LSAT For Dummies, 2nd Edition (2014)
Part II. Analytical Reasoning: Following the Rules of the Logic Game
Setting Up Your Game Board
LSAT analytical reasoning questions often consist of a paragraph or two of facts, followed by a set of conditions. Setting up a game board helps you tackle such questions. Here’s an example:
A gourmet ice cream parlor offers a super-deluxe banana split intended to be shared by a group of people. The banana split comes in a long dish that contains five individual cups positioned side by side in a straight line. Each cup can hold up to two scoops of ice cream. A group of teenagers orders one of these banana splits. They request seven scoops of ice cream — three chocolate and four vanilla. Each scoop has one topping: Two scoops are topped with sprinkles, and five scoops are topped with nuts. The teenagers specify the following conditions:
· A cup containing a scoop of vanilla with nuts cannot be immediately next to a cup containing a scoop of chocolate with sprinkles.
· No cup can contain both vanilla and chocolate ice cream.
Find out the best way to approach an analytical reasoning question that asks for the minimum or maximum number of possible orderings or groupings with a free article at www.dummies.com/extras/lsat.
In this part…
· Overcome the often-overwhelming analytical reasoning (also known as logic games) questions and maybe even learn to love them.
· Distinguish between ordering and grouping logic games.
· Discover how to create a useful game board for each logic game so that you can answer the questions more efficiently.
· Learn why the first question in the set is almost always the easiest to answer.
· Analyze each logic game's rules more thoroughly by knowing about contrapositives.
Chapter 4. Gaming the Analytical Reasoning Questions
In This Chapter
Knowing analytical reasoning section basics
Establishing a strategy to tackle analytical reasoning problems
Using certain tactics to maximize your analytical reasoning score
The LSAT's analytical reasoning section intimidates most LSAT-takers. It's the bugaboo, the bête noir, the boogeyman, the nemesis of otherwise calm, cool, and collected would-be law students. No one does problems like these logic brain-drainers in school, so they're a completely new experience for many people.
But here's the good news: These problems are totally teachable, and in fact they can be fun! So fun we also refer to them as logic games. This chapter provides you with tips that can improve your score significantly. After you crack the code of a particular fact pattern, answering every single question in the set correctly is entirely possible. You may even find that the analytical reasoning section becomes one of your favorites.
In this chapter, we introduce the analytical reasoning section and describe techniques to tackle the two main problem types: ordering and grouping. In keeping with the spirit of seeing analytical reasoning problems as games, we show you how to set up a game board and then manipulate the game pieces according to the rules of each question set. We also introduce the three general question types and give you insight on how to approach each one. Master the game plan, and before long you'll know exactly how to play this section successfully.
Analyzing the Analytical Reasoning Section
The analytical reasoning section lasts 35 minutes. During that period, you experience four fact patterns with conditions followed by 5 to 8 questions, for a total of about 23 questions. So you have about 8 minutes and 45 seconds to work through each set of questions. The fact patterns present scenarios with a set or two of variables we call game pieces — people, dorm rooms, places around an office table, stuff like that — and introduce rules that govern how to use them. The questions test your ability to apply the given rules and make deductions, which (believe it or not) is a skill you use a lot in law school and the practice of law.
The thought processes involved in applying statutory and case law to a scenario aren't very different from the thinking and method involved in applying the rules to the facts in analytical reasoning problems. Furthermore, lawyers concentrate on arcane laws for long periods of time, and the LSAT indicates whether you can maintain that kind of attention to detail for an extended period. So, although working analytical reasoning problems won't be part of your grueling first year of law school, you need the analytical skills and attention to detail these problems test to endure the Socratic teaching methods that your law professors may implement.
Setting Yourself Up for Success Step by Step
Analytical reasoning problem sets vary in topic. You may be asked to undertake a somewhat silly task, such as choosing toppings for ice cream flavors, or you may find yourself taking on the role of city planner, positioning buildings on a new construction site. Regardless of their subject matter, you tackle every analytical reasoning problem in much the same way.
