S

7 Z

8 Q

Clowns: Q R S T V W Y Z

This follows the rules, so this (answer C) is the answer. The procedure for doing this without deductions is the same as the procedure for doing it with deductions; by this stage in the game you should have the sense that R, T, and V should go in low-numbered spots, because they show up in so many rules, so your first instinct should be to put them in first. Even if you didn't see that, you'd put them in low spots because they are empty. After that, you just work through the remaining rules. Question 4 Should we use previous diagrams on this question? It is an If-question, so we can; it is also a "What must be true?" question, so previous diagrams would be helpful. We need a previous diagram where T is 4th. Unfortunately, none exists. We are going to have to test this out. Draw a diagram and put T 4th. 1 __

2 __

3 __

4 T

5 __

6 __

7 __

8 __

Clowns: Q R S T V W Y Z

Before we look at our rules, look at what our original diagram tells us. We know that V can only be 3rd, 4th, or 5th, but the rules tell us that V has to be after T, so it can only be 5th. 1 __

2 __

3 __

4 T

5 V

6 __

7 __

8 __

Clowns: Q R S T V W Y Z

Go through the rules again. Rule 1 tells us that V will be followed by Y, Q, and S, but we don't know what order they will go in. Rule 5 tells us that R is before T, but we don't know where. No other rules tell us about R or V, so that is all we can figure out. Let's look at the answers; remember, this is a "What must be true?" question, so we test the answers by doing something other than what they describe. Answer A Since this is a "What must be true?" question, let's not put R 1st. Put R 2nd (that's the only other place it can go, according to our original diagram, so don't mark it with a star or dot). 1 __

2 R

3 __

4 T

5 V

6 __

7 __

8 __

Clowns: Q R S T V W Y Z

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Game Nine

Now go through the rules. We already know that V is before Y, Q, and S, so put them in. 1 __

2 R

3 __

4 T

5 V

6 Y*

7 Q*

8 S*

Clowns: Q R S T V W Y Z

6 Y*

7 Q*

8 S*

Clowns: Q R S T V W Y Z

6 Y*

7 Q*

8 S*

Clowns: Q R S T V W Y Z

R is before W (rule 7), so put W 3rd. 1 __

2 R

3 W

4 T

5 V

All that is left is Z, so put him 1st. 1 Z

2 R

3 W

4 T

5 V

This works. We can eliminate answer A. We can also eliminate answer B because Z doesn't have to be 2nd. As we look through the answers to see if we can eliminate any others, we see that D has to be the right answer – V must be 5th, which we figured out in our initial diagram for this question. So we are done. This question is a bit harder without deductions, but it's still do-able. You probably won't see that V has to go 5th, but you will see that V, Y, Q, and S have to go at the end (because V is after T, and Y, Q and S are after V). When you test answer A, you'll put R 2nd, as we did, not because you know he has to go there, but because it's the next available spot after 1 (or because question 2 had taught you R had to go 1st or 2nd). You'll mark R with a star. After that, you put in V, Y, Q, and S (possibly with a little trial and error to get the right order), and then W. That leaves Z, and you have a working diagram. This diagram eliminates answers A, B, and E. So then you have to test out C, and you'll realize that D is the right answer. Question 5 Will previous diagrams be useful on this question? Potentially, because it is a "What can't be true?" question, and we normally use previous diagrams on them. But, because it is an If-question, we need a diagram that matches the condition in the "if." But none of our previous diagrams have Q 5th, so we have to test this out by hand. 1 __

2 __

3 __

4 __

5 Q

6 __

7 __

8 __

Clowns: Q R S T V W Y Z

Go through your rules. Rules 2, 4, and 5 tell us that R is before T, which is before V, which is before Q. However, there are four spots open before Q, so we don't know exactly where these three will go. We have to test out the answers. Since this is a "What can't be true?" question, we simply try each answer and see if we can make it work. Answer A Put Z 1st; once you look back at your original diagram, you will see that this forces R to go 2nd. 1 Z

2 R

3 __

4 __

5 Q

6 __

7 __

8 __

Clowns: Q R S T V W Y Z

Game Nine

215

Go through the rules. Rule 5 tells us that R is before T, which is before V, which is before Q, so we now have the first five spots filled. 1 Z

2 R

3 T

4 V

5 Q

6 __

7 __

8 __

Clowns: Q R S T V W Y Z

Now we have S, W, and Y left. We don't have rules relating one to the other, so we can put them however we like. 1 Z

2 R

3 T

4 V

5 Q

6 Y

7 S

8 W

Clowns: Q R S T V W Y Z

This shows answer A is possible, so we can eliminate this answer. It also shows that answer E is possible, so we eliminate that answer as well. On this question, even if we hadn't made our deductions about R, T, and V, our experience with this game would show us that R, T, and V should go early on. Once we put them in the earliest available spots, everything else works out well. In addition, doing answer B on question 2 showed us that R can only be 1st or 2nd, even if we hadn't deduced that before looking at the questions; thus, the R deduction is potentially available to us even if we hadn't worked everything out beforehand. Answer B Copy the starting diagram for this question, with Q fifth, and then put T 2nd. 1 __

2 T

3 __

4 __

5 Q

6 __

7 __

8 __

Clowns: Q R S T V W Y Z

This forces R to go 1st (rule 5, or the brackets in our original diagram tell us this). 1 R

2 T

3 __

4 __

5 Q

6 __

7 __

8 __

Clowns: Q R S T V W Y Z

Rule 1 is about V, so let's think about V now. It's a safe bet to put V 3rd, but we'll mark it with a star so that we can move it if this doesn't work out. 1 R

2 T

3 V*

4 __

5 Q

6 __

7 __

8 __

Clowns: Q R S T V W Y Z

At this point we have S, W, Y, and Z left. We look through our rules. Z has to go before Q (rule 3), and there is only one empty spot before Q. 1 R

2 T

3 V*

4 Z

5 Q

6 __

7 __

8 __

Clowns: Q R S T V W Y Z

Now we have only S, W, and Y left. There are no rules that say one has to go before the other, so we put them wherever we like (by the way, you might have noticed that S and Y are equivalent (see Advanced Techniques) – both have to go after V, but are not limited by any other rules). 1 R

2 T

3 V*

4 Z

5 Q

6 S

7 W

8 Y

Clowns: Q R S T V W Y Z

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Game Nine

This shows us that answer B is possible, so we can eliminate this answer. And it shows us that C is possible, so we can eliminate C. This leaves only D, so D is the answer. The process for doing this answer without deductions is exactly the same as the procedure we just went though. Question 6 Can we use previous diagrams on this question? Although it's an If-question, it's also a "What must be true?" question, so we normally would; do we have any previous diagrams that have R in position 2? Look through your previous diagrams – there's one! Question 4, answer A (there's one more previous diagram that we can use, but one at a time). OK, so we can use this previous diagram just the way we would for any "What must be true?" question. If the diagram shows a scenario that is different than what an answer describes, the answer is wrong. Well, answer A is gone, because this diagram doesn't have S before T. Answer B gets eliminated because T is not before W. Answer C stands, because W is before V. Answer D stands, because Y is before Q. And E stands because Z is before W. Alright, look for the next relevant diagram. We look for diagrams one at a time – it doesn't do you any good to spot three relevant diagrams at once, because you can only use them one at a time. Spot one, use it, and then keep looking until you run out of diagrams. There is another diagram we can use. The diagram for question 5, answer A has R 2nd. Let's see if it can help us eliminate answers C, D, or E. W is not before V, so we eliminate C. Y is not before Q, so D gets eliminated. And that's it, E is the answer. Question 7 Because this is a "What can be true?" question, we can't use our previous diagrams. We just have to test out the answers. The "if" gives us the condition that V is before Z. Write this down. V before Z This eliminates one more place that V could go – it can no longer go 5th, only 3rd or 4th – because for every person who goes after V, V can't go in one of the last spots, and we have now been given one more person who goes after V. But we don't know where V will go. This "if" condition also affects T and R; since they are before V, they must be before Z as well. Each of them can go in one less spot. This means that T can only go 2nd or 3rd, and R can only go 1st. We can put this in our diagram. T 1 R

2 __

V 3 __

4 __

5 __

6 __

7 __

8 __

Clowns: Q R S T V W Y Z

Now let's look at the answers. This is a "What can be true?" question, so any answer that breaks a rule is wrong. Answer A R can't be 2nd; this is obviously wrong.

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217

If you hadn't made the deductions, this would take some more work. You'd put R 2nd; then you'd put T 3rd and V 4th – you know that you want to put them as early as possible. Then you go through the rules. You have to put Z, Y, Q, and S after V and W after R. This means that you have to fit six people in five spots; it won't work, so this answer is wrong. Answer B You can't put T 4th, because we figured out when we started doing this question that T has to be 2nd or 3rd (see the diagram above). This is obviously wrong. Without deductions this one will be a little bit slower too. The rules tell you that V is after T; then the rules tell you that you have to put in Z, Y, Q, and S after V (rules 1, 2, and 6, and the "if" condition for this question); you soon realize that you don't have enough room. Answer C Put Q 4th. T 1 R

2 __

V 3 __

4 Q

5 __

6 __

7 __

8 __

Clowns: Q R S T V W Y Z

Just looking at our diagram, we see that V has to be 3rd, because it's either 3rd or 4th and Q is already 4th. This forces T to be 2nd, since T can only be 2nd or 3rd. T 1 R

2 T

V 3 V

4 Q

5 __

6 __

7 __

8 __

Clowns: Q R S T V W Y Z

Now we look through the rules. Rule 3 tells us that Z has to be before Q, but there isn't any room to put Z in. This won't work. We also learned that Q couldn't be 4th from question 2. If we had written that down, we wouldn't have had to test this out. Put Q 4th, then go through the rules. V has to be before Q, as does Z (rules 2 and 3). This leaves us no room for T, who has to be before V (rule 4), so this won't work. Answer D V can't be 5th, because V has to be 3rd or 4th. This is wrong. V must be followed by Z (the "if" condition of this question), Y (rule 1), Q (rule 2), and S (rule 6). If V is 5th, there are only three spaces after it, and we can't fit four people (Z, Y, Q, and S) into three spaces. So E has to be the answer.

Summary What is the lesson of this game? This is a challenging game. Not because the rules are hard to understand, or the setup is strange, but because you have to deal with a lot of

218

Game Nine

variables and answer a lot of questions. The questions don't make it easy on us – we don't get to reuse our previous diagrams much at all. Now, anyone who masters the fundamentals of logical reasoning can get four or five of these questions right in 8 minutes. And, in fact, if you follow my guidelines for managing your time (see Timing), you would have almost 11 minutes to answer these questions – this was the longest game in it's section, meaning that you should do it last – which would most likely be enough time to get all the questions right. But this game can be nerve-wracking. Even if you get a good enough feeling for the rules that you realize you should generally put R, T, and V in the lowest-numbered spots possible, it's hard to be sure that they can or can't go in certain places without working out the possibilities. That requires time, and it requires effort, and these are commodities we'd rather not use. Making the deductions makes the game easier. The deductions give us no information we didn't already have, nor do they radically change the way we approach the game. But they give us a certain sense of surety, and they allow us to reuse the same thoughts over and over. Once we know that R has to be first or second, we no longer have to figure out where R goes. We can just recycle our thoughts, and we all know that recycling is a good policy. So why not make these deductions. They are fairly straightforward to make. You know that they are there to be made, because we have rules that say "before." You don't even really have to catch every single deduction. All you have to do is count up how many clowns go after each of the major players – R, T, and V. It's easy to spot that R, T, and V are the important ones because they are related, by rules, to so many different clowns (V explicitly, in rules 1, 2, and 6, and R and T mostly implicitly, through being related to V). R, T, and V should jump out at you as the clowns to consider; you count up the number of clowns that must follow them, and you are in business. It is a systematic, rule-governed process. You can memorize when to do it, you can memorize how to do it, and it is easily practiced and mastered. Just the way I like it. Notice, though, that if you keep your eyes open on "What can be true?", "What can't be true?", and "What must be true?" questions (but not on If-questions), you can make many of these deductions in the process.

What Do I Do Next? Review your notes on this game. If you want to learn to make deductions, think about how they are made. Relax for a while. Then do this game without any notes; if the deductions give you a hard time, do it without them. See what skills you are still having trouble with. Once you feel that you have learned what this game has to offer, go on to Game Ten.

Answer Key 1. 2. 3. 4. 5. 6. 7.

E D C D D E E

Game Ten

219

220 Game omitted from electronic version of book.

Game Ten

Game Ten

221

Game Ten (From LSAT 38) Try this game on your own and then read my explanations.

Step 1: Read the Setup/Draw a Diagram From what we are initially told, we are trying to figure out which of the six tasks is done by each volunteer. We know that each volunteer will only demonstrate two tasks, but we know next to nothing about the tasks. Thus, our diagram should be based around the volunteers, because we know more about them. We write down the volunteers' names, and we put two blanks under each, since each will demonstrate two tasks. F __ __

G __ __

L tasks: H M P S T W __ __

Step 2: Read the Rules The first rule talks about the order in which the volunteers will demonstrate the tasks. But up until now the game hasn't talked about putting the volunteers or the tasks in order. This is something our diagram isn't built for. Quickly look through the other rules and see if there are any more like this. There are: the next rule talks about the first and last tasks, and the last rule talks about M being after T. This is a game about ordering the tasks, as well as assigning volunteers to tasks. Our diagram is wrong. For some of you (like me), when you first see the rules about order, you might think that by "first task" the game means H, and by "last task" it means W. That is to say, maybe the order of tasks refers to the order they were told to us in – H is first, M is second, P is third, etc. I thought this was possibly what they meant, but I wasn't sure. However, a quick look at the questions tells us otherwise – question 8 has the tasks all in a different order than they are given to us. Also, the last rule has M coming after T, which is not the order in which the tasks were initially given to us. This means that the tasks aren't already in the right order – we have to find the order. Remember, if the setup confuses you, look at the rules to help figure the game out. If the rules confuse you, glance at the questions. So we have to go back and make a new diagram. Cross off the diagram we have. What are we trying to figure out in this game? We want to put the tasks in order, and figure out who does what task. So we have three types of things that we are trying to match up: order, tasks, and volunteers. Which do we know more about? We know more about the order – 1 is before 2, 2 is before 3, and so on. So we'll build our diagram around that. Since there are six tasks, and none are done at the same time (it says "No two tasks will be demonstrated concurrently.") we have to have first through sixth. 1

2

3

4

5

6

We want to figure out what task goes with each number. But we also want to figure out what volunteer does each task. So we need two spaces under each number, one for tasks and one for volunteers. We also need to remember that each volunteer goes twice; it's easiest to write this as a rule.

