McGraw-Hill Education GRE 2019

Strategy 2: Back-Solve

Like plugging in numbers, back-solving is specific to Discrete Quantitative

questions. Back-solving is an option when the choices provide values for a variable

in the question. Again, back-solving is a way to avoid algebra. Instead of working

out the manipulations in the question, you can work backward to determine which

choice provides a value that matches the restrictions in the question. Let’s look at

an example:

After a 20% decrease, the price of a shirt was $120. What was the original

price of the shirt?

A $10 0

B $14 4

C $150

D $160

E $180

Though you can certainly answer this question algebraically, let’s focus on

back-solving.

S T E P 1: Start with Choice B. Take the value in Choice B and determine how it

relates to the information in the question. If the original price of the shirt was

$144, then the new price of the shirt would be $144 − 0.2($144) = $115.20. When

the original price of the shirt is $144, the reduced price of the shirt ($115.20) is less

than $120. Thus $144 is too small a value for the original price of the shirt. Since

the value in B is too small, the value in A must be too small as well. The correct

answer is C, D, or E.

STEP 2: Back-solve with Choice D. Why Choice D? There are three possibilities:

Either D is the answer, D is too small, or D is too big. If D is too small, then the

answer must be choice E. If D is too big, then the answer must be choice C. No

matter what happens, you won’t have to test choices C and E. Thus by testing B and

then D, you ensure that you will never have to test more than two choices.

Let’s see how the value in D relates to the given information. If the original price

of the shirt was $160, then the reduced price of the shirt would be $160 − 0.2(160) =

$128. $128 is greater than the reduced price in the question. You can thus infer that

$160 is too large of a value for the original price of the shirt. The value in Choice D

is too large. If the value in Choice D is too large, then the value in Choice E must be

too large as well. The correct answer must be C.

CHAPTER 7 ■ TWO ESSENTIAL QUANTITATIVE REASONING STRATEGIES 153

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