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# If xy+z=x(y+z), which of the following must be true? A) x=

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Intern
Joined: 22 Jul 2008
Posts: 44
If xy+z=x(y+z), which of the following must be true? A) x= [#permalink]

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23 Aug 2008, 15:37
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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

The OA is E. Can anyone please explain why
Director
Joined: 12 Jul 2008
Posts: 514
Schools: Wharton
Re: GMAT PRep - PS question [#permalink]

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23 Aug 2008, 17:16
rnemani 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

The OA is E. Can anyone please explain why

Please don't put OA in the first post.

xy + z = x(y+z)
xy + z = xy +xz
z = xz

Therefore, either x = 1 or z = 0.
SVP
Joined: 07 Nov 2007
Posts: 1789
Location: New York
Re: GMAT PRep - PS question [#permalink]

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24 Aug 2008, 21:01
rnemani 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

The OA is E. Can anyone please explain why

xy + z = x(y+z)
xy + z = xy +xz
z = xz --> xz-z =0
--> z(x-1)=0
$$z=0 or x=1$$
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Re: GMAT PRep - PS question   [#permalink] 24 Aug 2008, 21:01
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