222

Game Ten 1 tasks: __ vol.: __

2 __ __

3 __ __

4 __ __

5 __ __

6 __ __

HMPSTW FGL

F, G, L used twice Another handy way to write down that the volunteers will be used twice is to write two Fs, two Gs, and two Ls, like this: F F G G L L. Then you can cross them off as they get used, and you'll see that you have to use two of each. Now, why didn't I just tell you this right out, instead of making us draw the wrong diagram? There's a valuable lesson here. No one could have looked at that setup and known that they had to put the tasks in order. Well, OK, not no one – the fact that the setup told you "No two tasks will be done concurrently" hints that we have to put the tasks in order. But most people, most smart, good-at-the-LSAT people, would not have realized, just from reading the setup, that they were supposed to put the tasks in order. And that's OK. If you've learned what I've taught you, it doesn't take you very long to put together a diagram. So realizing that your diagram is wrong isn't that big of a blow; just stay calm and put together a new diagram. Not so hard, is it? No, it isn't. What we just experienced is something that happens once in a while on the LSAT. It happens to me from time to time, and it'll happen to you when you practice. You've got to accept that it is possible and not worry about it. What I don't want you to do is worry about every setup, agonizing over every possible scrap of meaning you might be able to get out of it. Take what they say literally, and use it to put together a diagram. If your diagram isn't right, the rules will tell you. Have confidence in your ability to understand what the LSAT is telling you, but don't expect that you will be infallible. As long as you apply what you've learned from this book, making mistakes won't be so bad, because they won't cost you a lot of time and you can recover easily from them, just as we did here. With that all said and done, let's go through the rules. The first one is a little odd, so let's take it apart piece by piece. You are told that F demonstrates "exactly one task" before G. What does "exactly one" mean? It means one and only one. Frank will end up demonstrating two tasks. Exactly one of these is before both Gs, the other isn't. It doesn't have to be after both Gs, but it has to be after one G. So when we write this rule down, we want to make it clear that one F is before both Gs, but not the other. So here we understand the rule by understanding important LSAT words like exactly. one F before both G (other F not before both Gs) The next few rules are straightforward. F not 1 F not 6 G not H G not M L not H L not T The last rule is also straightforward; it tells you that T is before M, and they are right next to each other. Remember, even though the rule says "after," you rewrite it using "before."

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223

There are several ways to write this rule. I like just writing TM, which, because I'm used to doing it; I know means that T and M are next to each other, in that order. But you might not be used to it, so there's nothing wrong with writing down a little more: TM (next to each other, in this order) Here is how our original diagram and rules turn out: 1 tasks: __ vol.: __ 1. 2. 3. 4. 5. 6. 7. 8. 9.

2 __ __

3 __ __

4 __ __

5 __ __

6 __ __

HMPSTW FGL

F, G, L used twice one F before both G (other F not before both Gs) F not 1 F not 6 G not H G not M L not H L not T TM (next to each other, in this order)

The Deductions There seem to be some deductions that we can make here. After all, we have the rule that one F is before both Gs, which has a "before" in it, and we have the rule that T is before M. So these are the types of deductions we know how to make. We know that one F is before two Gs. So that F can't be 5th or 6th. But what about the other F? Can it go 5th or 6th? Well, it can't go 6th because of rule 4. But can it go 5th? I don't see any reason why not – there are no other rules about the second F. So we can't deduce that F won't go 5th, because that would mean that neither F could go there. If this discussion confuses you, feel free to ignore it. As I did in the previous game, I will give an analysis of how to look at each answer without having made these deductions in a box after each answer. If we didn't use any deductions in evaluating a given answer, I won't bother to have a separate, boxed explanation. Sticking with the same rule, what about the Gs? Well, they both must go after F, so neither of them can go 1st. We can write this in our diagram, or as a rule. I'm going to write it as a rule, because I don't see us writing a lot of other deductions in the diagram. That means that we won't have much reason to look at the diagram, and may forget to do so; if you have only one or two deductions, writing them with the rules makes them easier to spot. 10. G not 1 We also have rule 9, which tell us that T is before M. So T can't go 6th and M can't go 1st. 11. T not 6 12. M not 1 And these are our deductions. Now, there is at least one other possible deduction, but I am not going to tell you what it is yet. Why not? Two reasons: 1) The deduction either jumps

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out at you or it doesn't; if it doesn't, I don't want you looking for deductions like it, because that will slow you down; if it does jump out at you, you don't need me to tell you what it is. 2) We'll make the same deduction as we do the questions.

Step 3: Answer the Questions Here's the order in which we should do the questions: Question Number 8 10 11 13 9 12

Question Type What can be true? If If What can be true? What must be true? What must be true?

Question 8 This is a "What can be true?" question, so we eliminate any answer that breaks a rule. Since the answers spell everything out for us, we don't need to draw any test diagrams. Answer A This violates rule 3, "F not 1." Answer B This breaks rule 2, since both Fs are before both Gs – the rule tells us that only one of the Fs is before both Gs. Answer C F, G, and L are all used twice. Only one F is before both Gs. F is not 1 or 6. G doesn't do H nor M. L doesn't demonstrate H or T. And T (threshing) is immediately before M. So this follows all the rules. It is possible; copy it down so we will recognize it as a possible diagram later on. 1 tasks: P vol.: L

2 S F

3 T G

4 M L

5 H F

6 W G

Question 10 Since this is a "What can be true?" question, we don't bother to use our previous diagrams. We have to test the answers out. First draw a new diagram and put L fourth. 1 tasks: __ vol.: __

2 __ __

3 __ __

4 __ L

5 __ __

6 __ __

HMPSTW FGL

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225

Now let's go through the rules. We have to use one more L. The rules about F don't seem relevant, nor do the rules about G. Ahh, we know that position 4 can't be H or T (rule 8). We can write that in. 1 tasks: __ vol.: __

2 __ __

3 __ __

4 __ L no H no T

5 __ __

6 __ __

HMPSTW FGL

Continuing through the rules, we see that T and M are next to each other, in that order (rule 9). Since T can't be 4, M can't be 5. 1 tasks: __ vol.: __

2 __ __

3 __ __

4 __ L no H no T

5 __ __ no M

6 __ __

HMPSTW FGL

That is it for our rules. Let's look at the answers. This is a "What could be true?" question, so we test each answer out and see if we can make it work. The question asks us where H could be, so we put H in the place the answer tells us and try it out. Answer A Let's put H first. 1 tasks: H vol.: __

2 __ __

3 __ __

4 __ L no H no T

5 __ __ no M

6 __ __

HMPSTW FGL

Now we go through the rules. Skim until we see a rule that is relevant; ahh, rule 6 talks about H, as does rule 7. We know that H can't be with G or L. So G and L can't go 1st. That leaves F to go first. 1 tasks: H vol.: F

2 __ __

3 __ __

4 5 __ __ L __ no H no M no T Go back through the rules. Rule 3 tells us that F Cross off the diagram and eliminate the answer.

6 __ __

HMPSTW FGL

can't go first. So this answer is wrong.

Now, before we go on, I want to point out a couple of things. Finding this answer was in no way dependent on where L was, was it? So, no matter where L goes, can H go 1st? No, it can't. This is a deduction. Also, no matter where L goes, who will go with H? G can't and L can't, so F has to. We know that H and F go together, no matter what. So this answer points us in the direction of two deductions. If you keep your eyes open for things that have to be true as you go through the answers, you will pick things like this up.

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Answer B Let's try this out. We just learned that H goes with F, so put F 2nd as well. One thing to be aware of in a game like this: when you have two types of blanks (for two types of things), make sure you write the right type of thing in the right blank. For example, don't put L in the "tasks" row, or you might think you have run out of spots for tasks. 1 tasks: __ vol.: __

2 H F

3 __ __

4 __ L no H no T

5 __ __ no M

6 __ __

HMPSTW FGL

Let's go through the rules. One F has to go before both Gs, so let's see where we can put the Gs. We can't put either of them 1st, because then there would be no room for F to be before them. Can we put one 3rd? Put it in there, but mark it because we don't know that it has to go there. 1 tasks: __ vol.: __

2 H F

3 __ G*

4 __ L no H no T

5 __ __ no M

6 __ __

HMPSTW FGL

Now, where do the other F and G go? It seems like they can go in either order – all the rule tells us is that the second F can't go before both Gs. We can't put the other F 1st, because then two Fs would be before both Gs, and also rule 3 says “F not 1.” So put the F in the next available spot, and G after, but mark them because we decided to put them there. We also put L in the last spot left open, spot 1. 1 tasks: __ vol.: L

2 H F

3 __ G*

4 __ L no H no T

5 __ F* no M

6 __ G

HMPSTW FGL

We continue through the rules. G can't go with H or M (rules 5 and 6). Since H is already in, just note that M can't be 3rd or 6th. 1 tasks: __ vol.: L

2 H F

3 __ G* no M

4 __ L no H no T

5 __ F* no M

6 __ G no M

HMPSTW FGL

L can't go with H or T (rules 7 and 8); again, only write about T, since H is already assigned a spot. 1 tasks: __ vol.: L no T

2 H F

3 __ G* no M

4 __ L no H no T

5 __ F* no M

6 __ G no M

HMPSTW FGL

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227

T has to go immediately before M (rule 9). Where can these two go? Try every space until you find a possible pair. They can't go 1st and 2nd, because H is already 2nd. They can go 3rd and 4th, because T can go 3rd and M can go 4th. In fact, they can't go anyplace else – you can't put T in 4 (because it says "no T" under 4), and you can't put T in 5, because M can't go 6th. 1 tasks: __ vol.: L no T

2 H F

3 T G* no M

4 M L no H no T

5 __ F* no M

6 __ G no M

HMPSTW FGL

We've got P, S, and W left. But we don't have any rules about these, so just put them wherever. 1 tasks: P vol.: L no T

2 H F

3 T G* no M

4 M L no H no T

5 S F* no M

6 W G no M

HMPSTW FGL

Alright, this works, so this (answer B) is the answer. Getting this is just a matter of going through the rules one by one and writing everything down. Question 11 Check your previous diagrams before you do anything else, since this is an If and a "What must be true?" question. Do you have any diagrams that fit what the If tells you (G demonstrates P, P is immediately before T, and F demonstrates T)? No, we don't, so we've got to test this out. They've given us a little block of people. G is before F, G demonstrates P, and F demonstrates T, so we write this down. Here is the way I like to write it – just the way it will end up looking in our diagram, with volunteers on bottom and tasks on top: P T G F Let's go through our rules. We know that one of the Fs has to be before both Gs (rule 2), so the F we have here is not the first one, because it is after G. There must be an F before this. We also know that F has to demonstrate H (we deduced that in question 10); the second F is demonstrating T, so the first F must be the one that demonstrates H. Let's add this on to what we have written down. H F before

P T G F

Then rule 9 tells us that M has to follow T. So put the M in here: H P TM F before G F

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Game Ten

Finally, one last look through the rules tells us that G can't learn M, so we can't have a G immediately following the F. That might mean that the G comes before the F (and before the other G) or after the F, but just not next to it. H P TM F before G F no G OK, that's a lot to have figured out. Let's work through the answers. This is a "What must be true?" question, so we'll test the answers by doing something other than what they describe. Answer A We don't want to put F 2nd. Let's try putting it someplace else. It can't go 1st (rule 3), so try it 3rd (and star it, so we can move it if it doesn't work). 1 tasks: __ vol.: __

2 __ __

3 H F*

4 __ __

5 __ __

6 __ __

HMPSTW FGL

We have to have P, T, and M following the H/F pair. Since there are only three spots left, they have to go in these spots. Put everything we have in that block in along with them (including G, F, and the "no G"): 1 tasks: __ vol.: __

2 __ __

3 H F*

4 P G

5 T F

6 M __ no G

HMPSTW FGL

Now let's go through the rules. Rule 2 says that one F has to go before both Gs. We have both Fs in, so both Gs have to go after the first F. But the only space open says "no G." This won't work. The only thing we have starred is F, so that is the only thing we can change about this diagram. We are always consistent about the way we move our marked people; we always move them from left to right. We always put people in the earliest spot (the leftmost spot) we can, so there is no reason to move them to the left – they are already as far to the left as possible. But F can't go any further to the right – there already is too little room to fit everyone in that has to go after F. So there is nothing we can do to make this diagram work. Since this is a "What must be true?" question, what does this tell us? It tells us that this (answer A) is the answer. Question 13 This is a "What can be true?" question, so we test each answer out and see if we can make it work. Answer A We know that H has to go with F; but rule 3 tells us that F can't go 1st. So H can't go 1st. This is a wrong answer. If we hadn't deduced that H and F go together, we could still do this answer. We put H first. Rule 5 tells us that G can't go with H, so G can't go first. Rule 7 tell us that L can't go with H, so L can't go first. That leaves F. But F can't go first.

