Grow Your Brain

I believe that most students can improve on the LSAT, for two reasons. First, I’ve seen it done. Second, I suspect that the brain actually grows when it is repeatedly exercised. Recent research supports this idea.

Researchers at Berkeley studied a group of students who are preparing for the LSAT. They imaged their brains before and after a three-month BluePrint course, and compared those results to a control group of similar students who weren’t preparing for the LSAT. They found that the LSAT students had measurably more “white matter” (the axons that connect the “gray matter” of the neurons). Here’s a popular write-up and here’s the published research.

I work on the assumption that repeated stimulation of neurons changes them in some way. The neural network experts assure me that the receiving end of a neuron (the “dendrite”) changes with use, and the Berkeley research shows that there is some change to the sending end (the “axon”) as well. I assume that thinking hard, long, and often about any topic will increase the number of possible connections between nerve cells, resulting in long-term change to the brain itself.

To boil this down to a bumper sticker, you are what you think. Think a lot about any given topic, and you’ll wind up thinking more about it.  That’s bad news if the topic is lust, rage, greed, or fear. It’s good news if you want to go to law school and you’re thinking about logical reasoning!

 

Time Tactics: Simple Global Must Be True Questions

Before I decided I needed time tactics, I often spent two minutes on a logic game question that I should have gotten right in ten or fifteen seconds. The question would be something simple: “Which of the following must be true?” Time after time, I would slog my way through answer choice A, B, C, and D, proving that each one might be false. Then I would reach answer choice E and realize that it must be true–I already had it penciled in on my diagram. The geniuses who write the LSAT know all about people like me, and they routinely set us up for failure. But once you study time tactics, you can beat them at their own game.

A question like “which of the following must be true” is a global “must be true” question. In subsequent chapters, we will talk about “local” questions (where the question begins with an “if” that established a new condition for just that one question) and “must be false” questions. As we explore the different variations of “must be” questions, we will discover the optimal path through all such problems. For now, our “must be method” is very simple:

Must Be Method:
1) Could be easy!

Let’s try this out on the following simple sequencing game. Here are the scenario and rules:

Six law students–Allison, Briyant, Clarence, Daniel, Elisheva, and Faith–decide to chase Pokémon instead of studying. Each student catches exactly one Pokémon at a time. The order in which they catch them is determined by the following rules:

Elisheva catches hers before Daniel,
Allison gets hers first or last.
Neither Elisheva nor Faith catches the first one.
Clarence catches his before Allison or Briyant but not both.

Here is my sketch for this game. The blue items on the diagram are spelled out in the initial rules; the orange items are deductions I have made.

Note: several of our time tactics depend on being able to quickly and accurately check through all the rules, so I list all of the rules in order. If a rule can be completely expressed directly on the diagram, I note that to the left of the rule number; otherwise I write in the rule to the right of the rule number.

Turn on your stopwatch app and see how long it takes you to answer the following question.

Which of the following must be true?

A) At least two students catch a Pokémon before Allison.
B) At least two students catch a Pokémon before Briyant.
C) At least two students catch a Pokémon before Clarence.
D) At least two students catch a Pokémon before Daniel.
E) At least two students catch a Pokémon before Elisheva.

How long did that take? Think about the way you went about answering the question.

Now let’s apply our “could be easy” tactic to this same question. Every single answer mentions “at least two students,” which ought to focus our attention somewhere on the diagram. If at least two students must go before somebody, that somebody can’t go first or second. A quick look at the diagram shows that Daniel is the only student who can’t go second–and he can’t go first, either. Answer choice D is about Daniel–and we’re done!

Your elapsed time for this question, which includes reading the question, looking at the answers, checking the second spot on the diagram, and finding answer choice D should be about fifteen to twenty seconds.

Note–this kind of speed depends on having deduced that Daniel couldn’t catch the second Pokémon when you first set up the game. If you don’t routinely see such deductions when you first go through the rules, you need more work on logic game basics. Don’t worry about that now, however–throughout this book, you’ll have my diagrams in front of you as you tackle each question.

