McGraw-Hill Education GRE 2019

Which of the following equals the average (arithmetic mean) of (a − 2)^2 and

(a + 2)^2?

A a^2

B a^2 + 2

C a^2 + 4

D a^2 + 2x

E a^2 + 8x

S T E P 1: Choose a value for the variable in the question. When choosing a value

for a variable, keep in mind the following recommendations:

■ Never choose 0 or 1.

■ Never choose a value that will yield a 0 or 1.

■ Avoid repeating the same value throughout the question.

■ Always work with integers.

So what value should you choose for a? Based on number 1, you won’t choose 0

or 1. Based on number 2, you won’t choose 3. Why? Because if you plug in 3 for

a, (3 − 2)^2 = 1^2 , so 3 yields a value of 1. Based on number 3, you won’t choose 4:

(4 – 2)^2 = 2^2. 2 will appear multiple times in the question. So you can’t choose 1,

2, 3, or 4. Go with 5. It does not violate any of the rules given earlier, and it is a

prime number, which you generally want. Once you have chosen the value, label

it on your paper: a = 5.

STEP 2: Answer the question using the value that you chose. Since you let a = 5,

the question now becomes: Which of the following equals the average (arithmetic

mean) of (5 − 2)^2 and ( 5 + 2)^2? Solve:

(5 − 2)^2 = 3^2 = 9 and (5 + 2)^2 = 7^2 = 49.

The average of 9 and 49 is:

9 + 49

2 =

58

2 = 29

The value above is called the “goal.” Write that answer on your paper and

circle it.

29

STEP 3: Plug the value you chose for the variable into the choices. The choice

that yields a value that matches the goal will be the correct answer. This step is

straightforward, except for the following caveat: Check all the choices! Occasionally,

more than one choice will yield the correct answer, in which case you will need to

choose a new value for the variable. This is obviously not an ideal situation, which

is why you want to follow the rules in Step 1 about which numbers to avoid.

150 PART 3 ■ GRE QUANTITATIVE REASONING

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