1. Read the facts.
Each logic game introduces the scenario with a paragraph or two that indicates whether the problem involves ordering or grouping, lists the variables (game pieces), and otherwise provides the information you need to set up a diagram we call the game board.
2. Analyze the rules.
Also referred to as conditions, the rules dictate the limitations for arranging or grouping the game pieces on the game board.
3. Answer the questions.
After you've analyzed the effects of the rules and recorded them and their corollaries on your game board, you've established the foundation for tackling the questions that follow.
The rest of this chapter provides you with the details on how to follow these three steps for every logic game you encounter. We're very thorough, but if you want even more detailed information about how to master this section of the LSAT, we suggest you read LSAT Logic Games For Dummies, by Mark Zegarelli (Wiley). This helpful text devotes itself to only the analytical reasoning section; it covers how to deal with some of the more unusual logic games and provides you with many more practice questions.
Get the facts, decide between ordering and grouping, and set up your game board
The first paragraph of a logic game sets up the facts. As you read the information, complete these tasks:
· Establish whether the logic game is an ordering or grouping problem. We define these two types of logic games in much more depth in Chapters 5 and 6, but the general difference between them is that ordering problems require you to place game pieces in relationship to one another and grouping problems ask you to group game pieces together in two or more sets.
· List the initials of the elements you need to order or group. These are your game pieces. Each element always begins with a different letter, so referring to pieces by their first initial is quick and easy. You have only the space provided in your test booklet to create your game board, so write compactly.
· Create the foundation of your game board. The most common game board for logic games is a very simple box chart with the positions or group names as column headers, below which you place the game pieces according to the rules.
So if the LSAT presents you with this sample first paragraph for an ordering logic game, you know what to do:
A college radio station schedules six disc jockeys — Gary, Harriet, Jamal, Lucy, Marco, and Penelope — during a 24-hour period. Each one of the six disc jockeys hosts exactly one 4-hour program, and the programs are scheduled one after the other during that period.
As you read the example paragraph, note the key word schedules. This is a big clue that you're dealing with a logic game that requires you to place the pieces in order according to some type of schedule. You have six game pieces — the six disc jockeys. Although the paragraph doesn't clearly specify that you're dealing with six positions, you can gather this fact from the wording. Knowing there are six 4-hour programs in a 24-hour period, one scheduled right after the other, tells you that you need to list the six disc jockeys in six scheduled spots from first to last. Every possible ordering in this game includes all six game pieces and all six spots.
Create your game board as you read. List the initials of the disc jockeys — G, H, J, L, M, and P — on your test booklet. Draw a simple box chart with six columns headed 1, 2, 3, 4, 5, and 6 to designate the six daily program spots from first to last. Your board looks something like this:
Consider the rules and modify your game board
The second half of the logic game is a list of conditions that specify how the game pieces may be arranged or grouped. Some rules allow you to place a game piece in a permanent spot on the game board. We call these targetrules. An example of a target rule is, “Gary is scheduled last.” Unfortunately, very few rules in LSAT logic games are targets. Some indicate where game pieces don't belong, such as, “Gary is not scheduled last.” Others give you information about where pieces belong relative to one another, such as, “Lucy is scheduled before Marco.” And others tell you something is true about a game piece contingent on when the condition is true of another game piece, such as, “If Marco is scheduled before Penelope, Harriet is scheduled before Gary.”
As you read the rules, record them in shorthand under your game board. Shortcuts save time and space and allow you to refer to the rules just by looking at your game board. Different kinds of rules call for different recording methods, and rules for ordering games may be worded a bit differently from those for grouping games. We cover analyzing the rules and writing them in shorthand in more detail in Chapters 5 and 6, where we provide specific information about how to handle the two general types of logic games.