Let’s sum up what we’ve learned about the “could be easy” rule. A “must be true” question could be so easy that you can just look at your diagram and find the answer in a matter of seconds. This is especially likely to be true if you made some good deductions on your setup. When you see a global “must be true” question, quickly skim through all five answers to find out whether you have already figured out the answer. If you have, grab that answer and go–you don’t need to look any further!

Time Tactics: Orientation Questions

The first question in most logic games is very predictable–it asks which of the following five answers are acceptable outcomes.  The Law School Admission Council refers to these as “orientation questions,” since they are intended to orient you to the setup conditions. In The Official LSAT Superprep II, the LSAC tells you exactly how to answer such questions:

For such questions, probably the most efficient approach is to take each condition in turn and check to see whether any of the answer choices violates it. As soon as you find an answer choice that violates a condition, you should eliminate that answer choice from future consideration–perhaps by crossing it out in your test booklet. When you have run through all of the setup conditions in this fashion, one answer choice will be left that you haven’t crossed out: that is the correct answer.

This paragraph is the gold standard for “how to solve a logic game problem.” It is short, accurate, and authoritative. It not only tells you how to get the problem right every single time, it tells you how to get it right as efficiently as possible. What The Official LSAT Superprep II doesn’t do is explain why this is the fastest and best way to answer such questions, nor does it explain why other methods are slower and less reliable.

There are three ways to solve an orientation question. The first (which is far too common) is to have no strategy. The second is to tackle the question rule by rule, as the LSAC suggests. The third is to start with answer choice A, go through the rules one by one, eliminate it if it breaks a rule, and move on to answer choice B. This “answer by answer” approach will usually produce the right answer–but it is significantly slower and less reliable than the “rule by rule” approach. Let me explain why.

The “rule by rule” approach is optimal because it minimizes time-consuming steps and eliminates the possibility of “false positives.” By “false positive,” I mean an answer that appears to obey all the rules but really doesn’t. The people who write logic games know how most people try to solve them, and they can and will use that against you. Thus, if answer choice C appears to follow every rule, it can still be wrong–some other rule may be buried in the initial paragraph that spells out the scenario. You can’t really be sure that C is right until you know that every other answer is wrong,

Here are the steps for a “rule by rule” solution:

  1. Look at the rule.
  2. Figure out what you’re looking for in a wrong answer (i.e., “if A comes before B, that breaks this rule”).
  3. Skim through each answer choice, looking for that pattern.
  4. Cross off any answer(s) that break the rule.
  5. Go back to step 1 and repeat until only one answer is left.

Compare that to the “answer by answer” approach:

  1. Look at the answer.
  2. Go up to the first rule.
  3. Figure out what you’re looking for in a wrong answer (i.e., “if A comes before B, that breaks this rule”).
  4. Go back to your answer, looking for that pattern.
  5. Cross off the answer if it breaks the rule and jump ahead to  step 18.
  6. Otherwise, go up to the second rule.
  7. Figure out what you’re looking for in a wrong answer (i.e., “if A comes before B, that breaks this rule”).
  8. Go back to your answer, looking for that pattern.
  9. Cross off the answer if it breaks the rule and jump ahead to step 18.
  10. Otherwise, go up to the third rule.
  11. Figure out what you’re looking for in a wrong answer (i.e., “if A comes before B, that breaks this rule”).
  12. Go back to your answer, looking for that pattern.
  13. Cross off the answer if it breaks the rule and jump ahead to step 18.
  14. Otherwise, go up to the fourth rule.
  15. Figure out what you’re looking for in a wrong answer (i.e., “if A comes before B, that breaks this rule”).
  16. Go back to your answer, looking for that pattern.
  17. Cross off the answer if it breaks the rule.obeys
  18. This is the step where you get in trouble. Is this the final answer choice? Is it the only one that isn’t crossed off? If you haven’t reached answer choice E yet, you could be making a big mistake right here. So if you aren’t at E yet, move on to the next answer and go back to step 1.

