Source: Official Guide for GMAT Review 2016 Problem Solving; #17

4

# If k^2 = m^2, which of the following

If k^2 = m^2, which of the following must be true?

### 1 Explanation

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Jeffrey Braganza

Since the Q states K^2 = M^2
Means (5)^2 = (-5)^2 or (-5)^2 = (5)^2
K can be +ve or -ve
M can be +ve or -ve
[Every number has two square roots: positive and negative]

Now that we know what K & M should be: looking at answer choices (process of elimination)
A: K = +M
But K can be -ve too. Incorrect

B: K = -M
Again K can be +ve, Incorrect

C & D Incorrect for the same reason as A & B

E: |k| = |m|
Irrespective if K & M is +ve or -ve, taking the modulus will render only positive values. Hence E is the right answer
{Not sure if this is the right way to solve this}

Dec 31, 2015 • Comment

Cydney Seigerman, Magoosh Tutor

Yes, this is a valid approach to solve this problem :) Based on the original statement, k and m can be positive, negative, or 0. Since |k| = |m| regardless of the sign of either value within the absolute value, E satisfies the conditions of the statement.