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Mentor Exercise

 
Directions: Each group of questions is based on a set of conditions. In answering some of the questions, it may be useful to draw a rough diagram. Choose the response that most accurately and completely answers each question. Hints, insights, partial solutions, and answers are provided in the right-hand column.

Six people—Roger, Susan, Tim, Ulrika, Vic, and Walt—are competing for a job at Consolidated Conglomerate. They have been evaluated on a letter scale A, B, C, D, or E, with A the highest possible evaluation.
 
Exactly two people received Bs.
 
Only one person received a D, and only one person received a C.
 
Neither Roger nor Tim received a B.
 
Susan’s evaluation was lower than everyone else’s.

This is a moderately hard hybrid game. Half of the elements are “wild”, so the situation is very fluid. This makes the game difficult: throughout the problem we will be groping for something concrete.
 
Begin by symbolizing the conditions. The condition “Neither Roger nor Tim received a B” is naturally symbolized as (R&T)B. The condition “Susan’s evaluation was lower than everyone else’s” can be symbolized as S=lowest. The condition “Exactly two people received Bs” can be symbolized as 2Bs. The remaining conditions can be symbolized in like manner. This yields
 

R, S, T, (U, V, W “wild”)

 

(R&T)B

 

S=lowest

 

2Bs, 1C, 1D
 

The diagram will consist of five boxes in a row—with the lettered evaluations listed at the top, the number of each evaluation listed in each box, and restrictions listed at the bottom:
 

A

B

C

D

E

 

2

1

1

 

 
~R
~T
 
One further condition should be drawn before turning to the questions. Since one person is assigned a D and everyone is evaluated above Susan, she must have received either a D or an E. Note this as follows:
 

A

B

C

D

E

 

2

1

1

 


 
Question-1
Which one of the following CANNOT be determined based on the information given?
  1. Ulrika did not receive an E.
  2. At most one person received an E.
  3. At least one person received an E.
  4. Roger did not receive an E.
  5. Tim did not receive a B.
Solution
Since this question asks for the answer-choice that cannot be determined, we attempt to construct a valid counter-example for each choice. The one for which this is not possible will be the answer.
 
Choice (A) can be determined from the initial conditions since Susan received the lowest evaluation.
 
Next, choice (B) necessarily follows from the given conditions. (Why?) This eliminates (B).
 
As to (C), suppose that S received a D:
 
A B C D E
  2 1 S  
~R
~T

Then both U and V could receive Bs, without violating any conditions:
 
A B C D E

 
U
V
1 S
 
 
Finally, both R and T could receive As and W could receive a C—all without violating any condition:
 
A B C D E
R
T
U
V
W S
 
 
This is a valid counter-example. Hence, the answer is (C)—it cannot be determined from the given conditions.
 
 
Question-2
If Vic and Walt received the same evaluation, which one of the following could be true?
  1. Vic did not receive a B.
  2. Walt did not receive a B.
  3. Susan received a C.
  4. Roger received a B.
  5. Roger received a D.
Solution
Again, this problem requires an indirect proof. With problems like these, don’t necessarily start with choice (A). Instead, scan the choices for a likely candidate.
 
As to (A), it is a poor candidate: we may have to construct a different diagram for each of Vic’s four possible positions. The same holds for choice (B).
 
Next, choices (C) and (D) violate the original diagram—eliminate.
 
Finally, (E) is a good candidate because it fixes the position of an element.
 
Now try to construct a valid diagram, with Roger assigned a D.
 
The answer is (E).
 
 
Question-3
If Vic and Walt received the same lettered evaluation, then which of following must be true?
  1. Both Vic and Walt received an A.
  2. Both Vic and Walt received a B.
  3. Ulrika received an A.
 
  1. I only
  2. II only
  3. III only
  4. I and III only
  5. II and III only
Solution
Start with I. Place Vic and Walt on the diagram as follows:
 
A B C D E
V
W
2 1 1
 
 


Now since Roger, Tim, and Susan cannot receive a B, only Ulrika can be assigned a B. But this violates the first condition, “Exactly two people received Bs.” So I is false, which eliminates both (A) and (D); they both contain I.
 
As to II, since Vic and Walt cannot both be assigned either a C or a D (not enough room), they must both receive a B. So II is true, which eliminates (C).
 
Unfortunately, we have to check III. Given the fluidness of the diagram and the fact that Ulrika is “wild”, it is unlikely that III must be true. Nonetheless, you should construct a diagram to check this.
 
The answer is (B).
 
 
Question-4
If only Vic received an A and Roger received a score higher than Tim, which one of following must be true?
  1. Susan received an E.
  2. Roger received a D.
  3. Ulrika received a C.
  4. Tim received a C.
  5. Susan received a D.
Solution
To start, place Vic in box A:
 
A B C D E
V 2 1 1  
 


Next, since neither Roger nor Tim can be in box B, one must be in box C and one in box D:
A B C D E
V 2 R T  
 
 
But this forces Susan into box E. Hence, the answer is (A).
 
 
Notice: To solve this problem, we did not need the obfuscating condition “Roger received a higher score than Tim.” It is not uncommon for the LSAT writers to introduce superfluous conditions. So don’t become alarmed if you don’t use all the conditions when solving a game. This may indicate an oversight on your part—it may not. Many students, upon discovering that they did not use all the conditions, will fruitlessly check and recheck their work, wasting precious time. If you don’t use all the conditions, make a cursory inspection of your work. If no mistakes are found, cut your losses and move on—taking solace in the hope that the unused conditions were extraneous.




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