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

[VJesus12]

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

(A) k = m
(B) k = −m
(C) k = |m|
(D) k = −|m|
(E) |k| = |m|

[spoiler]OA=E[/spoiler]

Source: Official Guide

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Hi VJesus12,

We're told that K^2 = M^2. We're asked which of the following MUST be true. This essentially means "which of the following is ALWAYS true no matter how many different examples we can come up with?" These types of questions often require a bit more 'thoroughness' than normal - so you might have to do a bit more work than you initially think you will have to.

When dealing with squared terms, you should be prepared to look for multiple answers (for example X^2 = 4 has TWO solutions: +2 and -2). Here, we have a squared term equal to ANOTHER squared term, so there will be FOUR possible outcomes. Here's how you can TEST VALUES to quickly 'map' those options out:

K=3, M=3
K=3, M= -3
K= -3, M=3
K= -3, M= -3

Thus, we could have two positives, two negatives or one of each. Using these 4 options, you can quickly run through the answer choices and eliminate any answer that does NOT account for all 4 options. For example, Answer A can be eliminated because K=3, M=-3 is not a solution to that equation. You'll find that only one answer covers all 4 options...

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

[Scott@TargetTestPrep]

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

(A) k = m
(B) k = −m
(C) k = |m|
(D) k = −|m|
(E) |k| = |m|

[spoiler]OA=E[/spoiler]

Source: Official Guide

Recall that √(x^2) = |x| for any real value x, so when we square root of both sides of the equation, we will have |k| = |m|.

Alternate Solution:

If we take k = m = 1, we eliminate answer choices B and D. If we take k = -1 and m = 1, we eliminate A and C. The only remaining answer choice is E.

Answer: E

[Brent@GMATPrepNow]

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

(A) k = m
(B) k = −m
(C) k = |m|
(D) k = −|m|
(E) |k| = |m|

[spoiler]OA=E[/spoiler]

Source: Official Guide

The question asks us what MUST be true. So, if we can find a case where a statement is not true, we can eliminate that answer choice.

So, for example, one solution to the equation (k² = m²) is k = 1 and m = 1
Now let's check the answer choices.
A. k = m. Test: 1 = 1. Works. Keep A.
B. k = -m. Test: 1 = -1. DOESN'T WORK. ELIMINATE B.
C. k = |m|. Test: 1 = |1|. Works. Keep C.
D. k = - |m|. Test: 1 = -|1|. DOESN'T WORK. ELIMINATE D.
E. |k| = |m|. Test: |1| = |1|. Works. Keep E.

Okay, so the correct answer is A, C or E

Let's try another case. Another solution to the equation (k² = m²) is k = -1 and m = 1
Now let's check the remaining answer choices.
A. k = m. Test: -1 = 1. DOESN'T WORK. ELIMINATE A.
C. k = |m|. Test: -1 = |1|. DOESN'T WORK. ELIMINATE C.
E. |k| = |m|. Test: |-1| = |1|. Works. Keep E.

By the process of elimination, the correct answer is E

Cheers,
Brent