That’s the theory. Let’s put it into practice. Here’s a simple orientation question for a logic game:

Allison, Bradley, Clarence, Daniel, Elisheva, and Faith are so tired of prepping for the LSAT that they have all decided to play Pokémon Go. Between them, they manage to catch and hatch Pheremosa, Quagsire, Relisprout, Solgaleo, Togetic, and Uxie. Each Pokémon is caught one at a time, but not every law student necessarily catches a Pokémon. The order in which the students catch the Pokémon obeys the following rules:

Bradley refuses to catch a Pokémon until Allison gets one.
None of the girls try to catch more than one Pokémon.
Uxie is caught first or last.
Pheremosa is  caught after Relisprout.

Question 1: Which of the following is an acceptable list of the order of students and the Pokémon they catch?

A) Daniel catches Uxie, Allison catches Relisprout, Bradley catches Pheremosa, Faith catches Quagsire, Bradley catches Sogaleo, Clarence catches Togatic.

B) Allison catches Relisprout, Bradley catches Uxie, Daniel catches Pheremosa, Faith catches Quagsire, Elisheva catches Sogaleo, Bradley catches Togatic.

C) Clarence catches Uxie, Daniel catches Sogaleo, Faith catches Relisprout, Allison catches Pheremosa, Bradley catches Quagsire, Faith catches Togatic.

D) Allison catches Relisprout, Faith catches Quagsire, Bradley catches Pheremosa, Daniel catches Sogaleo, Bradley catches Togatic, Daniel catches Uxie.

E) Bradley catches Uxie, Allison catches Relisprout, Clarence catches Pheremosa, Faith catches Togetic, Elisheva catches Quagsire, Daniel catches Sogaleo.

I solved this problem “answer by answer.” It took me 1:16, and I sort of cheated because I stopped when I got the answer that obeyed all the rules. (If this had been a tricky question with a rule buried in the scenario, I would have gotten it wrong.) I did the same problem “rule by rule” and it took my 0:36. That’s just under half as long and the answer was more trustworthy–I eliminated four wrong answers and the only answer left had to be right.

Try this yourself. If you don’t see a dramatic difference between the “answer by answer” and the “rule by rule” approach, leave a comment below. If you do find that the “rule by rule” approach is significantly faster (and more reliable), make sure you use it from now on. You’re on your way to learning time tactics!

Time Tactics: Introduction

LSAT logic games remind me of the “countdown scene” in a Hollywood thriller where our heroes have only fourteen seconds to disarm the nuclear warhead that will wipe out Manhattan. Have you noticed that Tom Cruise always manages to cut the right wire at the last second? That’s because he has a team of Hollywood scriptwriters behind him. You don’t. That’s why you need LSAT Time Tactics. This little book spells out the fastest way to get the right answer on the different question types in the logic games.

I wrote this book because I need it. Allow me to introduce myself. I was an Ivy League Philosophy major who needed a paying job, so I started programming computers back in 1980, back when computers were slow and computer memory was expensive. We used to fight for bytes the way some people try to squeeze a whole relationship crackup into one 140 character tweet.

As much as I enjoyed programming, I wanted more out of life, and decided to be a lawyer. I took the LSAT at age 29, scored at the 99th percentile, and went to Harvard. I spent fourteen fabulous years as a public interest attorney defending some of the most remarkable people on earth, and ten more years as an entrepreneur developing an award-winning educational publishing business. My wife and I bought a forty-acre farm deep in the Allegheny Mountains and handed the family business on to the next generation. I’m not quite ready to retire, so I started teaching the next generation of law students.

At 58, I’m twice as old as I was when I first took the LSAT, and it shows. I crushed the logic games in 1988. I have trouble with them now. I don’t have any trouble doing games or getting answers right–I just keep running out of time. At 58, I hope I am twice as wise as I was at 29, but I am definitely twice as cautious. I wanted to make sure each answer was right before I moved on–which is why I kept running out of time.

I could have just decided I was too old and stupid for logic games, but I’m much too vain for that. I went back to thinking like a programmer. There must be faster way to do LSAT logic games. More specifically, there should be a theoretically optimal solution path for each type of question in the games. If I could figure out what that path is, and follow it every time, I ought to get the games done faster.

