Question: Which of the following is equal to the average (arithmetic mean) of (x + 2)^2 and (x - 2)^2?

1. x^2
2. x^2 + 2
3. x^2 + 4
4. x^2 + 2x
5. x^2 + 4x

Correct Answer: (C)

Approach Solution 1 :

The average will be [(x+2)^2 + (x-2)^2] / 2
We can solve this problem by an easy process of expanding and simplifying,

=> [ (x+2)^2 + (x-2)^2 ] / 2
=> [ (x^2) + 4x + 4 + (x^2) - 4x + 4 ] / 2
=> x^2 + 4

Approach Solution - 2 :

Let x=0 in the equations so that they are valid for all values of X.
As a result, we get (0+2)^2=4 and (0-2)^2=4
The average of these two numbers is 4.
Only the third option gives us this value.

“Which of the following is equal to the average (arithmetic mean)” - is a topic that is covered in the quantitative reasoning section of the GMAT. To successfully execute the GMAT Problem Solving questions, a student must possess a wide range of qualitative skills. The entire GMAT Quant section consists of 31 questions. The problem-solving section of the GMAT Quant topics requires the solution of calculative mathematical problems.

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