Your rule shortcuts don't have to be fancy as long as you use them consistently. Some common shorthand symbols include:
· Arrows (→) to mark the spatial relationship between pieces
· = or ≠ to mark positive or negative relationships between pieces
slash through a letter to indicate that a piece can't be someplace or do something
· Underscores (_) to mark spaces that must be filled by unknown pieces
Check out the conditions that apply to the sample logic game.
A college radio station schedules six disc jockeys — Gary, Harriet, Jamal, Lucy, Marco, and Penelope — during a 24-hour period. Each one of the six disc jockeys hosts exactly one 4-hour program, and the programs are scheduled one after the other during that period. To accommodate each disc jockey's schedule, the station must abide by the following conditions in setting up its daily programming:
· Both Lucy and Marco are scheduled before Harriet.
· Both Lucy and Penelope are scheduled before Jamal.
· If Marco is scheduled before Penelope, then Harriet is scheduled before Gary.
· Gary's program is not the last program of the day.
Analyze each condition.
· The first tells you that both Lucy and Marco come before Harriet. You can write this rule in shorthand next to your game board: L → H; M → H. Note that this rule means that L and M can occupy any position before Harriet, not necessarily the one immediately before Harriet.
· The second condition is similar. Write its shortcut next to the game board: L → J; P→ J.
· The third rule provides a contingency, an “If/then statement.” You can write this rule next to the game board like this: If M → P, H → G. The contrapositive, if G → H, P → M, is also true. We discuss contrapositives in more detail in Chapters 5 and 6.
· Condition four tells you where Gary doesn't go. You can record this rule directly on the game board by writing a G in the sixth spot and crossing it out.
None of the four rules is a target, so you don't know exactly where any one of the game pieces fits on the board.
As you examine each rule, pay attention to the consequential truths that arise and look at your shorthand list for rules that concern the same piece. Record your findings on the board.
· If L is scheduled before H, L can't be 6, and H can't be 1. Furthermore, if M is before H, M can't be 6, and H can't be 1 or 2. Record these truths by adding the pieces to the game board with slashes through them.
· If L is before J (and also before H according to the preceding rule), L can't be 5 or 6, and J can't be 1. If P is before J, P can't be 6, and J can't be 1 or 2.
· Because the third rule is conditional, you can't represent it permanently on your game board, but you can show the conditions of the two alternatives for when P is before M and when M is before P, like this:
Your game board reveals that when M is before P (and thus H is before G), J has to be 6, and only L or M can be 1. Focus on what's true for the first and last positions, but fill in the available pieces for the middle spots, too, as we've done in the game board.
When P is before M, only G, L, or P can be 1, and only H or J can be 6.
You can take your deductions even further by writing out some of the possible orders whenever M is scheduled before P:
So whenever M is before P, the following are true:
· L or M must be 1.
· M must be 1 or 2.
· H must be 3 or 4.
· G must be 4 or 5.
· P can be 2, 3, 4, or 5.
· J must be 6.
Congratulations! You've just completed your working game board. Now you can tackle the questions.
Not every logic game allows you to come up with just a few possible orders or groups. If you don't come up with a few possibilities right away, begin answering the questions. Don't spend so much time considering all options that you don't have time to finish the section.
Answer the questions
Creating the game board for logic games is key, but you don't get points unless you answer the questions. Most of the questions you experience in this section fall into four types:
· Possible listing/assignment questions: Almost all logic games begin with a question that asks you for the answer that provides a possible listing (for order problems) or assignment (for grouping problems) of the game pieces.
· Quantity questions: For these questions, you usually determine how many game pieces could occupy a particular position, so they're most common in ordering-problem sets.
· Add-a-rule questions: Some questions provide an additional condition to use to answer only that question.
· Open questions: This question type simply asks what's true, false, or possible based on the original conditions.
We show you how to answer each type of question in the rest of this section.
Possible listing/assignment questions
The easiest logic game question type to answer is the possible listing/assignment question. It's usually the first question of the set. You don't need to refer to the game board to answer it; you simply apply each condition to the answer choices and eliminate the four answers that violate a condition.