To make a long story short, there is an optimal path through each type of question, and I did figure it out, and I do follow it every time. And where it had been taking me 40 minutes to get a perfect score on a logic game section, on average, it now takes me 25 minutes to get the same results.

I needed this book. If you’re reading it, you probably do, too. Let’s see if you get the same kind of improvement I did!

 

How to Train with 7Sage.com

I grew up way below the poverty line, so I am always thinking about free or inexpensive ways for students to excel on the LSAT. One of my favorite resources is 7Sage.com, which offers several priceless helps at no charge. In this post, we will explain how to make the most of 7Sage’s free tools for learning logical reasoning.

7Sage offers a free LSAT database that allows you to bubble in answers, score individual tests, and then sort and sift those results to find out where you need to focus your efforts. The more practice tests you enter into your personal database, the more you can see the patterns in your performance. The table that shows your results contains a lot of useful information, and you can select and sort what information you see with just one click. It is a free, simple, user-friendly “power tool” for LSAT success.

Your first step towards improving your score is to create your free 7Sage account. Sometimes “free accounts” just generate a ton of spam, but I have never felt that way about my 7Sage account. I do get occasional emails from J.Y. Ping, the Harvard Law graduate and educational genius who helped found 7Sage, but since I actually care about what he has to say, that isn’t a problem.

Once you have an account, click on the “Resources” tab and then select “LSAT Analytics” from the drop-down menu. You will see that you can score an LSAT, check your “trends,” or look at the “question table.” The “trends” and “question table” are both based on LSAT data you have previously entered, and you haven’t entered anything yet, so it’s time to score an LSAT. Dig out a test you have completed and scroll down the “Select PrepTest” list to get going.

Note–if you have done a lot of practice tests and have them lying around the house, it is well worth your while to bubble in the oldest test first, where “oldest” means “the first test you took,” not “the first test the LSAC published.” The “trends” feature will allow you to measure your progress from test to test, based on the date you entered your data. Starting with your oldest test makes those trend lines more meaningful.

Bubbling in the answers is easy. You can click each bubble with your mouse or other input device or use the keyboard. (Type “1” for A, “2” for B, etc.) 7Sage works on the iPad, so I can bubble in answers as fast as I can touch the screen. Once your data is in, just hit the “Save and Score LSAT” button at the bottom and check out your results.

The first thing to notice when you score your test is that 7Sage gives you two scores–one in black and one in blue. The blue number represents your “blind review” score. 7Sage has a fabulous approach to LSAT study called the “blind review” method, which is built right into the database at every level. We won’t cover that in this post, though, because today we’re focusing on using past practice tests to zero in on problem areas. These techniques are even more powerful when you add the blind review tools–but we’ll save that for another post. For the moment, you can just ignore the blind review results.

Scroll down a few inches and look at the “Question Performance” section. There should be an empty box that says “filter,” followed by a list of 100 questions. Look at the column headings–“question,” “type,” “tags,” your answer,” “answer choices,” “question difficulty,” “passage/game difficulty,” “priority,” “explanation,” and “quick view.” Each of these columns is sortable–just hover over the label and then click on the up or down arrow that appears.

Try clicking the “question difficulty” icon for one of the questions. The “filter box” at the top of your chart will suddenly read “+Hardest” (or “+Easiest,” “+Easier,” “+Medium,” or “+Harder,” depending on your choice).  Click on the “your answer” label to sort these questions out into “questions you got right” and “questions you got wrong.” Scroll down to the bottom of the chart and you will see how many questions of this difficulty level are on this test. Erase the “+Hardest” in the filter box and you’ll see all the questions again.

The 7Sage analytics are most useful for working on logical reasoning questions, so let’s limit your chart to those questions. Type “+LR” in the filter box, and only logical reasoning questions will show up. Now click the “tags” label to sort these out by question type. Hover over the first tag on your chart (usually “AP”) and it should pop up with an explanation for what that means (“Argument Part”). Click on that AP and your filter box will suddenly include “+AP” and your chart will only show Argument Part questions. Click the “your answer” label to sort these out by “questions you got right” and “questions you got wrong.” Take a look at the “question difficulty” to see whether you tend to miss easy questions for this particular type.

