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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]

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Updated on: 25 Aug 2010, 23:26
7
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:14) correct 32% (01:46) wrong based on 333 sessions

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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

Originally posted by vanidhar on 25 Aug 2010, 23:20.
Last edited by vanidhar on 25 Aug 2010, 23:26, edited 1 time in total.
##### Most Helpful Expert Reply
Math Expert
Joined: 02 Sep 2009
Posts: 50624
Re: confusing Question from GMAT Prep test  [#permalink]

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26 Aug 2010, 04:24
3
2
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]

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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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Re: confusing Question from GMAT Prep test  [#permalink]

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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
Status: Apply - Last Chance
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Re: confusing Question from GMAT Prep test  [#permalink]

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26 Aug 2010, 01:00
1
XY+Z = XY +ZX
Cancel XY
Z=ZX
Z(X-1)=0
so Z=0 or X=1
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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, 02:56
1
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!
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Re: If XY+Z=X(Y+Z), which of the following must be true ?  [#permalink]

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22 Mar 2017, 11:39
Really easy one.
it might be a sub 600 level question, or even sub 500 level.
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Re: If XY+Z=X(Y+Z), which of the following must be true ? &nbs [#permalink] 22 Mar 2017, 11:39
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# If XY+Z=X(Y+Z), which of the following must be true ?

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