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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

\(xy+z=x(y+z)\) --> \(xy+z=xy+xz\) --> \(xy\) 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.

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

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04 Feb 2014, 19:15

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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, 03:56

1

This post received KUDOS

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 !

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

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22 Mar 2017, 12:39

Really easy one. it might be a sub 600 level question, or even sub 500 level.
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