McGraw-Hill Education GRE 2019

Here’s the question again:

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

SOLUTION: Plug in 5 for a, and identify which choice yields a value of 29.

A 52 = 25 → No

B 52 + 2 = 27 → No

C 52 + 4 = 29 → Ye s

D 52 + 2(5) = 35 → No

E 52 + 8(5) = 65 → No

The only choice that yields a value that matches the goal is C, so C is the

correct answer.

Plugging In Numbers with Multiple Variables

Sometimes, you will have a candidate for plugging in numbers, but there will be

more than one variable in the question. Look at the following example:

If a + b = 11c, what is the average of a, b, and c, in terms of c?

A 3 c

B 3 c + 1

C 4 c

D 5 c

E 5 c − 1

When there are multiple variables in a plug-in question, you must choose values

that satisfy the restrictions in the question. For example, in the previous question,

you cannot simply choose 2 for a, 3 for b, and 5 for c. When you plug those values

into the equation, you will arrive at 2 + 3 = 11(5) = 55. This is not a true equation.

Instead of arbitrarily choosing values, you must let the values for one or more of

the variables determine the other variable. In the previous example, let’s choose

values for a and b and let those values determine c.

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