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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).
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]
04 Feb 2014, 19:15
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