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# Is x = |y - z|?

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Is x = |y - z|? [#permalink]  21 Sep 2010, 06:23
00:00

Difficulty:

25% (medium)

Question Stats:

62% (01:36) correct 38% (00:36) wrong based on 65 sessions
Is x = |y - z|?

(1) x = y - z
(2) y > z
[Reveal] Spoiler: OA

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Re: Absolute value DS [#permalink]  21 Sep 2010, 06:36
Expert's post
rxs0005 wrote:
is x = | y - z | ?

x = y - z

y > z

Is $$x=|y-z|$$?

If $$y-z\geq{0}$$ then the question becomes is $$x=y-z$$?
If $$y-z\leq{0}$$ then the question becomes is $$x=-(y-z)$$?

Basically the question ask whether the distance between $$y$$ and $$z$$ on the number line equals to $$x$$. Note that $$x$$ as it's equal to the distance (or to the absolute value) can not be negative.

(1) $$x=y-z$$, not sufficient, because we don't know whether $$y-z>\geq{0}$$.
(2) $$y-z>0$$ --> $$|y-z|=y-z$$, but still not sufficient as no info about $$x$$.

(1)+(2) From (1) $$x=y-z$$ and from (2) $$|y-z|=y-z$$ --> $$x=|y-z|=y-z$$. Sufficient.

Similar questions:
ds-question-97761.html?hilit=similar%20question#p753020
abs-equation-from-gmatprep-84821.html
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Re: Absolute value DS [#permalink]  21 Sep 2010, 09:39
rxs0005 wrote:
is x = | y - z | ?

x = y - z

y > z

Since absolute value can't be negative, for x to be equal to |y - z|, x must be greater than or equal to 0.

(1) If y > z, then x is positive and x = |y - z| = y - z. However, if y < z, then x is negative and cannot be equal to the absolute value. Insufficient.

(2) This tells you nothing about x. Insufficient.

Together: Since y > z, we know that y - z > 0. Therefore |y - z| = y - z, and we know that x = y - z. Sufficient. (C).
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Is x = |y - z| ? [#permalink]  05 Jul 2013, 09:20
(1). x = y - z
(2). y > z

Can someone explain to me why (1) isn't sufficient?

Thanks!

Sourced from "Total GMAT Math"
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Re: Is x = |y - z| ? [#permalink]  05 Jul 2013, 09:27
Expert's post
WholeLottaLove wrote:
(1). x = y - z
(2). y > z

Can someone explain to me why (1) isn't sufficient?

Thanks!

Sourced from "Total GMAT Math"

Merging topics. Pleas refer to the solutions above.

Similar questions to practice:
is-a-b-c-1-c-a-b-2-a-97761.html
is-x-y-z-1-x-y-z-2-x-84821.html

Hope it helps.
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Re: Is x = |y - z|? [#permalink]  05 Jul 2013, 09:35
Hi,

So what you are saying is that the stem asks whether positive x (because its set to an absolute value) is = to y-z or z-y but #1 could allow for x to be a negative value? Thus making it insufficient?
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Re: Is x = |y - z|? [#permalink]  06 Jul 2013, 00:47
Expert's post
WholeLottaLove wrote:
Hi,

So what you are saying is that the stem asks whether positive x (because its set to an absolute value) is = to y-z or z-y but #1 could allow for x to be a negative value? Thus making it insufficient?

Yes. For (1) x could be negative (when y - z is negative). Now if x is negative it cannot equal to absolute value.

Hope it's clear.
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Re: Is x = |y - z|?   [#permalink] 06 Jul 2013, 00:47
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