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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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14 Oct 2015, 21:24
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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.

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

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

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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|

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

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15 Oct 2015, 00:11
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1
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.

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 08 Aug 2015 Posts: 8 Re: If k^2 = m^2, which of the following must be true? [#permalink] ### Show Tags 24 Oct 2015, 02:18 1 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|. Director Status: Professional GMAT Tutor Affiliations: AB, cum laude, Harvard University (Class of '02) Joined: 10 Jul 2015 Posts: 664 Location: United States (CA) Age: 38 GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42 GRE 1: Q168 V169 WE: Education (Education) If k^2 = m^2, which of the following must be true? [#permalink] ### Show Tags 11 Apr 2016, 16:32 2 Attached is a visual that should help. Attachments Screen Shot 2016-04-11 at 4.31.20 PM.png [ 80.7 KiB | Viewed 8816 times ] _________________ Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching, both in-person (San Diego, CA, USA) and online worldwide, since 2002. One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong). You can download my official test-taker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y94hlarr Date of Birth: 09 December 1979. GMAT Action Plan and Free E-Book - McElroy Tutoring Contact: mcelroy@post.harvard.edu Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 3161 Location: United States (CA) Re: If k^2 = m^2, which of the following must be true? [#permalink] ### Show Tags 03 May 2016, 08:49 4 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| 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 _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Director Joined: 02 Sep 2016 Posts: 734 Re: If k^2 = m^2, which of the following must be true? [#permalink] ### Show Tags 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. _________________ Help me make my explanation better by providing a logical feedback. If you liked the post, HIT KUDOS !! Don't quit.............Do it. Math Expert Joined: 02 Sep 2009 Posts: 47946 Re: If k^2 = m^2, which of the following must be true? [#permalink] ### Show Tags 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|. _________________ Director Joined: 02 Sep 2016 Posts: 734 Re: If k^2 = m^2, which of the following must be true? [#permalink] ### Show Tags 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? Math Expert Joined: 02 Sep 2009 Posts: 47946 Re: If k^2 = m^2, which of the following must be true? [#permalink] ### Show Tags 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. _________________ Manager Joined: 10 Sep 2014 Posts: 74 Re: If k^2 = m^2, which of the following must be true? [#permalink] ### Show Tags 15 Apr 2018, 07:36 VeritasPrepKarishma, Bunuel could you please share your approach explaining each option? Thanks. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8187 Location: Pune, India Re: If k^2 = m^2, which of the following must be true? [#permalink] ### Show Tags 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) _________________ Karishma Veritas Prep GMAT Instructor Save up to$1,000 on GMAT prep through 8/20! Learn more here >

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