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

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Attached is a visual that should help.
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Re: If k^2 = m^2, which of the following must be true? [#permalink]

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mkarthik1 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|

[Reveal] Spoiler:
In the above question, Both C and E seem to be correct to me .

The official answer is E. Why should it not be C? can someone please explain.

what is the difference between C and E



Solution:

We are given that k^2 = m^2, and we can start by simplifying the equation by taking the square root of both sides.

√k^2 = √m^2

When we take the square root of a variable squared, the result is the absolute value of that variable. Thus:

√k^2 = √m^2 is |k| = |m|

Note that answer choices A through D could all be true, but each of them would be true only under specific circumstances. Answer choice E is the only one that is universally true.

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 06 Sep 2017, 06:29
Hello Bunuel

I inferred that square or even power of a number is always positive. Therefore k^2 and m^2 are positive. So |k|=|m|, no matter what the signs are.
I don't see why in the official guide its mentioned that we need to take root of k^2 and m^2 when we know that ^2 always gives positive number.
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Re: If k^2 = m^2, which of the following must be true? [#permalink]

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New post 06 Sep 2017, 22:39
Shiv2016 wrote:
Hello Bunuel

I inferred that square or even power of a number is always positive. Therefore k^2 and m^2 are positive. So |k|=|m|, no matter what the signs are.
I don't see why in the official guide its mentioned that we need to take root of k^2 and m^2 when we know that ^2 always gives positive number.


Do not follow what you mean bu the point is that \(\sqrt{x^2}=|x|\), so if we take the square root from k^2 = m^2, we'll get |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 06 Sep 2017, 22:59
    Bunuel wrote:
    Shiv2016 wrote:
    Hello Bunuel

    I inferred that square or even power of a number is always positive. Therefore k^2 and m^2 are positive. So |k|=|m|, no matter what the signs are.
    I don't see why in the official guide its mentioned that we need to take root of k^2 and m^2 when we know that ^2 always gives positive number.


    Do not follow what you mean bu the point is that \(\sqrt{x^2}=|x|\), so if we take the square root from k^2 = m^2, we'll get |k| = |m|.



    Hi. Sorry for being not so clear :-)

    I meant to say that even powers ^2,^4, etc. always gives positive outcome no matter what the sign of the base is. For example:
    (-2)^2= 4
    and
    (2)^2= 4

    So what I inferred is that k^2 and m^2 are positive (no matter what the sign of k and m are). Therefore we can say that |k|=|m|.

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

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    New post 06 Sep 2017, 23:05
    Shiv2016 wrote:
      Bunuel wrote:
      Shiv2016 wrote:
      Hello Bunuel

      I inferred that square or even power of a number is always positive. Therefore k^2 and m^2 are positive. So |k|=|m|, no matter what the signs are.
      I don't see why in the official guide its mentioned that we need to take root of k^2 and m^2 when we know that ^2 always gives positive number.


      Do not follow what you mean bu the point is that \(\sqrt{x^2}=|x|\), so if we take the square root from k^2 = m^2, we'll get |k| = |m|.



      Hi. Sorry for being not so clear :-)

      I meant to say that even powers ^2,^4, etc. always gives positive outcome no matter what the sign of the base is. For example:
      (-2)^2= 4
      and
      (2)^2= 4

      So what I inferred is that k^2 and m^2 are positive (no matter what the sign of k and m are). Therefore we can say that |k|=|m|.

      Is this good?


      Apart from knowing that the even roots and absolute values give non-negative result, we should also deduce that from k^2 = m^2 we can get |k| = |m|. Else, what would you say if one of the options were k^4 = |m|? Here both sides are also non-negative, but can we say from k^2 = m^2 that k^4 = |m| is true? No.
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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 2018, 07:36
      VeritasPrepKarishma, Bunuel could you please share your approach explaining each option? Thanks.
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      Re: If k^2 = m^2, which of the following must be true? [#permalink]

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      New post 16 Apr 2018, 10:11
      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.


      What does \(k^2 = m^2\) imply?

      Only that |k| = |m|

      (A) k = m
      Not necessary e.g. k = 5, m = -5

      (B) k = −m
      Not necessary e.g. k = 5, m = 5

      (C) k = |m|
      Not necessary e.g. k = -5, m = 5

      (D) k = −|m|
      Not necessary e.g. k = 5, m = 5

      (E) |k| = |m|
      Always necessary. Note that absolute values of the two most be equal for the square to be equal. We cannot say anything about their signs though.

      Answer (E)
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      Re: If k^2 = m^2, which of the following must be true?   [#permalink] 16 Apr 2018, 10:11
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