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Answer B Let's try putting M 2nd. 1 tasks: __ vol.: __

2 M __

3 __ __

4 __ __

5 __ __

6 __ __

HMPSTW FGL

6 __ __

HMPSTW FGL

Go through the rules. G can't be with M (rule 6). 1 tasks: __ vol.: __

2 M __ no G

3 __ __

4 __ __

5 __ __

Keep going through the rules. T is right before M; that puts T first. 1 tasks: T vol.: __

2 M __ no G

3 __ __

4 __ __

5 __ __

6 __ __

HMPSTW FGL

Since we've added to the diagram, we go back through the rules again. L can't go with T (rule 8). 1 tasks: T vol.: __ no L

2 M __ no G

3 __ __

4 __ __

5 __ __

6 __ __

HMPSTW FGL

Rule 10 (one of our initial deductions) tells us that G can't go 1. Which leaves F for first. But F can't go first (rule 3). So this won't work. Cross off the diagram and eliminate the answer. What if we hadn't initially deduced that G couldn't go 1st? We know that L can't go with T, so L doesn't go first, and F can't go 1st. That leaves G to go 1st. But rule 2 tells us that one F has to go before both Gs. If G is 1st, then there is no room for F to go before it. This tells us that this is the wrong answer, and also makes us realize that G can't go first. Answer C We just saw that T can't be 1st, so eliminate this. Answer D This contradicts one of our initial deductions, that T can't go last. If you hadn't made that deduction, you'd put T last and then you'd go through the rules. When you got to rule 9 (T immediately before M), you'd see that there was no place to put M, so this answer must be wrong. Answer E must be the answer.

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Game Ten

Question 9 By this stage in the game this is an easy question. We know answer A is right just by looking at it, since we've already figured out that F and H have to go together. If you hadn't realized that, here's how you'd do the question. It's a "What must be true?" question, so if the answer describes a situation that isn't in every previous diagram, it is wrong. Answer B gets eliminated by previous diagrams: the diagram for 8C doesn't have F with M, nor does the diagram for 10A. C also gets eliminated by previous diagrams: 8C doesn't have F with T, nor does 10A. The same thing happens with answer D. But answer E is different; in each of our previous diagrams, one of the Gs demonstrates W. Now, if you understand how equivalence works (see Advanced Techniques), you will have realized that S and W are equivalent. So you can switch the S and the W in the diagram for 8C (or 10A), and you will have G demonstrating T and S, instead of T and W. Thus, G doesn't have to demonstrate W, and A is the right answer. If you don't understand equivalence, you'd have to test out either A or E. You'd test out A because it's first, and you'd soon realize that F has to demonstrate H; if it didn't then G or L would have to, but they can't (from rules 5 and 7). So A is the right answer. Question 12 Use previous diagrams before you do anything else. This is a "What must be true?" question, so if we can find a previous diagram that has a situation different from what the answer describes, the answer is wrong. Each of our two previous diagrams has F in position 2, so we skip answer A. Neither of our previous diagrams has G 4th, so we eliminate B. Both previous diagrams have G 6th, so we skip C. Both have L 1st, so we skip D. Neither has L 2nd, so we eliminate E. We have to test out A, C, and D. Answer A We don't want to put F 2nd. We can't put him 1st (rule 3), so put him 3rd, and mark him with a dot or a star so we know that we had a choice. 1 tasks: __ vol.: __

2 __ __

3 __ F*

4 __ __

5 __ __

6 __ __

HMPSTW FGL

Now go through the rules. We know that F has to be before both Gs, but we can't have both Fs before both Gs. We might have the second F between the Gs, or after the Gs. Let's put him between the Gs, star him, and move him if we have to (as it turns out, we couldn't have the F after the two Gs, because that would break rule 4, that F is not 6th; you might not have thought of this, but if you actually tried to put F 6th, you would have realized that this doesn't work when you looked back at the rules). 1 tasks: __ vol.: __

2 __ __

3 __ F*

4 __ G

5 __ F*

6 __ G

HMPSTW FGL

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231

This leaves the two Ls to go 1st and 2nd. 1 tasks: __ vol.: L

2 __ L

3 __ F*

4 __ G

5 __ F*

6 __ G

HMPSTW FGL

Go through the rules. We know that G and L can't go with H, which reminds us that one of the Fs has to demonstrate H. Give it to the first F, but star it since it didn't have to go there. 1 tasks: __ vol.: L

2 __ L

3 H* F*

4 __ G

5 __ F*

6 __ G

HMPSTW FGL

The next rule says G can't go with M, and later we see that M has to go after T. Where do T and M go? They can't go 1st and 2nd, because L can't go with T; it looks like they can go 4th and 5th (and it turns out that they can't go 5th and 6th, because G can't go with M). 1 tasks: __ vol.: L

2 __ L

3 H* F*

4 T G

5 M F*

6 __ G

HMPSTW FGL

We have P, S, and W left, and there are no rules about them, so put them wherever you'd like. 1 tasks: P vol.: L

2 S L

3 H* F*

4 T G

5 M F*

6 W G

HMPSTW FGL

This works, so we eliminate this answer. Unfortunately, this diagram doesn't help us eliminate any other answers. Answer C G is 6th in the diagram we just made, so we can't eliminate this answer based on the work we just did (and L is first, so we can't eliminate that one either). Or can we? We have the star next to the F in position 5. That means we can move F over, making G not 6th! Except when we check the rules, we see that F can't go 6th. So let's work this out the old fashioned way. We want G not to be 6th. Put a "not G" under 6 and let's try putting G someplace and see where we can fit it. We start putting G as early as possible, and marking it with a star. If it doesn't work, we move it one over and try again. We know that G can't be 1st (one of our initial deductions, and something we also deduced from question 13, answer B). So we put G 2nd. 1 tasks: __ vol.: __

2 __ G*

3 __ __

4 __ __

5 __ __

6 __ __ no G

HMPSTW FGL

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Game Ten

Go through the rules. Rule 2 tells us that one F has to be before this G. That F will have to go 1st. But the next rule tells us that F can't go 1st, so G can't be 2nd. So we look at what we can change. G is starred, so move it over one. 1 tasks: __ vol.: __

2 __ __

3 __ G*

4 __ __

5 __ __

6 __ __ no G

HMPSTW FGL

Now we put one of the Fs in front of this G (but not in position 1). 1 tasks: __ vol.: __

2 __ F

3 __ G*

4 __ __

5 __ __

6 __ __ no G

HMPSTW FGL

We know that we have to have an F and a G after this G. We don't want to G to go last, so let's just put it in position 4 (that's the first available spot), and I'll put F in position 5 (the next available spot). I'll star both of these, since they didn't have to go where I put them. This also leaves the two Ls in 1 and 6 (don't star them, because they have to go there). 1 tasks: __ vol.: L

2 __ F

3 __ G*

4 __ G*

5 __ F*

6 __ L no G

HMPSTW FGL

Phew. Now we assign tasks. I'm going to put H with F, because I know that they go together; I star it because H could have gone with the other F. I hope I don't have to go back and rework this diagram, because we've got a lot of things we could change (if we did, though, we'd probably have an idea of where the diagram went wrong, and we could change the thing most relevant to that). 1 tasks: __ vol.: L

2 H* F

3 __ G*

4 __ G*

5 __ F*

6 __ L no G

HMPSTW FGL

Now go through the rules again. The Gs won't go with M (or H, but H is already put down), and we've got to put in TM. Put TM in 4 and 5 or 5 and 6. 1 tasks: __ vol.: L

2 H* F

3 __ G*

4 T G*

5 M F*

6 __ L no G

HMPSTW FGL

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This leaves P, S, and W, who can go anywhere. 1 tasks: P vol.: L

2 H* F

3 S G*

4 T G*

5 M F*

6 W L no G

HMPSTW FGL

This works, so the answer is wrong. This also shows us that L doesn't have to be 2nd, so E is wrong. D is the answer.

Summary This is a tough game, but if you keep a cool head, you can do it. The setup doesn't give you enough information to draw a diagram, but the rules and questions do. The questions really rely on your ability to test things out, but they don't require any amazing insights, just a willingness to be methodical. If you keep having to remind yourself what to do next in a game like this, you'll never finish it. But, if you plug in what the answers say, look at the rules, put people in the first open spots, and move marked people from left to right when diagrams don't work, all without much hesitation, you'll do great.

What Do I Do Next? Review your notes on this game. Relax for a while. Then do this game without any notes. See what skills you are still having trouble with. Go back to the chapters that discuss those skills and review them. Once you feel that you have learned what you need to from this game, go on to Game Eleven.

Answer Key 8. 9. 10. 11. 12. 13.

C A B A D E

234 Game omitted from electronic version of book.

Game Eleven

Game Eleven

235

Game Eleven (From LSAT 38) Given what you already know, You should be able to handle this game except for question 16. Go ahead and work through the game on your own, and then take a look at what I have here.

Step 1: Read the Setup/Draw a Diagram Read the setup, spot what types of things are involved in this game, and figure out which you know more about. Ready… go! That was fast. OK, we have two types of things in this game: applicants and positions. We know more about the positions – we know the number of applicants that get matched with each position. So we will build our diagram around the positions. We write them down horizontally, and put as many blanks under them as there are applicants that will be matched to them – management gets one; production, three; and sales, three. M __

P __ __ __

S __ __ __

applicants: F G H I W X Y

I like a nice, straightforward diagram like this. Alternately, we could use this diagram: F G H I W X Y __ __ __ __ __ __ __

m ppp ss s

We assign each applicant a position and cross the positions off as they are used. Since there is more than one p and s position, we have more than one of these to cross off. This diagram is a little clunkier than the one we'll use, but it would work.

Step 2: Read the Rules Here is how I wrote the rules; nothing fancy here. Did you do the contrapositive of the "If… then…" rule about X? H with Y F not with G If X in S, then W in P If W not in P, X not in S F in P

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Game Eleven

I'm also going to put F in a blank under P, so I can see that he goes there. If it's possible to put someone directly into a diagram, it's best to do so. This leaves only two open spots under P. Here is how my rules and original diagram end up looking: M __

1. 2. 3. 4. 5.

P F __ __

S __ __ __

applicants: F G H I W X Y

H with Y F not with G If X in S, then W in P If W not in P, X not in S F in P

The Deductions I don't have any rules that say who goes before whom, so I'm not going to make any of that type of deduction here. I also don't have any people in multiple rules (well, F is in rules 2 and 5, so we know that G can't be in P, but that isn't a very exciting deduction), so the other type of deduction is out as well.

Step 3: Answer the Questions Here is the proper order in which to do the questions: Question Number 14 18 19 17 15 16

Question Type What can be true? If If What can't be true? Which is a complete and accurate list? How many diagrams are possible?

Question 14 The fact that the question says "Which one… could be a complete and accurate list…" makes this a "What can be true?" question. Answer A This follows rules 1 (H with Y) and 2 (F not with G), but breaks rule 3. X is in S, but W is not in P. Answer B This has F in sales, not production, violating rule 5. This should have jumped right out at you, since F is under P in our original diagram. This doesn't break any other rules, though. Answer C This breaks rule 1 – H is not with Y. Answer D This breaks rule 1 also, because H and Y aren't together.

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237

Answer E must be the answer. Copy it down so you can use it as a previous diagram. M X

P F I W

S G H Y

Question 18 Since this is a "What can't be true?" question (even though it is also an If-question), the first thing we do is look to see if we have a relevant previous diagram. But our single previous diagram doesn't have F with X, as the "if" part of the question stipulates, so we have to work this out. Draw a new diagram and add what you are told. The question tells you that F is with X; since we know F is in P, X must be in P as well. M __

P F X __

S __ __ __

applicants: F G H I W X Y

Let's go through our rules. Rule 1 says that H and Y are together. Well, there is only one place they could go – S (because there is not enough room for both of them in either P or M). So let's put them there. (If you hadn't realized that, you could still get this question right; I'll explain how in the boxed text, at the end of the question.) M __

P F X __

S H Y __

applicants: F G H I W X Y

Rule 2 says that F is not with G. So we can write "no G" under P. M __

P F X __ no G

S H Y __

applicants: F G H I W X Y

Rule 3 says "If X in S," but S isn't in X, so we ignore this rule (see Game Three for more on when to ignore "If… then…" rules). The same applies to 4 – we don't know whether or not W is in P, so we ignore this one. Our last rule tells us that F is in P, but we already knew that. Since we added more stuff to the diagram, we go back through the rules, but nothing new comes up. We're done looking at the rules. Let's check out the answers. The question is an EXCEPT question (because it has the word "EXCEPT" in it). These questions describe the wrong answers to us; here, we know the wrong answers will be things that can be true. This means that the right answer can't be true – this is a "What can't be true?" question (see The Fundamentals for more on different ways questions can be worded).

