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

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If k^2 = m^2, which of the following must be true? [#permalink]

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New post 14 Oct 2015, 21:24
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A
B
C
D
E

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89% (01:18) correct 11% (00:28) wrong based on 303 sessions

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Re: If k^2 = m^2, which of the following must be true? [#permalink]

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New post 14 Oct 2015, 21:28
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|k| = |m| suffice the condition of k^2 = m^2.

so ans: E

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Re: If k^2 = m^2, which of the following must be true? [#permalink]

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New post 14 Oct 2015, 22:21
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k^2=m^2
Taking the non negative square root of both sides of the equation ,
|k| = |m|
Answer E
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Re: If k^2 = m^2, which of the following must be true? [#permalink]

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New post 14 Oct 2015, 22:35
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Bunuel wrote:
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|

Kudos for a correct solution.


With Even powers of variables the signs can't be predicted about them

Hence, We can't say anything about the sign of k and m being positive or negative
therefore, Option A, B, C and D are ruled out as all these options are hinting towards specific and known sign of k and/or m

For any sign of k and m, their absolute values must be same because k^2 = m^2, therefore, |k| = |m|

Answer: Option E
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Re: If k^2 = m^2, which of the following must be true? [#permalink]

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Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.


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|



Since k^2=m^2 we have 0=k^2 – m^2 =(k-m)*(k+m). So k=m or k=-m.
So only (A) and only (B) cannot be an answer.
The choice (C) tells us that k should be greater than or equal to 0.
Similarly the choice (D) tells us that k should be less than or equal to 0.
So neither (C) nor (D) cannot be the answer.

The answer is, therefore, (E).
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Re: If k^2 = m^2, which of the following must be true? [#permalink]

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New post 24 Oct 2015, 02:18
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Bunuel wrote:
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|

Kudos for a correct solution.


As squaring hides the sign of a number, k^2 will equal m^2 for every possible positive/negative combination of the two values.

The only statement we can make for sure is therefore (E) |k| = |m|.

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Re: If k^2 = m^2, which of the following must be true? [#permalink]

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New post 15 Apr 2017, 21:34
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Re: If k^2 = m^2, which of the following must be true?   [#permalink] 15 Apr 2017, 21:34
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If k^2 = m^2, which of the following must be true?

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