# Mastering the Analytical Reasoning

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This chapter is from the book

## Exam Prep Questions

1. The two most common diagrams that you'll rely on to solve logic games are the sequence and the matrix. Let's start by looking at our initial example question, which can be best solved using the first of these two diagrams.

• Charles has to put together a roster for his company's annual softball game against their cross-town rival. He's got eight healthy people that want to bat for the team: Corwin, Dorian, Hal, Joseph, Kamal, Peter, Ralph, and Seth.

If Ralph plays, Hal must play immediately after Ralph on the roster.

Two of the three managers, Dorian, Kamal, and Ralph, have to be on the team.

Corwin and Seth can't be next to each other on the roster.

If Kamal is on the team, then Joseph can't be picked.

Peter has to play either first or second.

In this game, you can expect the LSAT testers to ask you to solve for two different things. First, you may have to pick five people out of eight, so expect to get three basic questions posed in one form or another:

• Who can be in the group?

• Who must be in the group?

• Who cannot be in the group?

Second, the most likely follow-up question you will encounter in a question when you have positions discussed (for example, Peter has to play first or second) is that you'll have to pick a specific order of the team.

This means you'll have to worry about positions of people in the roster, such as

• Who is first/second/third/fourth/last?

• Which of these rosters can be submitted?

• Which of these rosters is not possible?

Before you even jump to the questions, it's best to diagram out the conditions so that you can answer whatever the testers plan to throw your way. One simple way to do this here is to represent your answer as a five letter sequence, or roster, from left to right. This would visually signify the order that the people can play in. For example, let's say you choose Corwin, Dorian, Hal, Joseph, and Kamal to play in that specific order. You'd represent it diagrammatically as

C-D-H-J-K

If you're unsure of a certain spot in the roster, just represent it with a question mark (?).

Next, represent the additional conditions cited in the question as "sub-chains" or pieces of the puzzle to help us determine the final solution.

Rule 1: If R, then R-H.

If Ralph plays, then we know two players on the roster: Ralph, and Hal immediately after him.

Rule 2: From set (D, K, R), exactly two will play.

Basically, out of the set of three people (Dorian, Kamal, Ralph), exactly two will play. Notice that this isn't "can" play, we know that two of these people will be on the roster.

Rule 3: Not (C-S) AND Not (S-C)

Basically, Corwin and Seth cannot be immediately before or after each other, if they are to play on the team.

Rule 4: If K, then not J

If Kamal plays, then Joseph isn't playing. Of course, we can reverse this rule to come up with the corollary:

Rule 4 (reverse): If J, then not K.

If Joseph is on the team, then Kamal can't be on the team, because if he was, it would violate the fourth rule.

Rule 5: P-?-?-?-? or ?-P-?-?-?

We use the roster representation to show that Peter is either on the first or second position on the roster.

Next, apply your newly diagrammed rules to the question that applies to this logic game. Use the rules as tools to go through and eliminate wrong answers, those that break one of the rules given to us, until we're left with one correct answer.

Question:

Which one of these rosters can be submitted?

1. Peter, Hal, Corwin, Kamal, Ralph

2. Peter, Dorian, Kamal, Corwin, Seth

3. Dorian, Ralph, Hal, Peter, Joseph

4. Dorian, Peter, Ralph, Hal, Seth

5. Peter, Seth, Joseph, Ralph, Hal

1. Our second sample question also pertains to the order of objects in a group (in this case puppies instead of softball players). While this could also conceivably be solved with the sequence diagram, if you need more visual representation of a problem, the "matrix" diagram may be more useful.

The premise and conditions of the logic game are

On the third Thursday of every month, eight Labrador Retriever puppies (Anne, Boris, Cassie, Daisy, Early, Fancy, Gloria, and Harley) from the Guiding Eyes for the Blind visit the veterinarian's office for their monthly checkup. Each puppy is either a black lab or a yellow lab. The puppies each arrive at the office at a different time. The following conditions apply:

• Gloria arrives at the vet's office before Fancy but after Anne

• Cassie arrives at the vet's office before Gloria

• Boris arrives at the vet's office after Anne but before Fancy

• Fancy arrives at the vet's office before Daisy.

Again, let's diagram out the conditions so that you can answer whatever the testers plan to throw your way in this game. The first condition tells you the following about the order of arrival of the puppies at the vet's office:

Anne

Gloria

Fancy

The second condition tells you that Cassie arrived before Gloria, but does not tell you whether or not he arrived before Anne. So at this point, either one of the following orders is possible:

 Alternative #1 Alternative #2 Cassie Anne Anne Cassie Gloria Gloria Fancy Fancy

The third condition tells you that Boris arrived after Anne but before Fancy, but does not tell you whether or not he arrived before or after Gloria, or before or after Cassie. So now the following are possibilities:

 #1 #2 #3 #4 #5 Cassie Cassie Anne Anne Anne Anne Anne Cassie Cassie Boris Boris Gloria Boris Gloria Cassie Gloria Boris Gloria Boris Gloria Fancy Fancy Fancy Fancy Fancy

The fourth condition tells you that Fancy arrives before Daisy, providing the following alternatives:

 #1 #2 #3 #4 #5 Cassie Cassie Anne Anne Anne Anne Anne Cassie Cassie Boris Boris Gloria Boris Gloria Cassie Gloria Boris Gloria Boris Gloria Fancy Fancy Fancy Fancy Fancy Daisy Daisy Daisy Daisy Daisy

No information is provided about the relative arrival time of Early or Harley.

If you now provide that Cassie arrives after Boris, but keep all of the other conditions intact, the relative order must be as set forth in Alternative #5:

1. Anne

2. Boris

3. Cassie

4. Gloria

5. Fancy

6. Daisy

Although no information is provided about when Early or Harley arrived, you know that at most the arrival order of all of the others dogs can only shift down one or two spots from the order shown previously.

Finally, apply your newly diagrammed rules to the question and eliminate wrong answers, until we’re left with one correct solution. With this information mapped out, you can proceed to answer the following question:

Question:

If Cassie arrives after Boris, which one of the following must not be true?

1. Anne is the second of the puppies to arrive at the vet's office.

2. Boris is the fifth of the puppies to arrive at the vet's office.

3. Cassie is the third of the puppies to arrive at the vet's office.

4. Daisy is the sixth of the puppies to arrive at the vet's office.

5. Fancy is the seventh of the puppies to arrive at the vet's office.