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Answer A Recopy our diagram and put G under S. M __

P F X __ no G

S H Y G

applicants: F G H I W X Y

This leaves I and W to go in our last two spots. Look through the rules. Rule 5 says "If W not in P, X is not in S." Well, if we put W in M, it won't be in P. That means that X can't be in S. X isn't in S, so that's no problem. If we put W under P, rule 4 wouldn't apply (since it tells you what happens if W isn't under P). And there are no rules about where I goes. So either one of them can go either place. Let's just put them in alphabetical order (I going in before W). M I

P F X W no G

S H Y G

applicants: F G H I W X Y

This follows the rules, so it is the wrong answer. It also helps you eliminate answer E, since we see that W can be under P. If you are really canny, you'll see that we can eliminate D as well – we could have put W under M if we wanted to. Answer B We already figured out that H had to be under S before we tested the answers, so this can't be true. This is the right answer. If we hadn't seen earlier that H and Y had to go under S, we'd have to work out answer B. You'd put H under P, and then you'd look at the rules. Rule 1 would tell you that H and Y had to go together, and you'd see that there was no room for Y, so you'd know that this couldn't work. Question 19 Although this is an If-question, so it seems like we potentially can use previous diagrams, it's also a "What can be true?" question; thus, we really can't. The question doesn't tell us where X goes, but it tells us where X won't go, so we can write that in our new diagram. M __

P F __ __ no X

S __ __ __

applicants: F G H I W X Y

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Let's go through the rules. Rule 1 says H is with Y, but we don't know where they will go (I guess we know that they won't go under M, but that's it). F is not with G, so we can write "no G" under F. M __

P F __ __ no X no G

S __ __ __

applicants: F G H I W X Y

We don't know if rule 3 applies, because we don't know if X is in S or not, and we don't know if rule 4 applies because we don't know about W. So we can't really figure anything out here. Let's look at the answers; this is a "What can be true?" question, so we will test out answers until one works. Answer A We don't even have to try this out, because we know that F can't be in sales; if F can't be in sales, we can't have both F and H in sales (since "both" means "the two of them"). Answer B Let's put both H and W in sales. M __

P F __ __ no X no G

S H W __

applicants: F G H I W X Y

Now go through the rules. Rule 1 tells us that H and Y go together, so put Y with H. M __

P F __ __ no X no G

S H W Y

applicants: F G H I W X Y

Rule 2 says that F is not with G. Well, if G isn't with F, where will it go? There's only one place left that isn't with F, and that's M. So we put G there. It's easy to miss something like this – you just rush through the rules saying "Yeah, yeah, I already looked at that," and boom, you miss something important. That's why you have to be systematic and really go through each rule every time. M G

P F __ __ no X no G

S H W Y

applicants: F G H I W X Y

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Game Eleven

Now we only have two people left (I and X), and two spaces open (both under P). I and X both have to go under P. But we have "no X" written under P. You may not remember why you have it written down there, but there it is (you have it written because it's what the If part of the question told you). So this won't work. Cross off the diagram and move on. Answer C Let's try putting both F and Y under P. Recopy the diagram for this question. F is already under P, so put Y there as well. By this point I remember that H and Y go together without having to look through the rules, so let's put H under P as well. M __

P F H Y no X no G

S __ __ __

applicants: F G H I W X Y

So far so good – we haven't put X or G under P. Look through the rules. We've already followed rule 1. Rule 2 tells us that G will be under M or S, but we don't know where. Rule 3 says that if X is in S, then W is in P, but we don't know if X is in S. Rule 4 says that if W is not in P, X is not in S. Well, can we have W in P? No, because P is all filled up. So rule 4 applies here. X is not in S. If X is not in S, where is it? It has to be in M, which leaves everyone else in S. M X

P F H Y no X no G

S G I W

applicants: F G H I W X Y

Does this follow all the rules? Yes it does. So this (answer C) is the answer. Question 17 Each of the answers is supposed to be two of the three people (hence "partial list") under S. This is an EXCEPT question, so it describes the wrong answers to us. Since it says "could be," we know that the right answer can't be an accurate partial list. We can use previous diagrams and eliminate any answers that we know are possible. We eliminate answer A based on the diagram for 19B (the one we just did), since that has G and I in sales. We don't see G and X together in any of our previous diagrams, so skip that one. We see G and Y together in 14E and 18A (although you should just see one of these diagrams and stop looking), so we can eliminate C. We don't see H and W together in sales, so skip answer D; nor do we see H and X. Remember, this is a "What can't be true?" question. So we have to test out at least one of B, D, and E.

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Answer B Let's try putting G and X together in sales. M __

P F __ __

S G X __

applicants: F G H I W X Y

Let's go through the rules. Rule 1 says that H has to be with Y. Where will these two go? Well, there's only one place with room enough for both of them – P. So we put them there. M __

P F H Y

S G X __

applicants: F G H I W X Y

Rule 2 says that F and G aren't together, which is the case here, so that's fine so far. Rule 3 says that if X is in S, W has to be in P. Well, X is in S, so this is relevant. But W can't be in P. Why not? Not enough room. So this won't work. Cross off the diagram and circle this answer (answer B) (remember, we're looking for something that can't be true). Question 15 This is a "Which is a complete and accurate list?" question. We want an answer that is a complete and accurate list of people who cannot be in production. That means that if the list contains people who can be in production, it is wrong. If the list leaves out someone who can't be in production, it is wrong. We'll use our previous diagrams. If someone in the answer is in a previous diagram under P, the answer is wrong. Answer A Well, we know that F has to be in P, so this is immediately wrong. We can also eliminate any other answer with F in it (but none of the others has F, so that isn't too helpful). Answer B We know that G can't be in P (because it can't be with F). H and Y are in P in the diagram for 19B, so this is wrong. We can also eliminate answer C because it has H and Y. Answer D Is G the only person who can't ever be in P? This looks good, since we know that G can't be in P, but we don't know if the answer has left anyone else out. Look at E. Answer E Well, this answer leaves G out, so this has to be wrong. Answer D is the answer. Question 16 We haven't done a question like this before, which isn't surprising, because they are pretty rare. The question asks us under what conditions we could know exactly where everyone goes. That means that the wrong answers will give us a situation where we don't know exactly where everyone goes – someone will have more than one possible place to be. So we test out each answer and see if it forces everyone into certain positions. We can use our previous diagrams to a certain extent – if we see two previous diagrams that fit the description in the answer, but have some other differences, we know that the

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answer doesn't completely determine what happens. But we don't often have two diagrams that are both relevant to an answer, so we aren't going to count on this. Answer A We have two previous diagrams with F and W under P – 14E and 18A. These diagrams are not exactly the same: X and I are in different places. So having F and W both under P doesn't completely determine what happens in the game. We can eliminate this answer. Answer B 14E and 18A help us again – both have G and Y in sales, but they aren't exactly the same in every other way. We can eliminate this answer. Answer C We only have one diagram where I and W are under S (19B). Thus, we can't compare two diagrams and see if they come out the same. Skip this answer. None of our people or job categories are equivalent in this game – they are all subject to different rules (with the exception of I, who is subject to no rules). So we can't really rearrange any of our previous diagrams (see Advanced Techniques). Answer D We only have one diagram (14E) where I and W are under P, so skip this answer too. Answer E We don't have any diagrams where I and X are under P. So we have to test out at least one of C, D and E. Back to answer C. We test it by putting I and W in sales and seeing if anything is left up to us, or if everything else is forced to happen in a certain way. M __

P F __ __

S I W __

applicants: F G H I W X Y

Rule 1 tells us that H and Y have to be together. So we have to put them under P (since there is no place else that we could fit both of them). So far nothing is up to us. M __

P F H Y

S I W __

applicants: F G H I W X Y

Rule 2 tells us that G can't be with F, but since there is no room with F under P anyway, this is no problem. We ignore rule 3, because we don't know if X is in S or not. Rule 4 says "If W not in P," and W is indeed not in P (it's in S). So we know that X is not in S. There is no place to put X except M. So we put him there; we have no choice, he has to go there. M X

P F H Y

S I W __

applicants: F G H I W X Y

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This leaves G, who has to go under S. M X

P F H Y

S I W G

applicants: F G H I W X Y

Everything that we put in was totally determined by the rules. So C is the answer. Let's look at answer D. I want to show you how to eliminate an answer on one of these questions without using previous diagrams. So let's draw a test diagram and, like D says, put I and W under P. M __

P F I W

S __ __ __

applicants: F G H I W X Y

Now we go through the rules. H and Y have to be together, and they can't fit under M or P, so we put them under S. So far we have no options. M __

P F I W

S H_ Y_ __

applicants: F G H I W X Y

Rule 3 says "If X in S," but we don't know if X is in S or not. Rule 4 says "If W not in P," but this is not the case; W is in P. We've now run out of rules; it seems we can put G and X in either spot. Just to be sure, put them in one way, and then the other. M G

P F I W

S H_ Y_ X_

applicants: F G H I W X Y

M X

P F I W

S H_ Y_ G_

applicants: F G H I W X Y

Both of these follow all the rules; the only rule they might break is rule 4. In the first case, rule 4 is relevant because X is in S. But rule 4 is followed, because W is also in P. In the second case, rule 4 is irrelevant because X is not in S. Both of these diagrams work, so the answer doesn't completely determine where everyone goes; there is more than one option.

Summary Now we've seen a "How many diagrams are possible?" question, and you can probably understand why we save them for the end. Nothing else in this game is new to us, which is just how it's going to be on the LSAT – everything you'll see on the test will be something you already know how to handle. Doing well on the test is just a matter of showing up and doing exactly what you've practiced so many times before; no need to be tricky, or think of new and creative ways to approach questions.

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What Do I Do Next? Review your notes on this game. Relax for a while. Then do this game without any notes. See what skills you are still having trouble with. Go back to the chapters that discuss those skills and review them. Once you feel that you are comfortable with this game and the skills it tests, go on to Game Twelve.

Answer Key 14. 15. 16. 17. 18. 19.

E D C B B C

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246 Game omitted from electronic version of book.

Game Twelve

Game Twelve

247

Game Twelve (From LSAT 38) Try this game out on your own. If you get confused, come back and read step 1, step 2, and the explanation of the first question (question 20). Then work through the rest of the questions on your own.

Step 1: Read the Setup/Draw a Diagram What are the types of things we are matching together in this game? We have the pieces (N, O, etc.), we have their order (first, second, etc.), and we have the instruments (fiddle, lute, etc.). How do I know that we are concerned with order? The setup says that the pieces are performed "successively (though not necessarily in that order)." "Successively" means "in a row," and "not necessarily in that order" mentions order. If that wasn't enough, you can glance at the rules and they talk about the order of the pieces (which are next to which, and which is performed second). The instruments are already matched with the pieces. F has to go with fiddle and lute, O has to be with harp and mandolin, etc. How do we know this? The setup tells us what pieces are performed with what instruments; that means that those pieces are performed with those instruments. We don't need to worry about assigning pieces to instruments, then. All we need to think about is the order the pieces are performed in. So, which of the types of things do we know the most about? This is a toss-up. On the one hand, I'm inclined to say that we know the most about the order – first is next to second, which is next to third, and so forth. On the other hand, we know quite a bit about the pieces – we know what instruments are assigned to which pieces. I have to admit that I prefer to base the diagram around the order, because I've done that sort of thing before and I'm comfortable with it. I know how a diagram like this, with 1, 2, 3, 4, and 5 in a row, works. But, you could have based your diagram around the pieces. So I'm going to do this game two different ways, in parallel. I will do the game with the first kind of diagram – based around the numbers 1, 2, 3, 4, and 5 – and accompany the analysis of each step with notes (in a box) on how to do it with the other sort of diagram. So here is our diagram. I put three blanks under each number because I want to put a piece and two instruments in with every number. 1 __ __ __

2 __ __ __

3 __ __ __

4 __ __ __

5 __ __ __

I also want to write down the names of the pieces, and which instruments go with which pieces. 1 __ __ __

2 __ __ __

3 __ __ __

4 __ __ __

5 __ __ __

pieces: N O S T V f h g f L L m h g m

I wrote the names of the instruments in lowercase for your sake, so you could easily tell one from the other (except I put L in uppercase because it looks too much like I in lower case).

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Game Twelve

If we base our diagram around the pieces, then we write them down in order, and put a blank under each where we'll put what number goes with the piece: N f L __

O h m __

S g h __

T V f L g m __ __

Step 2: Read the Rules There are only two rules. The first one is a little complex. It says that each piece has to have an instrument in common with one of the pieces before or after it. What does this mean? In understanding odd rules, it's easiest to think of a specific example and see how the rule would apply to it. Imagine N was 1st, for example. We know that N has to share an instrument with the piece before it or after it. If N is 1st, there's no piece before it, so it has to share an instrument with the piece after it, the 2nd piece. What instrument will this be? Well, N has f and L, so it has to share f or L with the next piece. What piece could that be? It could be T, which would share f with it, or V, which would share L with it. Let's keep thinking. What if N was 2nd? Well, then it would have to share an instrument with the piece before it, which would be the 1st piece, or the piece after it, which would be the 3rd piece. So T or V would have to be 1st or 3rd. We could also have both T 1st and V 3rd, since a piece can share with both the piece before and the piece after it. Does the rule make more sense now? Good. That took us a little while; was that wasted time? No. You cannot answer the questions unless you understand the rules. Take as much time as you need to make sure you know what the rules mean and how to apply them. Here we can afford it because there are only two rules anyway. Let's write down the first rule; I can't think of any fancy way to say it, so I'll just write it plainly: Each piece shares instrument with before OR after (or both) The second rule is much simpler: N or T is 2 Here is our original diagram and rules: 1 __ __ __

2 __ __ __

3 __ __ __

4 __ __ __

5 __ __ __

pieces: N O S T V f h g f L L m h g m

1. Each piece shares instrument with before OR after (or both) 2. N or T is 2 You go through the same thought process to figure out the rules if you diagram this game the alternate way. You end up with very similar-looking rules. Here is the alternate original diagram and rules:

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diagram and rules: N f L __

O h m __

S g h __

T V f L g m __ __

1. Each piece shares instrument with before OR after (or both) 2. N or T is 2 The Deductions There are no deductions to make in this game – we only have two rules to combine, neither has "before" in it, and neither has anything in common with the other, as far as we can see.

Step 3: Answer the Questions Here is the order in which you should do the questions: Question Number 20 22 24 21 23

Question Type What can be true? If If What can't be true? What can't be true?

