McGraw-Hill Education GRE 2019

QUANTITY A QUANTITY B

A B C D

Choose:

A if Quantity A is greater

B if Quantity B is greater

C if the two quantities are equal

D if the relationship between the two quantities cannot be determined

SOLUTION: When x = 1, the value of Quantity A = 3(26) = 78. In this case, the

value of Quantity A is greater. Since it is not possible for Quantity B to always

be greater or for the two quantities to always be equal, you can eliminate

choices B and C.

Now that you have determined that Quantity A is sometimes greater, the

next step is to see whether any values will provide a counterexample to that

relationship. For reasons that will be further explained in the next chapter, a

good number to choose is 0.

When x = 0, the value of Quantity A will equal 3(25) = 75. In this case, the

values in the two columns are equal. You have now found a counterexample

to the relationship that was obtained when x = 1. Since different values for

x give different relationships for the columns, the relationship cannot be

determined. The answer is Choice D.

QUANTITY A QUANTITY B

A B C D

Choose:

A if Quantity A is greater

B if Quantity B is greater

C if the two quantities are equal

D if the relationship between the two quantities cannot be determined

When y = 1, the value of Quantity A = 17, and the value of Quantity B = 20.

Thus in this case, Quantity B is greater, and the answer must be Choice B or

D. When y = 0, Quantity A = 0, and Quantity B = 0. In this case, the columns

are equal. You have found contradictory relationships, so the answer is D.

Strategy: Plug In Numbers with Interesting Properties

When plugging in numbers for variables in Quantitative Comparison questions, it

might be difficult to determine where to start. After all, there are literally infinite

possibilities! However, because your ultimate goal is to prove Choice D, you should

choose numbers that will most likely give you contradictory relationships. The best

numbers to choose will therefore be numbers that have interesting properties. Of

all numbers, the best to choose are 0 , 1 , and −1.

3( x + 25) 75

17 y 20 y

CHAPTER 8 ■ QUANTITATIVE COMPARISON STRATEGIES 163

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