BTGModeratorVI wrote: ↑

Wed Apr 22, 2020 11:12 am

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|

Answer: E
Source: Official guide

So, we know that k^2 = m^2. Thus, there can be four scenarios. Let's say k^2 = m^2 = 4.

1. k = m = 2; both equal and positive
2. k = m = –2; both equal and negative
3. k = 2; m = –2; unequal with k positive and m negative
4. k = –2; m = 2; unequal with k negative and m positive

Let's see each statement one by one.

(A) k = m: This is not a must be true statement as per cases 3 & 4.

(B) k = −m: This is not a must be true statement as per cases 1 & 2.

(C) k = |m|: Since |m| is always positive, k is positive; however, as per cases 2 & 4, we see that k can be negative, too.

(D) k = −|m|Since |m| is always positive, –|m| is negative. Thus, k is negative; however, as per cases 1 & 3, we see that k can be positive, too.

(E) |k| = |m|: This is the correct answer. Since |k| and |m| give positive values, irrespective of the sign of k and m, we have |k| = |m|.

The correct answer: E

Hope this helps!

-Jay
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BTGModeratorVI wrote: ↑

Wed Apr 22, 2020 11:12 am

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|

Answer: E
Source: Official guide

Solution:

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