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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.
Re: If k^2 = m^2, which of the following must be true?
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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?
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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|
Answer: Option E
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Re: If k^2 = m^2, which of the following must be true?
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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.
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If k^2 = m^2, which of the following must be true?
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11 Apr 2016, 16:32
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Attached is a visual that should help.
Attachments
Screen Shot 2016-04-11 at 4.31.20 PM.png [ 80.7 KiB | Viewed 17758 times ]
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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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Help me make my explanation better by providing a logical feedback.
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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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|.
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?
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16 Apr 2018, 10:11
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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.
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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03 Jun 2019, 05:14
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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.
The question asks us what MUST be true. So, if we can find a case where a statement is not true, we can eliminate that answer choice.
So, for example, one solution to the equation (k² = m²) is k = 1 and m = 1 Now let's check the answer choices. A. k = m. Test: 1 = 1. Works. Keep A. B. k = -m. Test: 1 = -1. DOESN'T WORK. ELIMINATE B. C. k = |m|. Test: 1 = |1|. Works. Keep C. D. k = - |m|. Test: 1 = -|1|. DOESN'T WORK. ELIMINATE D. E. |k| = |m|. Test: |1| = |1|. Works. Keep E.
Okay, so the correct answer is A, C or E
Let's try another case. Another solution to the equation (k² = m²) is k = -1 and m = 1 Now let's check the remaining answer choices. A. k = m. Test: -1 = 1. DOESN'T WORK. ELIMINATE A. C. k = |m|. Test: -1 = |1|. DOESN'T WORK. ELIMINATE C. E. |k| = |m|. Test: |-1| = |1|. Works. Keep E.
By the process of elimination, the correct answer is E
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