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confusing Question from GMAT Prep test

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confusing Question from GMAT Prep test [#permalink] New post 26 Aug 2010, 00:20
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Question Stats:

60% (01:16) correct 40% (02:03) wrong based on 0 sessions
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] New post 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] New post 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
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Re: confusing Question from GMAT Prep test [#permalink] New post 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] New post 26 Aug 2010, 05:24
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).

Answer: E.

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: confusing Question from GMAT Prep test   [#permalink] 26 Aug 2010, 05:24
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