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# Is x = |y - z|?

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

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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]  19 Nov 2015, 00:20
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Re: Is x = |y - z|? [#permalink]  21 Nov 2015, 09:22
Expert's post
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is x = |y - z|?

(1) x = y - z
(2) y > z

|a|=a when a>=0,

There are 3 variables (x,y,z) but only 2 equations are given by the 2 conditions, so there is high chance (E) will be our answer.
If we combine the 2 equations,
from y-z>0, x=|y-z|? --> x=y-z?
this is always 'yes' so this is sufficient and the answer becomes (C).

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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Re: Is x = |y - z|? [#permalink]  28 Jan 2016, 19:32
y-z can be negative, in this case, x is not equal to |y-z|. 1 insufficient.
2 alone - insufficient, as nothing is specified about z.

1+2 -> we know that y-z is positive, and this is the same as |y-z|, thus both are sufficient.

C
Re: Is x = |y - z|?   [#permalink] 28 Jan 2016, 19:32
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