These questions ask you for the answer that provides an accurate ordering or grouping of the game pieces. The five answers supply five potential orders or groups for the logic games. Four of the orders or groups violate at least one condition and are therefore not possible. Only one provides a possibility that doesn't violate a rule.
The key to answering every possible listing/assignment question correctly is to read a rule and then eliminate the answer (or answers) that violates it rather than reading an answer choice and finding the rule(s) it violates. Here's a sample possible listing/assignment question for the disc jockey scenario to demonstrate what we mean.
Which of the following could be the programming order of the disc jockeys from first to last?
(A) Penelope, Marco, Lucy, Jamal, Gary, Harriet
(B) Lucy, Penelope, Marco, Harriet, Jamal, Gary
(C) Harriet, Lucy, Penelope, Jamal, Gary, Marco
(D) Gary, Marco, Penelope, Lucy, Harriet, Jamal
(E) Gary, Lucy, Jamal, Penelope, Marco, Harriet
This is an ordering problem, so the question asks for a possible order. When you see this question type for a grouping problem, it will likely ask for a possible assignment or matching of elements to groups. Here are the steps to answering this question:
1. Read the first condition.
It states that both L and M are before H. Look through the five answer choices to find the one that doesn't place L and M before H. Choice (C) puts H first, so neither L nor M is before H. Cross out Choice (C).
2. Read the second condition.
Both L and P are before J. Choice (E) positions J between L and P, so it can't be a possible order. Eliminate Choice (E).
3. The third condition pertains to when M is before P.
Of the remaining answers, only Choice (D) positions M before P. H is definitely after G in Choice (D), so that answer violates the third rule and is incorrect.
4. Check the last condition.
It's an easy one to evaluate. Gary can't be last, but Choice (B) puts Gary at the end. So Choice (B) must be wrong.
5. Do a quick rule check for the remaining answer Choice (A).
L and M are before H, L and P are before J, the third condition doesn't apply, and Gary isn't last. Its order is entirely possible.
Choice (A) is the answer.
See how easy this question type is when you approach it methodically? The good news is that virtually every logic game begins with one of these easy question types, so you're bound to answer the first question of every problem set correctly.
Note that you don't need to use the game board to answer this question. So even if you're having trouble setting up a board for a problem set, at least attempt to answer the first question.
When the answers to a logic game question are all numbers, you're likely dealing with a question that asks how many of the elements could occupy one of the positions in an ordering problem or be a group member in a grouping problem. Usually a question set contains no more than one of this type. You'll be glad you spent a little time creating your game board when you encounter a question that asks for how many.
1. First, check the position on your game board to see whether you've eliminated any of the pieces from the position in question.
2. Eliminate answers that are greater than the number of remaining possibilities.
So if your game board shows that three of six game pieces can't occupy the position in question, you can eliminate any answer that's greater than 3.
3. Test each of the remaining possibilities to see whether an arrangement exists that places it in the position in question without violating a rule.
4. Choose the answer that reflects the number of game pieces that could occupy the position.
For the sample logic game, you may see a quantity question like this one:
Exactly how many of the disc jockeys could be the one scheduled sixth?
When you look at the sixth position on your game board, you see that four disc jockeys — G, L, M, and P — can't possibly occupy that spot. Eliminate Choices (C), (D), and (E). You know that when M → P, only J can be sixth. But it appears that when P → M, H could also occupy the sixth position. You could trust that both H and J are possible in the sixth position and pick Choice (B). If you wanted to be absolutely sure, though, you could try H in the sixth spot to see whether it works. You could order the schedule like this: L, G, P, J, M, H. That arrangement puts H last and violates no conditions. So you know for sure that both H and J could be scheduled sixth, and Choice (B) is the answer.
