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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