Question 20 This is a "What can be true?" question, so work through the answers, one by one, and see which one doesn't break any rules. Answer A This breaks rule 2 – N or T isn't 2nd. I'll be honest with you – I checked out rule 2 first, because it was simpler. I normally wouldn't do this, but I only had two rules, so I knew that I wouldn't get confused looking at them out of order. Answer B This follows rule 2, so we have to see if it follows rule 1. We have to see who shares with whom. S is performed with g and h, so it has to share one of these with the next piece, T. T is performed with f and g, so S and T share. We don't need to worry about these two, then, because they share with each other. Remember, a piece has to share with the one before it or the one after, but doesn't have to share with both. So once we know that S and T share, we don't need for T to share with O (although it is OK if they do). Let's look at O. It has to share with either T or N. O is performed with h and m. T doesn't have either, and N doesn't have either, so this rule is broken. The answers to this question don't look like our alternate diagram. I took the answers and put what they told me in our diagram. I put 1 under S, 2 under T, and so forth. N f L 4

O h m 3

S g h 1

T f g 2

V L m 5_

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Then we go through the rules. Everyone has to share with someone numerically next to it. We go from left to right just like we always do. That means that we start with N. It has to share with either 3 or 5 (the pieces before and after it). It doesn't share with 3 (which is O), so it has to share with 5. It does – both have L. So now look at O, the next piece in our diagram. It has to share with 2 or 4. It doesn't share with T, which is piece 2 – neither of them have any instruments in common. And we already know that it doesn't share with N, which is piece 4. So this breaks the rules. It is possible that at this point, if you had diagrammed the game in this way, you would be feeling a little confused. That's OK, because of course there is an alternate way of diagramming the game, which the answers give you – just put the pieces in order, as each answer does. One nice thing about the way we approach games is that we don't spend a lot of time putting together a diagram, which means that if we decide to change the way we diagram the game, we have wasted barely any time at all. If you realized that this was a confusing diagram for you, don't stick to it; switch to the other form that this question presents to you. You end up having wasted only a few seconds. Answer C This follows rule 2, so we have to see if it follows rule 1. The first two pieces share f, so look at the 3rd piece. O has to share with either N or V, the pieces next to it. It doesn't share with N, but it shares m with V. So O and V are happy. This just leaves S. Since S is last, it has to share with V. V and S don't share any instruments, so this breaks the rules. We translate this into our alternate diagram: N f L 2

O h m 3

S g h 5

T f g 1

V L m 4_

Let's go through the instruments one at a time, from left to right. N is 2nd, so it has to share with the 1st or 3rd piece. It shares with the 1st. O is 3rd, so it has to share with the 2nd or 4th, and it shares with the 4th. S is 5th, so it has to share with the 4th, V. But the two don't share anything, so this breaks a rule. Answer D This follows rule 2. Go through the pieces in order and see if they share appropriately. T and N share f, so they are happy. Move on to S. S has to share with N or O. S and O share h, so they are happy. Move on to V. V has to share with O, since there is no piece after V. O and V share m. So everyone shares with one of the pieces before or after it; this follows the two rules, so this is the answer. Write it down so we'll remember to use it as a previous diagram. 1 T f g

2 N f L

3 S g h

4 O h m

5 V L m

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Translate the answer into our alternate diagram: N f L 2

O h m 4

S g h 3

T f g 1

V L m 5_

N has to share with S (3rd) or T (1st). N and T share f, so they are happy. O has to share with S (3rd) or V (5th). O shares with both of them. Lucky O. So that means O is happy. We've already seen that T and N share, and V and O share, so everyone shares appropriately. This is the answer. Question 22 This is an If-question. At first glance it may seem like it is changing the rules – now every piece has to share with the piece after it. You may assume that this means they can't share with the piece before it. You may also assume that the last piece won't share with anyone, since it says "except the fifth." But these would be wrong assumptions. When a question contradicts one of the rules, it will tell you that it is doing so. It will say "Suppose the rule that blah blah is changed," or "If such and such a rule is removed…" If you think a question is contradicting a rule, but the question doesn't say that it is changing or deleting one of the rules, you are wrong. In this case, the question adds a rule, but it doesn't tell us that it is changing or getting rid of any of the existing rules. So pieces still can share with the piece before them, they just have to share with the one after them. And the last piece has to share instruments with the 4th piece, because that is the only piece next to it. If the 4th and 5th didn't share, then the 5th would share with no one, and that would break the first rule. Write down this new rule: Each shares with piece after I have a gut feeling that there is some kind of deduction here, something that has to happen. But it doesn't immediately hit me what it is, and I don't know how to make it. This rule doesn't name any specific pieces; I have the feeling if I fooled around with the diagram and pieces for long enough, I could figure something out. Should I do this? No. The questions will give me concrete things to test out, which is much easier than just trying random things and hoping I learn something. If it isn't clear how to apply an "if" situation, work through the answers. I'm also not going to check previous diagrams, both because this is a "What can be true?" question and also because it would be too hard to figure out if their diagrams matched the "if" part here. This is a "What can be true?" question, so we'll test the situation each answer describes.

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Answer A Draw a new diagram and put V 1st. Put V's instruments under it. 1 V L m

2 __ __ __

3 __ __ __

4 __ __ __

5 __ __ __

pieces: N O S T V f h g f L L m h g m

V has to share with the piece after it, so whatever goes 2nd has to have L or m. The rules tell me, though, that N or T will go 2nd. N has L, so it could share with V. T doesn't have L or m, so it couldn't share with V. T can't go 2nd, then, so N has to. 1 V L m

2 N f L

3 __ __ __

4 __ __ __

5 __ __ __

pieces: N O S T V f h g f L L m h g m

Again, N has to share with the piece after it. So whatever goes 3rd has to have either f or L. O doesn't have either and S doesn't have either. That leaves only T (since we've already used V). T does share with N; since it is the only one left that does, it has to go 3rd. 1 V L m

2 N f L

3 T f g

4 __ __ __

5 __ __ __

pieces: N O S T V f h g f L L m h g m

T has to share with whichever piece goes 4th; since T has f and g, the 4th piece has to have one of them. O doesn't have either, but S does. That means S goes 4th and O goes 5th. 1 V L m

2 N f L

3 T f g

4 S g h

5 O h m

pieces: N O S T V f h g f L L m h g m

We aren't out of the woods yet. O has to share with S. And it does, so this works. This (answer A) is our answer. Let's do this with our other diagram. The steps we go through are the same; we just draw it differently. We put a 1 under V. N f L __

O h m __

S g h __

T V f L g m __ 1_

This means that piece 2 has to have L or m; since only N or T can be 2, we know that N has to be 2. N f L 2

O h m __

S g h __

T V f L g m __ 1_

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Likewise, piece 3 has to have f or L, since each piece must share with the one after. There is only one piece unused that has either – T – so it has to go 3. N f L 2

O h m __

S g h __

T f g 3

V L m 1_

The next piece has to have either f or g. Only O and S remain; only S can share with T, so S is 4 and O is 5. N f L 2

O h m 5

S g h 4

T f g 3

V L m 1_

Question 24 Since this is a "What can be true?" If-question, we don't check our previous diagrams. Draw a new diagram and put S 5th. 1 __ __ __

2 __ __ __

3 __ __ __

4 __ __ __

5 S g h

pieces: N O S T V f h g f L L m h g m

Now go through the rules. We know that each piece must share with the one before or after it. S doesn't have any piece after it, so it must share with the one before it. What piece could that be? Well, S has g and h, so the piece before it has to have g or h. O has h and T has g, and that's it. These are the only pieces that could go 4th. 1 __ __ __

2 __ __ __

3 __ __ __

4 5 __ S __ g __ h O or T

pieces: N O S T V f h g f L L m h g m

We might be able to go further with this – if T is 4th, then N has to go 2nd (rule 2). What happens next? I don't know, and I don't want to work it out. When you set up your initial diagram for an If-question, you want to figure out what has to happen, not what can happen, because the diagram has to apply to every answer. Let's save our work for the answers. This is a "What can be true?" question, so we'll test each out.

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Answer A Put N in position 3. 1 __ __ __

2 __ __ __

3 N f L

4 5 __ S __ g __ h O or T

pieces: N O S T V f h g f L L m h g m

Now go through the rules. I'm going to look at rule 2 because rule 1 is so much harder to apply, and we only have two rules. N or T has to go 2nd. Since I've put N 3rd, it can't go 2nd. That means that T will go 2nd. 1 __ __ __

2 T f g

3 N f L

4 5 __ S __ g __ h O or T

pieces: N O S T V f h g f L L m h g m

As I am writing in the T in position 2, I see that O or T has to go 4th. Well, T certainly can't be 4th, so O must be in position 4, which leaves V 1st. 1 V L m

2 T f g

3 N f L

4 5 O S h g m h O or T

pieces: N O S T V f h g f L L m h g m

Go through the rules. Each person must share with either the one before or the one after it. But V doesn't share with T; this breaks the rules, so this is the wrong answer. Cross off the diagram and cross off the answer. By now you should see that the process for doing these answers with the alternate diagram is exactly the same as doing them with our original type of diagram; we just write things down a little differently. So we'd put a 3 under N; this would force a 2 to go under T, which would force us to put a 4 under O, and a 5 under V. This breaks the rules in exactly the same way. Answer B Copy down the initial diagram for this question and put O 3rd. 1 __ __ __

2 __ __ __

3 O h m

4 5 __ S __ g __ h O or T

pieces: N O S T V f h g f L L m h g m

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255

Now I see that T has to go 4th, since either O or T is 4th. 1 __ __ __

2 __ __ __

3 O h m

4 5 T S f g g h O or T

pieces: N O S T V f h g f L L m h g m

Go through the rules. Rule 2 tells us that N or T is 2nd; since T is 4th, it can't go 2nd. This leaves N to go 2nd. That leaves only V, which must go in the last available spot (1). 1 V L m

2 N f L

3 O h m

4 5 T S f g g h O or T

pieces: N O S T V f h g f L L m h g m

Now go through the rules. Everyone has to share with someone before or after them. Does that happen here? V shares with L, so that's good. O, though, doesn't share with anyone. Poor O. This breaks the rules, so cross off the diagram and the answer. Again, we go through the same process in our alternate diagram; a 3 goes under O, which forces a 4 to go under T, a 2 under N, and a 1 under V. This breaks a rule, so it is wrong. Answer C Try putting T 4th. 1 __ __ __

2 __ __ __

3 __ __ __

4 5 T S f g g h O or T

pieces: N O S T V f h g f L L m h g m

As we've been seeing, this forces N to go 2nd. 1 __ __ __

2 N f L

3 __ __ __

4 5 T S f g g h O or T

pieces: N O S T V f h g f L L m h g m

But now we have O and V left, and I don't know where they have to go. Let's just try putting them in alphabetical order; I'll star them, so that if it doesn't work, we can switch them later. 1 O* h m

2 N f L

3 V* L m

4 5 T S f g g h O or T

pieces: N O S T V f h g f L L m h g m

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Does this follow the rules? O doesn't share with N, so this doesn't work. Switch O and V. 1 V* L m

2 N f L

3 O* h m

4 5 T S f g g h O or T

pieces: N O S T V f h g f L L m h g m

This doesn't work either – O doesn't share with either N or T. Switching O and V again won't do me any good, so I can't make this work. This answer is wrong; cross off both it and the diagram. I'll diagram this to show you how starring works in this diagram. We put 4 under T. This forces 2 to go under N. We have O and S left, and we don't know which will go 1st and which 3rd. So we just try it out one way. N f L 2

O h m 1*

S g h 5

T f g 4

V L m 3*

This won't work, because O doesn't share with N. So we switch O and V. N f L 2

O h m 3*

S g h 5

T f g 4

V L m 1*

This doesn't work either, because O doesn't share with either N or T. Answer D Put V 1st. 1 V L m

2 __ __ __

3 __ __ __

4 5 __ S __ g __ h O or T

pieces: N O S T V f h g f L L m h g m

Let's go through the rules. N or T has to go 2nd, and the 1st spot must share with the 2nd. Can I put N 2nd? Sure; it and V share L. Can I put T 2nd? No, T and V share nothing. So N has to go 2nd. 1 V L m

2 N f L

3 __ __ __

4 5 __ S __ g __ h O or T

pieces: N O S T V f h g f L L m h g m

This leaves O and T. I'm not sure which has to go where, so I'll try them in alphabetical order first (starring them because this was my choice; if it doesn't work out, I'll be able to move them).

Game Twelve 1 V L m

2 N f L

257 3 O* h m

4 5 T* S f g g h O or T

pieces: N O S T V f h g f L L m h g m

This doesn't work – O doesn't share with anyone next to it. So switch O and T. 1 V L m

2 N f L

3 T* f g

4 5 O* S h g m h O or T

pieces: N O S T V f h g f L L m h g m

This works – everyone shares with someone next to them. This (answer D) is the answer. We do the same thing with our alternate diagram. We put 1 under V. This forces 2 to go under N, since V has to share with someone, and either N or T is 2nd. This leaves O and T, and we don't know which goes where. We put them in one way, and star them. If that doesn't work, we try the other way. One of the two ways will work. Question 21 Since this is a "What can't be true?" question, let's use our previous diagrams. We look for previous diagrams to see what 3 and 4 share. We eliminate any answer that we see in a previous diagram because this is a "What can't be true?" question. The diagram for question 20D has S and O as 3 and 4. They share h, so I know that h can be shared by 3 and 4. Cross off answer D. The diagram for question 22A has T and S as 3 and 4. They share g, so I can cross off answer B. The diagram for 24D has O and T as 3 and 4, but they don't share anything. Darn it. They don't have to share, because 3 could share with 2, and 4 with 5. Oh well, we'll have to eliminate the other answers with test diagrams. Answer A How could 3 and 4 share f? Look for pieces that both have f. Only N and T both have f. We don't know which will be 3 and which will be 4, so we'll put them in alphabetical order, and star them. 1 __ __ __

2 __ __ __

3 N* f L

4 T* f g

5 __ __ __

pieces: N O S T V f h g f L L m h g m

Uh oh, this breaks rule 2 – either N or T has to be 2. But if they are 3 and 4, neither can be 2. There's no point in switching them; we can't make this work. This (answer A) is the answer. Let's use our alternate diagram. We want 3 and 4 to share f, so we have to put 3 and 4 under pieces that both have f. Only N and T have f. We'd put a 3 under N and a 4 under T, and star both because we might have put the 4 under N and the 3 under T. This means that neither N nor T has a 2 under it, which breaks the second rule. Switching them won't make a difference.

