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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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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
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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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14 Oct 2015, 22:35
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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15 Oct 2015, 00:11
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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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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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If k^2 = m^2, which of the following must be true? [#permalink]
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11 Apr 2016, 16:32
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Attached is a visual that should help.
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Screen Shot 2016-04-11 at 4.31.20 PM.png [ 80.7 KiB | Viewed 8283 times ]
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Re: If k^2 = m^2, which of the following must be true? [#permalink]
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03 May 2016, 08:49
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
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Re: If k^2 = m^2, which of the following must be true? [#permalink]
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06 Sep 2017, 06:29
Hello BunuelI 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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06 Sep 2017, 22:39
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Re: If k^2 = m^2, which of the following must be true? [#permalink]
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06 Sep 2017, 22:59
Bunuel wrote: Shiv2016 wrote: Hello BunuelI 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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06 Sep 2017, 23:05
Shiv2016 wrote: Bunuel wrote: Shiv2016 wrote: Hello BunuelI 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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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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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?
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