Now erase everything in your filter box except the “+LR.” Click one of your wrong answers (it will have a red circle around the letter you chose) and the term “+Incorrect” will appear in the filter box. Sort by “question difficulty.” Scroll down the list, noting which “easy” question types you got wrong. That’s a good place to begin your studies.

So far, we have only looked at test results for one preptest. You will get more insight into your weaknesses by looking at more than one test. Scroll all the way up to the top of the page, just under the “Question Analytics” header. Click the “Question Table” tab. You should see a line that says, “Review limited to 1 of 1 completed PrepTests” (unless you have already entered more than one test). You can select as many or as few tests as you choose by clicking the “tap to edit” button. If you have multiple tests saved, you will need the filter box to narrow down your data.

7Sage has built some remarkable tools into the remaining tab on the “Analytics” page. Click the “trends” button at the top of the page. There’s a tutorial video that explains these features. Take a look at the video–both to learn what you can do, and to “meet” J.Y. Ping, the master teacher who has made 7Sage the remarkable resource that it is!

 

Flaw Answer Choice Flashcards

[qwiz] [h] Flaw Answer Choices

[i] The LSAT requires no formal training in logic. This is usually an advantage, but creates some challenges when it comes to identifying logic errors and informal fallacies. A person who is familiar with the traditional names for fallacies may instantly identify a particular flaw as a case of “denying the antecedent” yet still be bewildered by the answer choices that are presented. These flashcards matches examples of actual LSAT answer choices (carefully paraphrased, out of respect for copyright) to the Wikipedia names for the respective fallacy.

 

[q multiple_choice=”true”] fails to consider that there may be other necessary conditions for the result beyond the specific condition that was identified

 

[c*] Affirming the Consequent

[f] Correct!

[c] May/Must Fallacy

[f] Not the best choice–but it has been credited as a correct answer for this situation.

[/qwiz]

Formal and Informal Fallacies

“Flaw” questions involve one of three types of errors–faulty assumptions, logical errors (technically known as “formal fallacies”), and other types of faulty reasoning (the “informal fallacies”). Unscrupulous people have exploited these fallacies for so many centuries that most of them have their own Latin names and all of them have their own Wikepedia page. The following is a list of fallacies that have appeared on LSAT preptests, in alphabetical order by Wikipedia entry.

Formal Fallacies

Most logicians use the term “antecedent” for the first term in a conditional statement and “consequent” for the last term. The LSAT never uses these terms, however. All LSAT materials call the “antecedent” the “sufficient term” and the “consequent” the “necessary term.”

Informal Fallacies
  • False dilemma
  • May/Must fallacy (surprisingly, Wikipedia has no entry for this)

Logical Error Flashcards

[qwiz] [i]

Logical errors (more precisely known as “formal fallacies”) involve errors that can be reduced to symbolic logic, regardless of the actual content of the argument.  This quiz identifies all the formal fallacies found in 10 Actual Official LSAT Preptests Volume V, using Wikipedia’s name for each error.

PowerScore has trademarked their names for these errors, so the first few entries take PowerScore’s definitions and match them to the Wikipedia names.

[q multiple_choice=”true”] Take a conditional statement (A->B) and then negate both terms (/A=>/B). This logical error is known as:

[c] A trademarked PowerScore error

[f] Well, yes, but that doesn’t help us much here, does it? You can find what PowerScore calls this in Chapter 6 of the Logical Reasoning Bible.

[c] Denying the Consequent

[f] No, that one isn’t a fallacy. If the “consequent” (which the LSAT refers to as the “necessary term” is false, the “antecedent” (a/k/a the “sufficient term”) must also be false.

[c*] Denying the Antecedent

[f] Good! The “antecedent” is the first term in a conditional, which the LSAT routinely refers to as the “sufficient” term.

[q multiple_choice=”true”] Take a conditional statement (A->B), assume the second term is true, and conclude that the first term must be true as well.

