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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