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If x = -|w|, which of the following must be true
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AliciaSierra
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If x = -|w|, which of the following must be true [#permalink] New post  17 Jul 2018, 19:01
Bunuel,
I couldn't understand OG explanation. Alternatively, if (x, w) is equal to either of the pairs (−1,1) or (−1,−1), then x = −|w| is true. However, each of the answer choices except x2 = w2 is false for at least one of these two pairs.

Could you explain me.

Thanks

adkikani , please try out this one
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adkikani
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Re: If x = -|w|, which of the following must be true [#permalink] New post  17 Jul 2018, 19:08
1
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Thanks ammuseeru , I think am better at single modulus ;)

My approach coincided with OptimusPrepJanielle
Did you care to took x or w as negatives or fractions even if nothing
was mentioned about them in questions stem?

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I honestly at time have a disliking for OG sol since at time they are crappy (you may find tons
of issues on verbal forums), I would rather validate my approach
on forums than spending time to understand them.

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Re: If x = -|w|, which of the following must be true [#permalink] New post  18 Dec 2018, 18:47
i just cannot seem to understand the rule of absolutes and always get these questions wrong. Just for absolutes, can someone recommend good studying source?
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Bunuel
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Re: If x = -|w|, which of the following must be true [#permalink] New post  18 Dec 2018, 21:16
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anum23 wrote:
i just cannot seem to understand the rule of absolutes and always get these questions wrong. Just for absolutes, can someone recommend good studying source?


10. Absolute Value



For more check Ultimate GMAT Quantitative Megathread


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Re: If x = -|w|, which of the following must be true [#permalink] New post  13 Sep 2019, 22:05
nalinnair wrote:
If \(x = –|w|\), which of the following must be true?

A. \(x = –w\)
B. \(x = w\)
C. \(x^2 = w\)
D. \(x^2 = w^2\)
E. \(x^3 = w^3\)


Given: \(x = –|w|\)

Asked: Which of the following must be true?

\(x = –|w|\)
Taking square of both sides
\(x^2 = w^2\)

IMO D
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Re: If x = -|w|, which of the following must be true [#permalink] New post  10 Jan 2020, 04:30
nalinnair wrote:
If \(x = –|w|\), which of the following must be true?

A. \(x = –w\)
B. \(x = w\)
C. \(x^2 = w\)
D. \(x^2 = w^2\)
E. \(x^3 = w^3\)

w =-4 x=-4 X^2 =W^2 i.e 16
so D
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gagansh1840
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Re: If x = -|w|, which of the following must be true [#permalink] New post  18 Aug 2020, 10:17
D is the answer

when we square, irrespective of sign., we get a positive answer
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If x = -|w|, which of the following must be true [#permalink] New post  22 Nov 2020, 04:55
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nalinnair wrote:
If \(x = –|w|\), which of the following must be true?

A. \(x = –w\)
B. \(x = w\)
C. \(x^2 = w\)
D. \(x^2 = w^2\)
E. \(x^3 = w^3\)


We can square both sides of \(x = –|w|\); Because \(|w|=\sqrt{w^2}\)

\(x^2 = (–\sqrt{w^2})^2\)

So, \(x^2 = w^2\)

The Answer is D
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Re: If x = -|w|, which of the following must be true [#permalink] New post  21 Jan 2021, 12:10
Ndkms wrote:
Corrrect answer D because

\(x^2 = ( - |w|)^ 2\)

DO NOT FORGET THAT by definition |w| = \((\sqrt{w})^2\) therefore

thus x^2 = \((-1)^2\) * \([ (\sqrt{w})^2 ] ^2\) = \(w^2\)



I think you are mistaken, the definition of absolute value is |w| = \((\sqrt{w^2})\)

if it was the case that the definition of absolute value was \((\sqrt{w})^2\) then you couldn't get the absolute value of any negative number (at least in terms of non-imaginary numbers). And I think that you would agree that for example, |-3| = 3 is a valid expression.
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Re: If x = -|w|, which of the following must be true [#permalink] New post  29 Jan 2021, 22:30
x = -1, w = 1
x = -1, w = -1

Both of the above test values satisfy the stem.

x^2 = w^2 is unequivocally true because the sign is hidden.

Answer is D.
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