If you're unable to limit your game board to the extent demonstrated by the example, you may find it helpful to skip the quantity question until you've answered a few of the other questions in the set. Sometimes your answers to other questions provide further enlightenment on which game pieces can occupy which positions. Eliminate as many answers as you can, mark the question to show that you still need to answer it, and go back to it after you've answered the other questions in the set.
Add-a-rule and open questions
The remaining questions in a problem set are usually ones that either add a temporary condition or ask an open question about the original conditions. Both types ask for answers that are true, false, or possible. Read the question carefully to make sure you know which answer type you're looking for and which answers to eliminate.
· True: For questions that seek a true answer, eliminate answer choices that either must be false or could be false. These questions may be worded like these:
· Which one of the following must be true?
· Each one of the following could be false EXCEPT:
· Which one of the following CANNOT be false?
· Which one of the following must be selected?
· False: For questions that seek a false answer, eliminate answer choices that either must be true or could be true. These questions often look like these:
· Which one of the following CANNOT be true?
· All the following could be true EXCEPT:
· Which one of the following must be false?
· Could be true: For questions whose answers are possible or true, eliminate answers that must be false. The questions may look like these:
· Which one of the following could be true?
· Each one of the following must be false EXCEPT:
· Could be false: For questions whose answers are possible or false, eliminate answers that must be true. Questions could be worded like these:
· Which one of the following could be false?
· Each one of the following must be true EXCEPT:
Generally, add-a-rule questions are faster to answer than the open type because they allow you to limit your game board a little more. To answer the questions that add a rule, apply the temporary condition to your game board and play with the new possible arrangements. Then, depending on whether the question asks for what's true, false, or possible, eliminate answers as we specify in the preceding list.
Here's a sample add-a-rule question for the disc jockey logic game.
If Lucy is scheduled directly before Gary, then which one of the following must be true?
(A) Penelope is scheduled first.
(B) Marco is scheduled before Gary.
(C) Lucy is scheduled in one of the first three programming spots.
(D) Harriet is scheduled last.
(E) Gary is scheduled in one of the last three programming spots.
This question adds the temporary condition that L comes immediately before G and asks for the answer that must be true. So add the rule to your game board and eliminate answers that either could be false or must be false.
Look at your original game board. None of the possible orders allows for L to come right before G whenever M → P because M → P forces H between L and G, which violates the first rule. So you're dealing with arrangements where P → M. If G comes right after L, then L can't occupy the fourth position because now there has to be room for G, J, and H after L. So when L is right before G, L can't be 4, 5, or 6, which is the same as saying that L has to occupy 1, 2, or 3. That's Choice (C).
Eliminate Choice (A) because it could be false. P doesn't have to be first. This order places L before G and doesn't violate any rules: L, G, P, M, H, J.
This arrangement also reveals that Choices (B), (D), and (E) could be false and are therefore wrong. M doesn't come before G, H isn't last, and G is in the 2 spot.
Choice (C) is correct.
Questions don't build on one another, so the temporary condition supplied by an add-a-rule question applies only to that question. Don't take it along with you to the next question in the set.
You handle open questions much the same way you do those that add a rule, except that you don't enter additional information on your game board. Focus on what type of answer — true, false, or possible — you seek, and eliminate choices accordingly.
Here's an open question that could appear in the disc jockey example:
Which one of the following CANNOT be true?
(A) Penelope is scheduled in the second programming spot.
(B) Penelope is scheduled before Marco.
(C) Lucy is scheduled in the fifth programming spot.
(D) Harriet is scheduled in the last programming spot.
(E) Harriet is scheduled before Gary.
An answer that can't be true must be false, so eliminate any answer choice that could or must be true. Your game board reveals that L is never 5, so the likely answer is Choice (C). See whether you can eliminate the other choices to be sure.
The game board shows P as a possibility in the second position, so Choice (A) could be true and is therefore wrong. All the options for when M is before P have H before G, so Choice (E) could be true. You were able to put H last when you worked out the answer to the quantity question, so you know Choice (D) could be true. And the order you created to answer the add-a-rule question shows P before M, so Choice (B) is wrong.
