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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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New post Updated on: 25 Aug 2010, 23:26
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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.
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Re: confusing Question from GMAT Prep test  [#permalink]

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

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

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New post 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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New post 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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New post 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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