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# If XY+Z=X(Y+Z), which of the following must be true ?

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If XY+Z=X(Y+Z), which of the following must be true ? [#permalink]

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26 Aug 2010, 00:20
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If XY+Z=X(Y+Z), which of the following must be true ?

A) X=0 and Z=0
B) X=1 AND Y=1
C) Y=1 AND Z=0
D) X=1 OR Y=0
E) X=1 OR Z=0
[Reveal] Spoiler: OA

Last edited by vanidhar on 26 Aug 2010, 00:26, edited 1 time in total.
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Re: confusing Question from GMAT Prep test [#permalink]

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26 Aug 2010, 00:23
You have got the options wrong. Z(X-1) = 0 means Z=0 or X=1.
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Re: confusing Question from GMAT Prep test [#permalink]

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26 Aug 2010, 00:28
whats the method .. cause for me even x=0 and z=0 made sense when i put them into the eq
Director
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Re: confusing Question from GMAT Prep test [#permalink]

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26 Aug 2010, 02:00
XY+Z = XY +ZX
Cancel XY
Z=ZX
Z(X-1)=0
so Z=0 or X=1
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Re: confusing Question from GMAT Prep test [#permalink]

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26 Aug 2010, 05:24
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vanidhar wrote:
If XY+Z=X(Y+Z), which of the following must be true ?

A) X=0 AND Z=0
B) X=1 AND Y=1
C) Y=1 AND Z=0
D) X=1 OR Y=0
E) X=1 OR Z=0

$$xy+z=x(y+z)$$ --> $$xy+z=xy+xz$$ --> $$xy$$ cancels out --> $$xz-z=0$$ --> $$z(x-1)=0$$ --> either $$z=0$$ (in this case $$x$$ can take ANY value) OR $$x=1$$ (in this case $$z$$ can take ANY value).

To elaborate more:
As the expression with $$y$$ cancels out, we can say that given expression $$xy+z=x(y+z)$$ does not depend on value of $$y$$. Which means that $$y$$ can take ANY value. So all answer choices which specify the exact value of $$y$$ are wrong.

Next: "AND" in answer choices means that BOTH values must be true, but "OR" in answer choices means that EITHER value must be true.

Hope it helps.
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Re: If XY+Z=X(Y+Z), which of the following must be true ? [#permalink]

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04 Feb 2014, 19:15
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If XY+Z=X(Y+Z), which of the following must be true ? [#permalink]

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26 Sep 2015, 03:56
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Simple and fast:

XY+Z=X(Y+Z)...... XY+Z=XY+XZ..... Z=XZ (we would eliminate all the answer options that regard Y)

Looking at the simplified equation, we come to a conclusion that Z is equal to ZX only when when X=1 or Z=0. You can also check the solution by testing each answer separately !

Hope it helps!
If XY+Z=X(Y+Z), which of the following must be true ?   [#permalink] 26 Sep 2015, 03:56
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# If XY+Z=X(Y+Z), which of the following must be true ?

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