The correct answer absolutely must be Choice (C).
Open questions can be the most time consuming. If your game board is thin, sometimes the only way to answer them is to apply each answer choice to the game board. So you may find it easier to answer some of the other question types in a set before you tackle this type.
In Chapters 5 and 6, we provide more strategies for answering logic games questions and talk a little about how to handle some of the rare questions that don't fit into one of the four main categories.
Attending to Some Analytical Reasoning Do's
As you tackle the logic games in the analytical reasoning section, follow these “to do's” to optimize your experience.
Take time to develop your game board
You may feel you're wasting precious time analyzing the rules and creating a game board. But if you spend several minutes setting up the board and extending the conditions, you'll spend very little time actually answering the questions.
Pick your battles
You don't have to answer the questions for a logic game set in order. In fact, sometimes working out answers to later questions in a set gives you the information you need to answer an earlier question.
When you get stuck on a question, skip it and move on. If answering other questions in the set doesn't help you solve it, eliminate answers that must be wrong, guess from the remaining ones, and get on with the rest of the test. (See Chapter 2 for some guidance on guessing.)
Don't skip the first question in the set, though. You can almost always answer this question by simply applying the rules one by one and eliminating answers that violate them.
Remember that four wrongs make a right
Identifying wrong answers is often a lot easier than searching for the right one. For many questions, violations of rules are easy to spot; answers that don't violate any rules can be harder to see. When you eliminate four of the answers, the right answer remains.
Panic destroys some potentially brilliant LSAT scores. A student starts to work on a problem, doesn't immediately see the relationships among the characters, looks at the clock, realizes she only has five minutes left and seven questions left to answer, looks back at the problem, gets increasingly flustered, looks at the clock again, sees her future sinking into the mire, and suddenly she's blown the whole thing. It happens all the time.
Guess what? That approach doesn't help! Sure, it's nerve-racking, facing down this scary test amidst a roomful of strangers and knowing that your professional life could be on the line. Take a deep breath and remind yourself you're just playing a few games. Get back on course by applying the game method we outline in this chapter and Chapters 5 and 6.
Decide which problem to confront first
Each analytical reasoning section contains four logic games. You don't have to work them in order. You can work the second one first, and then the fourth, the first, and the third if you want to. No one cares — as long as you answer them all.
How do you decide which problem to work first? One method is to skim all four logic games, rank them in order of difficulty, and then work them in order from easiest to hardest. The problem with this method is that distinguishing between the easy sets and the difficult sets may not be obvious at first and takes away from time you could be using to work the problems.
A less time-consuming method is to work the problems with the most questions first. If you see a logic game with eight questions and another one with five, work the one with eight questions first. Each fact pattern takes about the same amount of time to figure out, so if you choose the problem with the greatest number of questions, you maximize the payoff from your time investment.
Maintain your perspective
Don't let this section psych you out. The test provides you with every piece of information you need to answer each question. The LSAT doesn't expect you to have experience in cupcake decorating or city planning when it presents you with a logic game. It does try to make this section difficult by making problem sets seem more complex than they are. Simply remind yourself that you have the tools you need to ace this section.
If a particular logic game or question spikes your adrenaline and sparks your natural flight reaction to the point where you'd like to flee the room, give yourself a break. Sit back in your chair, close your eyes, and take a deep, cleansing breath to get the oxygen flowing to your brain.
You can solve every analytical reasoning problem on the LSAT. The test-makers have checked to make sure. When doubt arises, combat it with this important truth.
The best way to get better at answering logic games is to apply the strategies to a bunch of them. This book gives you access to three complete analytical reasoning sections in Chapters 15, 17, and 19. Additionally, we suggest that you work on the questions from prior LSAT exams that are available from the LSAC. Order copies of the most recent LSAT exams from www.lsac.org and work as many of them as you have time for before you sit for the exam.