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that neither N nor T has a 2 under it, which breaks the second rule. Switching them won't make a difference. Question 23 This is a "What can't be true?" question, so look at previous diagrams to see which piece can be 1st. Our previous diagrams only have T and V in position 1, so we eliminate answers D and E. Answer A Put N first and see if we can make this work. 1 N f L

2 __ __ __

3 __ __ __

4 __ __ __

5 __ __ __

pieces: N O S T V f h g f L L m h g m

By this point we probably remember that N or T has to go 2nd, so putting N first forces T to go 2nd. If we didn't remember this, a quick look at the rules would tell us the same thing. 1 N f L

2 T f g

3 __ __ __

4 __ __ __

5 __ __ __

pieces: N O S T V f h g f L L m h g m

So far so good – N and T share instruments, so this follows all the rules so far. We have O, S, and V left, but we don't know where they will go. Let's just put them in alphabetical order; we'll mark them with a star because they didn't have to go this way. If this doesn't work, we'll change one of them. 1 N f L

2 T f g

3 O* h m

4 S* g h

5 V* L m

pieces: N O S T V f h g f L L m h g m

Does this work? No, because V doesn't share with anyone. So let's change things. We always change things systematically; in general, we move things from left to right. We put O 3rd, so let's move it over one. This will put S in position 3 instead. (Another way of accomplishing the same thing is to see that we want V to share with someone; it could share with O, so put O next to V.) 1 N f L

2 T f g

3 S* g h

4 O* h m

5 V* L m

pieces: N O S T V f h g f L L m h g m

This works, so we can eliminate answer A, as this is a "What can't be true?" question. You'd do the same thing with your alternate diagram; by now you should see that it really doesn't make a difference which diagram you select for this game. I'll talk about this at the end of the section.

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Answer B Put O 1st. 1 O h m

2 __ __ __

3 __ __ __

4 __ __ __

5 __ __ __

pieces: N O S T V f h g f L L m h g m

Now, O has to share with someone next to it. Since O is 1st, only 2 is next to it, so whoever goes 2nd has to have h or m. We know that either N or T goes 2nd. But neither of them has h or m; they can't share with O. This is impossible, so this (answer B) is the answer.

Summary I like this game. It seems like a very strange one that would require all sorts of odd thinking and creativity, but you can get all the questions right in a decent amount of time by just being systematic and using the skills you have learned in this book. There are a couple of lessons I want you to take from this game: First, it is crucial to understand the rules. Do what it takes to figure what they mean. Don't jump to conclusions on your first reading of complex rules; really think about what the rules say before you try to apply them. Often considering a specific example, which you make up yourself, is the best way to get to the heart of a rule. Second, don't get hung up making diagrams. We could have done this game with two very different diagrams, but either would have worked. Now, this doesn't mean that the diagram never matters, or that some diagrams aren't better than others. A diagram based around the least changeable things in the game will be easier to work with than a diagram based around the more changeable. For example, consider Game Four (the one with cars getting washes in a certain order). If you had built your diagram around the cars, and tried to assign each a number and a wash, the game would have been harder to do. Just harder, though, not impossible. Setting up a game should generally be the quickest of the four steps; think about what the different types of things in the game are, and which is most definite. If you aren't sure, just pick a way of diagramming and use it. If it turns out to be too hard, you can always change it later without having wasted much time; in the end, you will save more time not worrying overmuch about your diagrams. Finally, I want to talk again about test diagrams. I've said this before, but 90% of teaching is repeating yourself (I just made that up – I don't think it's true, but I like to have a maxim for every occasion). Often you will go through the rules and just not be sure where to put people. Don't freeze up. Put them someplace, and then mark that this was your decision. You can always try them elsewhere later on. But be certain to be systematic about how you try them out. If you try someone 2nd, then 4th, then 1st, you are just going to confuse yourself. Move from left to right. Now, students are often nervous about just putting people in places. They think, "What if this is the wrong place… Won't I be wasting time?" Or they wonder, "Will I have to try every possible arrangement?" Both these questions have answers. Having to try more than one arrangement does take some time, this is true. But figuring out, in your head, what the best place to put someone takes more time in the long run. You may "waste" time on a single answer by putting the person someplace they can't go, but in the long run you'll be faster because you won't have to think much about how to test answers. In regard to the second question, the answer is "Not usually." You usually won't have to test every possible arrangement – either you'll find an arrangement

260

Game Twelve

that will work, so you're done, or you'll realize that no further changes will matter, and stop testing. The point is that it is easier to see these things when you have something concrete to work with than it is to see them in your head.

What Do I Do Next? First, as you've been doing, do this game by yourself, with no notes. Done that? Then read on. I've taught you everything I know about how to do individual logic games. At this point you can handle any logic game on any LSAT. Go ahead and start practicing them. You might have noticed that I've left a couple of games out of the Recommended Games lists at the end of Game Three and Game Eight. This was because those games were too difficult to do at those stages, but now you should be able to handle them. At this stage you should be doing all games under timed conditions. I'm going to explain how to time yourself in the next section, Timing. Read that section before you do any games. When you do a game under timed conditions, you are doing your best to treat the game exactly like you would a game on the LSAT. When you time yourself, don't do anything you wouldn't do on the real test. If you aren't certain how best to diagram the game, don't fuss over it, just use some diagram. If you don't know how to do a question, skip it. Don't try to make deductions if you don't have the time. Now, after you do a game, when you are in the third step of studying (which is reviewing what you have done; see the Study Guide), you can think about all this extra stuff – what would have been the best diagram, whether there were any deductions, exactly how you should have done the questions you skipped. But if you do these things when you are practicing, you'll be teaching yourself bad habits, and these habits might stick with you on the real test.

Answer Key 20. 21. 22. 23. 24.

D A A B D

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261

Timing (For the entire games section) This section is about how to manage your time on the games section as a whole. If you want to do each individual game as quickly as possible, you need to employ all the techniques I've already taught you. Doing the questions in the right order, being systematic, and knowing exactly what to do in every possible situation is crucial to speed; skipping steps and cutting corners will speed you up, but only by making you really fast at getting questions wrong. All that being said, we still need to talk about some techniques that will help you deal with the entire section.

Do All Four Games Before we go on and talk about timing strategies, we need to talk about goals. Your goal on the LSAT is to answer as many questions correctly as you can in the time given. Our goal is not to get a decent score, but a GOOD score. In fact, we won't settle for any less than they best score we are able to get. Now, many people sell themselves short. They decide that they are only going to do three of the four games. They reason that every time they start a new game, they spend some time setting the game up, writing down the rules, and making deductions. This is not time spent answering questions. Doing four games requires doing more of this non-question work than doing three games. Given that they don't have enough time to do all the questions, they figure that it's better to do only three games, to maximize the amount of time spent answering questions. This is bad reasoning. First, as you have been seeing, it doesn't take that much time to get through the setup and rules of a game; doing this for four games or three doesn't make a huge difference. Second, the questions that take the most time for each game are the hardest questions. These are also the questions that we are most likely to get wrong. You can often get two questions right in the time it takes to answer one hard question – and you have a better chance of missing that hard question. One of the main reasons people run out of time on the Games section is that they spend too much time working on hard questions. There aren't that many of these questions, but they sure do eat up time. Doing three games rather than four usually means that students spend more time working on these three or four difficult questions; however, it also means that they miss out on five or six other questions. That is a bad trade. These students who do three games often skip the easiest game (just by accident), which means that they missed out on several easy points. Finally, if you are planning to get in the mid- 160s and up, you can't afford to write off a whole game's worth of questions. The moral: do all four games.

Take Only Eight Minutes Per Game If you want to do all four games, and we do, then you need to make sure that you have enough time to do all four games. There is only one way to do that: make sure you don't spend too much time on any one game. You have 35 minutes for the entire section. Split among four games, that gives you 8 minutes and 45 seconds per game. We are going to round that down to 8 minutes per game (I'll explain why in a second).

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Timing for the Section

So, only spend 8 minutes per game. This rule is subject to a small exception which I'll get to in a second. This is an important rule to stick to – every extra minute you spend on one game is going to come out of your time on the last game. Lose too many minutes out of that last game and you aren't going to get very many points on it. There is only one way to avoid this: when your time is up on a game, move on. I mean it. This isn't that bad – if you do the questions in the right order, you should have answered all the questions, or all but the hardest, in 8 minutes. If you don't have enough time to do all of the questions, the ones you skip will be the ones that are difficult and time-consuming. But, more likely, using previous diagrams will allow you to get through all the questions in time. Now, 8 minutes for each of four games only uses up 32 of our minutes. That's good – it gives us a little breathing room, and it helps us with the next strategy…

Do the Games in the Right Order Before you start doing any game, quickly glance through and count the number of questions in each game. Do the games in order of the number of questions – the game with the fewest questions first, and the game with the most questions last. This strategy is counterintuitive. Most test-takers do the game with the most questions first. They reason that they may not have time to tackle every game, so they should make sure that, if they miss out on a game, it isn't the one with the most questions. This is a strategy for people intent on mediocrity. We aren't going to run out of time. Why not? Because we are going to watch the clock, and move on when our 8 minutes are up. So why do we save the game with the most questions for last? Well, what aspect of a game takes us the most time? Think about it… That's right, the questions. Which means that what should be true about a game with more questions? It should take us longer. And a game with fewer questions? It should be faster. This isn't always true – a game with fewer questions could be a hard one to figure out – but it is true the great majority of the time. At the beginning of the section, the first thing you should do is figure out the order in which you are going to do the games. After you've done that, go from game to game and write at the tops of the game the time at which you must finish with it. So, at the top of the first game you will do, write whatever time it will be in 8 minutes; at the top of the second game, write whatever time it will be in 16 minutes; at the top of the third game, write the time it will be in 24 minutes; at the top of the fourth game, write the time it will be in 35 minutes (not 32 – you get 35 minutes per section, so you have to finish with the last game by the time 35 minutes are up). So, if you start the section at 10:33, you write 10:41, 10:49, 10:57, and 11:08 at the top of the games, from shortest to longest game respectively. This makes it very easy to pace yourself on the games. When the time on your watch is the same as the time on the top of the page, you must move on. Here's a handy trick I learned when I was studying for the Bar exam: bring an oldfashioned watch to the test. That'll look cool, and that's got to be worth something. But wait, there's more to it. At the beginning of each section, you set the watch to noon (that's why you use an old fashioned one – they are really easy to set). You never have to do any hard math during the section to figure out how much time you have left. When the hands say "12:15," you've used 15 minutes. The game with the fewest questions should take us the least amount of time. In fact, it might take us less than 8 minutes. Which means that if we do it first, we will end up having extra time for the other games. We don't need to think about this during the test, however.

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263

That is to say, you don't ever need to say to yourself, "Oh, I only took 6 minutes on that game, so I have 2 extra minutes for the next games." The times you have written on the tops of each page will keep track of this for you. Let's say you were supposed to finish the first game by 12:08 and the second by 12:16. You finish the first game at 12:06. This means that you have 10 minutes before it is 12:16 and you have to move on; all you have to do is make sure you move on by the time at the top of the page. When we come to the last game, if we've been careful about watching the clock, we'll have almost 3 extra minutes to play with (remember, 8 minutes per game, times four games, equals 32 minutes, but the section is actually 35 minutes long). This is good, because this game will probably take us longer than 8 minutes, since it has more questions. And, if we end up with time left over, we can go back and answer any questions we skipped in previous games. Let me give a personal example of how this might work. I went and did all the games from LSATs 19 to 41 to practice these strategies. I found that I rarely spent exactly 8 minutes on a game. Generally, I would work through the shortest game (which typically has five questions) in 5 minutes. This would give me 3 extra minutes for the other games. I needed this; the other games sometimes took 9 or 10 minutes to work through, with the last game sometimes taking up to 11 minutes. In every case where the test had a really lengthy game, they always had a fast game to even it up. Other times, when the shortest game wasn't so fast, the other games ended up not being so slow, either. The LSAT isn't written to be impossible; if you stick to the strategies I discuss in here, you'll find that the timing takes care of itself. Now, what if I hadn't worked through the first game so fast? Well, I wouldn't have had enough time to answer all the questions on the other games, but, since I did the questions in the right order, I would have had to skip at most one question per game. Can I Go Over These Time Limits? People often feel that, if they are doing a really easy game, they should do all the questions, even if it takes them more than 8 minutes. This is bad thinking. If you hit 8 minutes on a game and haven't finished it, first, it isn't as easy as you think it is; and second, you have only hard questions left, and doing one of them is likely to take as long as two questions on another game. The only time you can go over 8 minutes on a game (except for the last game) is if you hit 8 minutes and you are just finishing a question – you have only one or two more answers to look at. Guessing Make sure you fill in an answer for every question you skip, whether you skip it because you are about to run out of time or because you don't know how to do it. I can't teach you how to guess well – if you don't know how to get the right answer, there isn't any way to eliminate the wrong ones (since we usually get the right answer by eliminating the wrong ones). The point of guessing isn't to get that question right; it's to give yourself a chance at getting that question right, and to do it fast so that you have time to get other questions right. Before you start the test, pick the answer you will put whenever you guess, and then always guess that. I like B, which stands for Brian. Of course, don't pick that answer if you've somehow eliminated it. When you have a minute or less left in the section (on any section on the LSAT), go over your answer sheet and make sure you've filled in an answer for every question. You aren't

264

Timing for the Section

allowed to write after the section ends, and if you are caught, many proctors will turn you in for cheating.

Take Breaks You are going to get tired during the games section. The only way to deal with this fatigue is to take breaks. Take a break at least after finishing each game. Take enough time to relax a little, catch your breath, move your torso and get blood flowing to your brain. This is important time, so don't skimp on it. You can take breaks more often than this. If you feel fuzzy-headed or confused or stressed out, take a break. You can't afford not to.