[c] A trademarked PowerScore error

[f] Well, yes, but that doesn’t help us much here, does it? You can find what PowerScore calls this in Chapter 6 of the Logical Reasoning Bible.

[c*] Affirming the Consequent

[f] Good! The “consequent” is the second term in a conditional, which the LSAT routinely refers to as the “necessary” term.

[c] Denying the Consequent

[f] No, that one isn’t a fallacy. If the “consequent” (which the LSAT refers to as the “necessary term” is false, the “antecedent” (a/k/a the “sufficient term”) must also be false.

[q multiple_choice=”true”] Only people in group A were cured. Therefore if anyone wasn’t cured, he must not have been in group A.

[c*]  Denying the Antecedent

[f] Correct! You can’t get from C->A to /C->/A. That would be like going from “If I live in California then I live in America” to “If I don’t live in California I don’t live in America.”

[c] Appeal to probability

[f] No, that would mean mistaking a condition that MIGHT happen for  a condition that MUST happen.

[/qwiz]

 

Flaw Questions

“Flaw” type questions come in three basic forms–assumptions, logical errors, and fallacies. Doing well on flaw questions means doing well on each of these three very different challenges.

Assumptions

Assumptions are easiest for people with no special training in logic. It is easy to spot an assumption type answer, since  it tends to start with a phrase like “fails to consider that” or “takes for granted that.” In a typical assumption scenario, the answer choice will provide a new fact that would make a big difference to the argument. You don’t need to be a logic whiz to figure out how that new fact might change things. Since each assumption-type answer is unique to the facts in that particular argument, there is no easy way to train up to do better on assumption answers.

Logical Errors

Logical errors, by contrast, do not involve new facts. They are technically known as “formal fallacies,” which means they are wrong because of the “form” of the argument. Any “formal fallacy” can be reduced to symbolic logic so that the actual terms under discussion no longer matter. A stimulus that says “Albion is in Britain” can be rewritten as “A->B.” In a “formal fallacy,” it doesn’t matter whether “B” stands for “Britain” or “Botswana.” For example, if I say “I am in Britain, therefore I am in Albion,” I have committed the logical error that PowerScore refers to as a “mistaken reversal.” To do well on this type of flaw question, you need to do well on conditional logic as a whole. I am working on a flashcard deck for logical errors.

  • Logical error flashcards
Fallacies

The third type of flaw is a specialized version of logical errors that cannot be reduced to symbolic logic. These “informal fallacies” involve a host of tricks and traps for the unwary. Unscrupulous people have been using these fallacies to dupe people for so many centuries that most of them have Latin names. These Latin names never appear on the LSAT, which adds an unintended degree of difficulty to the test. The LSAT answer choices that describe these informal fallacies can be more bewildering than Latin, especially to people who have some familiarity with the traditional names. To address this problem, I am working on two sets of informal fallacy flash cards–one that identifies all the most common and/or recent fallacies by their Wikipedia names, and another which then connects those names to wording that mimics the LSAT answer choices.

  • List of fallacies
  • Fallacy flashcards
  • Flaw answer choices

Informal Fallacy Flashcards

[qwiz] [i]

Informal Fallacies: This quiz identifies all the informal fallacies in 10 Actual Official LSAT Preptests Volume V. Since many fallacies have more than one name, we have chosen the name used by Wikipedia for each fallacy.

[q multiple_choice=”true”] presents a situation in which only limited alternatives are considered, when in fact there is at least one additional option.

[c]  Sampling bias

[f] No, that would involve some kind of survey error.

[c] Begging the question

[f] No, that would mean assuming what you are trying to prove.

[c*] False dilemma

[f] Good! 

[q multiple_choice=”true”]  infers that something is true of the whole from the fact that it is true of some (or even every) part of the whole

[c*] Fallacy of Composition

[f] Good!

[c] Argument from ignorance

[f] No, that would mean using a lack of proof as a way of proving something.

[c] May/Must Fallacy

[f] Wikipedia doesn’t know about this one–it is the error of saying something must be true just because it might be true.

[/qwiz]