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

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Manager
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If XY+Z=X(Y+Z), which of the following must be true ? [#permalink] New post 25 Aug 2010, 23:20
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

72% (02:14) correct 28% (01:43) wrong based on 44 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 25 Aug 2010, 23:26, edited 1 time in total.
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Re: confusing Question from GMAT Prep test [#permalink] New post 25 Aug 2010, 23:23
You have got the options wrong. Z(X-1) = 0 means Z=0 or X=1.
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Manager
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Status: GMAT Preperation
Joined: 04 Feb 2010
Posts: 105
Concentration: Social Entrepreneurship, Social Entrepreneurship
GPA: 3
WE: Consulting (Insurance)
Followers: 2

Kudos [?]: 24 [0], given: 15

Re: confusing Question from GMAT Prep test [#permalink] New post 25 Aug 2010, 23:28
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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Kudos [?]: 73 [0], given: 15

Re: confusing Question from GMAT Prep test [#permalink] New post 26 Aug 2010, 01:00
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, 04:24
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Expert's post
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: If XY+Z=X(Y+Z), which of the following must be true ? [#permalink] New post 04 Feb 2014, 18:15
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If XY+Z=X(Y+Z), which of the following must be true ?   [#permalink] 04 Feb 2014, 18:15
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