Some Final Words I can't emphasize enough that the key to speed is not in rushing. After a certain point, you won't be able to read faster, or write more quickly, or go through rules more rapidly, without losing accuracy. If you rush through these steps, you will miss questions. The only way to speed up is to eliminate waste – not to be fast and sloppy, but careful and efficient. Wasted time is time you spend doing things that I didn't talk about in this book. Wondering what you are supposed to do next is wasting time. Looking for extra deductions is wasted time. Trying to figure out a question you don't understand is wasted time. Memorize the approaches in this book. Visualize and practice them to the point where you can explain them to anyone, in order, without notes; to the point where you use them on practice tests without having to try to remember them. This will eliminate the waste of wondering what to do. Then stick to these approaches and don't do anything else. Make sure you read everything carefully and are methodical in writing out test diagrams and working through answers. Watch the clock and don't break your timing rules. Take breaks whenever you need them, and whenever you are supposed to. Do all of this and you will be fast.

What Do I Do Next? Now you are ready to study games under timed conditions. Every time you do a game from here on out, time yourself. When your time is up, stop answering questions, and move on to reviewing what you have done. Before you go on to do games you have never seen before, do sets of games that you have already done. This will allow you to practice timing without the pressure of having to figure out wholly new games. Once you feel somewhat comfortable with how you are supposed to manage your time, start doing new games. You don't need to completely master time management before you go on to new games – that's going to take a while – but you want to be able to remember what you are supposed to do and how it works without having to think before you try to apply these skills to new situations. Try to do games from the same section together, because the games in each section are written to be done in 35 minutes together. That is, there is a balance of difficulty between the games in the same section, so each games section averages out to be no more difficult than any other games section, even if a single game is very easy or very hard. You don't always need to do four games at a time, though. One thing you can do is to pick an LSAT games section and do one game at a time. Do the games in the order you would on the real test. Time yourself as you would on the LSAT, but stop when you either finish a

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265

single game or run out of time on a game. After you finish each game, you can review it, and then go on to the next game. You have to be very rigid with yourself when you do this; often you will want to fudge and let yourself have extra time on a game. You can't do this at first; you have no feeling for time, and won't be a good judge of when you should give yourself extra time. Teach yourself what you can do in 8 minutes by stopping when those 8 minutes are up, even when you are in the middle of a question. Soon you will reach a point where you want to do games in groups of four. Do this when you no longer feel that you need to review each game immediately after you did it; that is, when you start to have confidence that you know what you are doing. At this stage you can give yourself a little extra time here and there, as I discussed above. Read the next section at least a week or ten days before the LSAT.

266

Before the Test

Before the Test Am I Ready for the LSAT? There is an LSAT score that you need to get. Most likely this is the score you need to get into your law school of choice, but maybe it’s a goal you've set for yourself out of pure ambition. Getting this score is your sole reason for taking the test. If you aren't yet capable of getting this score, you aren't ready to take the LSAT. How do you know if you are capable of getting this score? It's easy. Sit down and take a sample LSAT; time yourself exactly like the real thing. If you score within a couple of points of where you want to be, you are ready. If you are way off, you aren't ready. A difference of a few points is OK, because there are a couple of things you will do or learn between now and the real test that you haven't done or learned yet; one of them is described below (and the rest are in the next chapter). Now, if you aren't ready for the test, you may have enough time to get ready. How much time it will take depends on you. Look at the kinds of improvements you have made so far, and how long it took you. See how much more you need to improve, and then ask yourself if you are honestly capable of improving that much in the time you have left. If you have less than a week left, and the improvement is more than a handful of points, the answer is no. If you aren't ready for the test, don't take it. Getting a score that won't get you into the law school of your choice is a waste of your time and money. In addition, it can hurt your chances of getting into that school at a later date. Even if you take the test again and do better, many schools average multiple LSAT scores (call individual schools to find out if they do). Even if they don't, the fact that you took the test more than once is reported to schools; if you cancelled your score, this fact is reported (but not the score you would have got). This won't help your chances of getting in; it won't necessarily hurt your chances, either, but why take the risk if you can avoid it? By the way, read the next section if you've made it all the way through this book, even if you haven't decided to take the LSAT yet.

Make a Plan At some point before the LSAT, you will be as ready as you are going to be for the logic games section. You have practiced, turned skills into habits, and are confident that you can get the score you want on the logic games section. This may come a week before the test; it may come three days before the test. When you reach that point, I want you to do the following: If you are not totally confident of your LSAT logic games skills, but have made it through this whole book and understood most everything, doing the following may help you become confident. Sit down, with no notes in front of you, and write down a step-by-step plan for the logic games section. This plan should include every single thing that you are going to do (and how you are going to do it) in the course of the section, in order. This plan is going to be slightly different for different people. Everyone is going to use the fundamental techniques I talk about in The Fundamentals. But some of you may not have made it to the intermediate or advanced techniques, or may have made it through these sections and

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decided not to use some or all of the techniques. That's OK; if you don't plan on using some of these techniques, leave them out of your plan. Some things will definitely happen in a certain order during the section. For example, you are definitely going to start the section by deciding on the order in which you will do the games. You are definitely going to write down the times at which you will finish each game at the top of each page (see Timing). You will definitely take short breaks at the end of each game. You are definitely going to think about each setup in a certain way, look at the rules in a certain way, and do the questions in a certain order. Put all of the things that definitely happen at certain intervals in your plan. Other things will definitely happen at some point during the section, but you don't know when. For example, you will definitely encounter a "What must be true?" question, but you don't yet know when. You will definitely encounter an "If… then…" rule, and want to write down its contrapositive, but you might not encounter one on any given game. Your plan should also include how to recognize these types of situations, and what you will do when they occur. Your plan must include how to go through the three steps you do on each game – reading the setup and making a diagram, writing down the rules, and answering the questions. Your plan must talk about how to deal with every question type – how to evaluate the answers, when you can use previous diagrams (and how to do so), and what order to do them in. Some things may happen during the test. You may panic. You may realize that you aren't sure how to diagram a game. The guy next to you may be very loud. Your plan should also include how you will deal with these things (I'll talk about them in the During the Test section). To summarize – your plan should include everything that can or will happen during the games section, how to know that it is happening, and what to do when it does. In the end, your plan will be an organized list of everything that you know about LSAT logic games, and how to deal with any situation that might possibly occur during the test. What is the point of this? There are several points. First, you may find that there are things you can't remember. You'd better learn these things – you don't get notes on the LSAT. Memorize these and then sit down and write your whole plan all over again. Second, writing this plan allows you to organize and review what you know about the test, which is helpful for being prepared for the test. It's one thing to have all these techniques somewhere in your mind; it's much more useful to have them all fitted together and ready to go. Third, once you can write down your entire plan with no notes, you know that you know everything. That's good; that's very good. At this point you are ready for the LSAT. All you have to do is show up and let yourself do well.

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During the Test In this chapter I will assume that you are ready to take the test (see Before the Test for instructions on how to determine if you are ready). Taking the LSAT can be scary and unpleasant. There are some negative things that are just built into the nature of the test, which none of us can avoid. I'm going to tell you how to deal with them here. There are also some bad things that happen to some of us during the test, and I'm going to tell you how to deal with them.

Psychological Warfare The LSAT messes with your head. No one can avoid this. You are going to be nervous; you may even be scared. Now, there is nothing wrong with being nervous about the test – it is an inevitable and natural reaction. Everyone gets nervous, even the best test-takers. If you think that you shouldn't be nervous, you are just going to scare yourself out even more. Accept some nervousness; what you shouldn't accept is a lack of confidence. This can negatively affect your performance. If you doubt yourself you may end up not applying the techniques you have worked so hard to master; you may find yourself second-guessing your diagrams, double-checking your work, looking twice at answers you know are wrong, and so on. This is bad. We are going to use a two pronged attack on our LSAT fear. First, we are going to try to build our confidence. Second, we are going to ignore any remaining lack of confidence. These skills are as important as any other aspect of studying, because at this point confidence is all that stands between you and a great LSAT score. Take this as seriously as you did learning everything else in this books – this stuff takes commitment, effort, and practice.

Building Confidence The key to confidence is honesty. There are two reasons people lack confidence about a task – 1) they don't know what they are doing, or 2) they are lying to themselves. By this stage in the book, and especially by the point when you have decided to take the test (as I discuss in the previous chapter), you know what you are doing on the logic games section. Have you read the previous chapter, Before the Test? No? Shame on you. Go read it. In it I talk about putting together your LSAT logic games plan. This is a huge part of having confidence on the test. If you know exactly what to do at every given moment of the test, you don't need to worry about what to do. And if you know you know, you will feel good about yourself. In addition, you have taken at least one sample LSAT and done as well as you wanted. There are no accidental good scores on the LSAT. If you did well once, it is because you are capable of doing that well again. If, at this point, you still lack confidence, you are lying to yourself. Look back at that plan. You made that. You know all of that stuff – there is nothing the LSAT can throw at you that you are not ready for. Look at that sample test score. You got that score. You can do it again. Doesn't that feel great? Yes, it does! You are ready for this test. Stop lying to yourself and start feeling the confidence you deserve. There are some other ways to build confidence in addition to honesty. Music can be very helpful – I am big on singing. I find that dressing up helps; when I took the bar exam I wore a three-piece suit every day of the test. Visualization is also useful. Think about

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times when you have been successful in the past; remember why you were successful (hint: it's because you are wonderful) and how it felt. I also like talking to myself – a few jokes, a few compliments, and I start to feel good. Whenever you start to worry again, just close your eyes and remember how great you are and how much you studied. This sort of thing may be embarrassing, but it works. In fact, the fact that it is embarrassing makes it more effective – laughing at yourself distracts you from fear.

Acting Confident If you can't be confident, at least act confident. It doesn't matter if you feel good during the test, as long as you perform well. Ask yourself, "What would a confident person do?", and do that. The most important thing is this: a confident person believes that they know what they are doing. When confronted with a difficult situation, they trust their skills and abilities, and do what they normally do, confident that they will do well. This is what I want you to do on the test. One of the worst things that people do during the LSAT is to change their approach. They start doing things differently than they practiced at home. This is bad for two reasons: First, the way you practiced at home is the best way you can take the test – that's why you practiced it. Second, you aren't thinking clearly on the LSAT; whatever new strategy you come up with is not going to be a good one. Pretend that you have confidence in the skills you have learned, and use them. A confident person also believes that they knew what they were doing. They believe that the work they have already done is correct. They don't double-check, they don't secondguess, and they don't worry about the previous questions. This is crucial. Once you've done a question, or made a deduction, or written down a rule, assume that it is right and act accordingly – either forgetting about it (if it's a question), or using it without questioning it (if it's a deduction or diagram or rule). This takes practice, but it can be learned. Start working on it today. Of course, if you see something that explicitly contradicts work you've already done, that is another story. I talk about what to do in these circumstances below. But until that moment, don't question your previous work. Having taken quite a few standardized tests myself, I have experienced most of what I talk about here (and I've seen students of mine go through all of it, many, many times). A few years ago I was taking the GRE. The GRE is computer adaptive. The questions are supposed to get harder when you do well and easier if you do badly. I was doing the verbal section, which is mostly vocabulary, and has a lot of antonym questions, where you have to pick the answer with the opposite meaning. The vocabulary words seemed to be getting easier and easier as I went along, which really worried me. Eventually I did an antonym question where I knew I had picked the right answer, but the next question was phenomenally easy. Suddenly I realized that I must be doing something wrong; the test was getting demonstrably easier, which meant I must be getting questions wrong. I knew I had picked the right antonym; if that wasn't the right answer, then maybe the questions were not antonym questions. I had assumed they were, and had not even read the instructions. Maybe the test had changed recently, and they were really synonym questions! If I wanted to salvage my score, I had to change my approach to the test and start doing the questions as if they were synonym questions. But, before I did this, I stopped myself. I said, "Brian, if you were one of your students, and they were in this situation, what would you tell them? You'd say, 'Never change your strategy during the test. Always trust yourself.'" I couldn't violate my own advice, even though I wanted to. I knew that it is really hard to make good decisions during the test, and that you shouldn't trust your own instincts. Instead, you follow your rules. You made these rules before the test, when you were thinking clearly, so you have to trust that they are right. I stuck to my guns and kept doing the questions as if they were antonyms.

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said, "Brian, if you were one of your students, and they were in this situation, what would you tell them? You'd say, 'Never change your strategy during the test. Always trust yourself.'" I couldn't violate my own advice, even though I wanted to. I knew that it is really hard to make good decisions during the test, and that you shouldn't trust your own instincts. Instead, you follow your rules. You made these rules before the test, when you were thinking clearly, so you have to trust that they are right. I stuck to my guns and kept doing the questions as if they were antonyms. What happened? I got an 800 on that section, the highest score possible. They were antonym questions, and I had been getting them right; I was just unable to judge how difficult they were while I was in the middle of the test. What's the moral of this story? Never change your approach to the test during the test, no matter how much you want to. Follow the strategy you developed before the test (which this book has taught you) and trust that you're doing things the right way. That's the only way to get a good score, and it works.

Take Breaks If you start to panic or lose confidence on the test, take a short break. Get your mind off what you are doing, breathe deeply, don't think about anything. When you calm down, remind yourself of that plan you put together. You know everything you need to know. It's all there in your head. Relax, and let it happen. Worst case scenario, you have to skip the question you are doing. No big deal.

A Trick or Two Here are my two favorite confidence-building/faking tricks. They may not work for you, but hopefully they will remind you of things that you do to build your confidence. The first is that I love to bring a lot of pencils to the test. When I took the LSAT for law school, I had maybe 40 pencils. Sure that gives me the advantage that I don't have to worry about them getting dull or breaking, but the real point is that there is something about seeing that huge pile of pencils that just makes me feel good. It's probably ridiculous, but I feel like everyone is looking at me thinking, "Man, that guy brought 40 pencils. I only brought two. He must know 20 times what I know." The second one is my absolute favorite. To understand it you have to have taken at least one test before in a large group. Think back; when the teacher or proctor tells you to start, what's the first thing you hear? You hear all the people in the room, in unison, opening their books. So here's what I do: I wait until the room gets quiet again, and everyone is busy starting the test (or the section), and then I open my book. The message I send is that I'm so smart I don't need to start when they do. Now, no one probably notices but me, but that's the important part. By acting like I feel confident, by putting forth that confident image to others, even though they don't notice it, I put forth the confident image to myself.

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Imagine the Worst Here are some of the scenarios students are concerned about, and how you should deal with them. What if I panic? I talked about this above. Take a break. Then, after your break, remind yourself of your plan, and the fact that you know everything that you need to know for this test. What if I don't know how to deal with a certain question? Skip it. Circle it and if you have time at the end do it then. What if I don't know how to deal with a certain game? Remember, you don't have to know how to make a great diagram for a game to do well at it – all you have to do is draw some diagram, understand the rules, and start answering questions. If the setup just doesn't make much sense, look at the rules. They will tell you what is going on in the game. If they don't help, look at the questions. The questions will always ask about the key issues in the game, so seeing what they are asking about will tell you what the game is about. For example, if the questions ask who is before whom, you know that ordering is an aspect of the game. If the questions ask who is in the same group as whom, you know that there are groups, and they are important. What if the game just flat-out makes no sense – what if it might as well be written in a foreign language? In all the times I've been asked this question, no student has ever given me an example that they really didn't understand. Every example was a case where the student didn't really read the whole setup, they just panicked halfway through. Calm down, take a short break, and read what they are telling you. If it still doesn't make any sense, save it for last. You'll have to change the times you are supposed to finish each game; make sure you give yourself exactly 8 minutes on all the other games, and spend whatever time is left on the game you are saving for last (write the adjusted times on the tops of each game, as we discussed in Timing). Once you've done the other games, you'll feel a lot better and most likely whatever psychological block is holding you back will evaporate. If it still doesn't, at least try to answer some questions. I've never met a student who couldn't answer at least one or two questions on any given game. The most insidious thing about this concern is that you have it at all. You can figure out every game there is. I promise you. Even if you think you can't, you really can. Just apply what you know. This is not something you should be concerned with. What if I realize that I missed a rule (or wrote a rule down wrong)? Step one: relax. Step two: write the rule down (or write it down correctly). Step three: circle (in your book, not on the bubble sheet) all the questions you have already done. Step four: cross out any diagrams you have made so far, so that you don't use them on future questions (since they might be wrong). Step five: ignore any deductions you have made up until this point. Step six: continue with the game as normal, except don't use previous diagrams from the questions you have circled. Do not go back and redo questions you have already done. Do not. Now, if you finish all the other questions and you have time left over, go back and do the ones you circled. If not, go on to the next game.

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Why not redo the questions? Well, the questions you have already done might be right. After all, the answers agree with most of the rules. It could be that the rule you missed, or the one you wrote down wrong, didn't apply to the answers you did, or that it wouldn't have made a difference if it did apply. This is often the case. So you have a decent chance of getting the questions you have done right without any more work. But you have next to no chance of getting the questions you haven't done right if you don't do them. Every time I have missed a rule or written it down wrong, and I've done it a few times, I have gotten right most of the questions I'd done before realizing my mistake. Think about it – if there are five rules, and you missed one, you've got 80% of them right. Those four rules that you have will push your answers towards correctness, even without the rule you missed. If you go back and redo those questions, you won't have time to do some of the questions at the end of the game. If you had, let's say, a 50/50 chance of getting right the ones that you have already done, you only have a one in five (20%) chance of getting questions right that you skip because you ran out of time. This means that, by re-doing questions, you gain 50% more chance of being right, in exchange for losing 75% chance of being right on other questions. That is a bad trade. What if I wrote the wrong diagram? If your diagram is false – it doesn't actually show what happens in the game – treat it as if you wrote a rule down wrong (see above). If you just realize that you could have used a different and better diagram, change to it now and use it on the remaining questions, but don't redo any questions you've already done. You did them, they're right. That's the most important point – assume that what you've already done is right. If you worry about the previous questions, you aren't going to focus on what you are doing, and you are going to make silly mistakes. If you are honest with yourself, you will realize that using a "bad" diagram still allows you to get questions right, just not as quickly. We saw that in this book when I showed how to do certain games with alternate diagrams. So any questions you've already done are right; forget about them. What if I have to go to the bathroom? How bad? Can you hold it to the end of the section without being significantly distracted? Logic games is probably the most time-sensitive of all the sections – losing time from this section makes a bigger difference than the other sections, since you get faster as you get further into a game (given previous diagrams). So if you can wait and then go to the bathroom during another section, you should. But if you find that you are being really distracted by having to go, go. It's better to lose a little bit of time than to be distracted for the rest of the section. Losing time may cost you a few questions, but being distracted may cost you the rest of the section. What if somebody is making noise and it is bothering me? First, take a short break. Chances are that they aren't making that much noise, and if it's distracting you it is because you are tired, and thus easily distractible. But if, after your break, you are still distracted, raise your hand and ask the proctor to ask them to be quiet. Do it as soon as you can; otherwise the distraction will just build as you get more and more annoyed. This completes the book. Assuming that you have learned everything in here, you now know everything I know about logic games. You too are a big fat genius.

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Glossary Underlined words in definitions refer to other words in the Glossary. Boldfaced words give chapter titles. Analytical Reasoning The official name for logic games. See Introduction. and Same as both – "X and Y have some trait" means that each of these two things, X and Y, have the trait. If one of them didn't have the trait, this would be contradicted. See "If… then…" Rules and Negations. at least "At least X" means X or more. It would be contradicted if there were less than X. See "If… then…" Rules and Negations. both Same as and. "Both X and Y have some trait" means that each of these two things, X and Y, have the trait. If one of them didn't have the trait, this would be contradicted. See "If… then…" Rules and Negations. contrapositive Every "If… then…" rule has a contrapositive. This is formed by switching the "if" and "then" parts, and making both negative. "If X, then Y" becomes "If not Y, then not X." See "If… then…" Rules and Negations. deduction Something you figure out must be true based on the rules of the game. Deductions can be made before you do the questions (see Advanced Techniques) or as you do questions (see Intermediate Techniques). definite (thing/person) Some of the types of things in the game change less than others. The definite things are those that change less. Your diagram consists of the definite things written down in a row. See also variable. See The Fundamentals. diagram A way of visually representing the information in a game. Every game has you matching one or more types of things; your diagram should have the more definite of these things written in a line, with blanks underneath for the variable things that will go with them. See The Fundamentals. each Same as putting "and" between all items (like both). "Each of X and Y are A" means "Both X and Y are A;" "Each of A, B, and C are happy" means "A and B and C are happy." either "Either of X and Y are A" means "X or Y are A." See or. equivalent Two people or things in a game are equivalent if they are subject to all the same rules, or to no rules at all. Equivalent variable things can be switched with each other whenever you want. You can switch all the variable things associated with two definite things (but you must switch all of them). See Advanced Techniques. exactly "Exactly X" means X, no more, no less. It would be contradicted if there were more or less than X. "Exactly the same" means no differences of any type. See "If… then…" Rules and Negations. EXCEPT question A question containing the word EXCEPT. These questions describe the wrong answers, whereas questions typically tell you something about the right answer. For example, "All of the following can be true EXCEPT" tells you that the wrong answers can be true, so the right answer can't be true. See The Fundamentals. "How many diagrams are possible?" question The hardest type of question. There are three versions. The first asks how many diagrams are possible, generally under a certain condition (given in an "if;" see If-question). The correct answer is the number of diagrams differing in at least one way from each other that can be generated (given the condition). Test the answers by making a test diagram and putting every variable thing in every place they can possibly be. A second version asks for how many of the things in the game can some quality be determined. To find this out, see how many of the things can only be put in the diagram one way. If an entity can be put in more than one position, or be matched with more than one other thing, do not count it. The third

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version of this question asks what information would allow you to determine the situation of every thing in the game. The answer will be information such that only one diagram can be drawn incorporating it. To test the answers, put in the information given and see if you can draw multiple different diagrams that follow the rules. If you can, eliminate the answer. If not, it is the correct answer. See The Fundamentals. If-question A question that puts a further limit on the game. This limitation is for this question only. If-questions generally begin with the word "if," but "suppose" also means "if." Whenever we come across an If-question, we first copy our original diagram. Then we add the constraint given in the "if." Then we go through the rules and add anything to our diagram that has to be true based on what we have been told. We use this diagram when testing the answers. If-questions are generally easier than other questions, so we do them first. See The Fundamentals. Using previous diagrams on If-questions is different than on other questions – see Advanced Techniques. "If… then…" rule A rule that takes the form "If X, then Y." It tells you that every time X is the case, Y has to be the case. However, if Y is the case, X may or may not be the case. "If… then…" rules always have a contrapositive, which you should write down. See "If… then…" Rules and Negations. logic games One of the sections of the LSAT, and the subject of this book. Officially called Analytical Reasoning. See Introduction. long list The list of everything you want to learn in logic games. As you come across new ideas, information, or techniques in this book, add them to your long list. See How to Study for LSAT Logic Games. mark (with a dot or star) If you are not certain where some thing has to go in a test diagram, when you put it someplace, you put a little mark (such as a dot or a star) next to it. This tells you that it could have gone someplace else. If the diagram ends up not working, you can move your marked things someplace else. It is best to put things as far to the left as you can initially, and when you move them, move them to the right. See The Fundamentals. neither "Neither X nor Y have some trait" means that X doesn't have the trait and Y doesn't have the trait. It would be contradicted if one (or both) of them had the trait. See "If… then…" Rules and Negations. or "X or Y has some trait" means that one (or both) of the two has the trait. It would be contradicted if neither had the trait. See "If… then…" Rules and Negations. original diagram The diagram you create during step one (the setup), before you look at any questions. Copy this diagram down every time you need to test something out. See The Fundamentals. previous diagram A diagram that you made while testing an answer to a question before the one you are currently doing. Since you cross off any diagram you make that breaks a rule, all non-crossed off previous diagrams give a possible way the game could end up. These diagrams can be used to eliminate answers on different question types. See The Fundamentals. question There are seven types of questions (in order of difficulty): What can be true?, What can't be true?, What must be true?, What can be false?, Which is a complete and accurate list?, Which is the maximum/minimum number of…?, and How many diagrams are possible? See The Fundamentals. rule Rules tell you what can and can't happen in a game. They are listed under the setup. See The Fundamentals. setup Every game starts with a paragraph describing the situation of the game, and the things involved in the game. This is the setup. The setup tells you how to diagram the game. See The Fundamentals. short list The list of skills you are currently most focused on learning. Each item on the list should be an instruction to yourself that you can follow when practicing. You should constantly refer to the list while studying to ensure that you practice the techniques on

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it. Your short list will change periodically as you improve or spot new problems. See How to Study for LSAT Logic Games. test (an answer) To test an answer we draw a diagram and see if it breaks the rules. We recopy our original diagram unless it is an If-question. To test an answer, you must fill every empty spot in the diagram until you break a rule or all spots are filled. We always cross off any test diagrams that break the rules. See The Fundamentals. variable (thing/person) Some of the types of things in the game change less than others. The variable things are those that change more. Your diagram should contain a blank under each definite thing for each variable things that will go with it; the variable things should also be written off to the side for quick reference. See The Fundamentals. What can be false? question The fourth-easiest (third-hardest) type of question. The correct answer does not have to be true; it may either be possibly true, or it may be definitely false. The wrong answers must be true. Test the answers as you would on a What must be true? question; either look at previous diagrams for situations other than what the answer describes, or make a test diagram that differs from what the answer describes. If you have a previous diagram, or can make a test diagram, which differs from what the answer describes, the answer is correct. If not, the answer is wrong. See The Fundamentals. What can be true? question The easiest type of question. The correct answer follows all the rules. The wrong answers break the rules. Test the answers by making a test diagram containing the situation the answer describes. If the diagram breaks the rules, it is wrong; if it follows the rules, it is right. We don't use previous diagrams on these questions. See The Fundamentals. What can't be true? question The second-easiest type of question. The correct answer breaks a rule, and the wrong answers follow all the rules. Use previous diagrams to eliminate answers before you test the answers. If a previous diagram contains the situation described by the answer, the answer is wrong. To test the answers, make a diagram containing the situation described by the answer. If you can fill all the spaces in the diagram without breaking a rule, the answer is wrong. See The Fundamentals. What must be true? question The third-easiest type of question. The correct answer is a situation that occurs in any possible diagram. Use previous diagrams to eliminate answers before testing answers. If a previous diagram contains a situation other than that described in the answer, the answer is wrong. To test an answer, make a diagram that does not contain the situation described in the answer. If you can fill all the spaces in the diagram without breaking a rule, the answer is wrong. If you can't, the answer is right. See The Fundamentals. Which is a complete and accurate list? question The fifth-easiest (third-hardest) type of question. The correct answer contains all the things that fit the description in the question; any answer which leaves an item out, or contains an item that doesn't belong, is wrong. Use previous diagrams to eliminate answers before testing them. Previous diagrams can tell you what things fit the description in the question; eliminate any answers that don't contain these. To test answers, test each thing in the list to see if it can fit the given description; if it can't, eliminate the answer. If one answer contains more items than another, test only the items that are not in one list. See The Fundamentals. Which is the maximum/minimum number of…? question The second most difficult question. The correct answer gives the largest or smallest number of things fitting a certain description. Check previous diagrams to find the largest or smallest number; eliminate any answer smaller/larger than this. Test answers by starting with the largest/smallest and creating a diagram with that number of items fitting the description in it. If this won't work, move to the next largest/smallest answer. See The Fundamentals; see also Game Three for an example.

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