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If xy < 0 and yz > 0, what is the following equation?

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If xy < 0 and yz > 0, what is the following equation?

by Max@Math Revolution » Mon Feb 24, 2020 12:48 am

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[GMAT math practice question]

If x/y < 0 and y/z > 0, what is the following equation?
|xy - yz| - \(\sqrt{\left(yz-xz\right)^2}\) + |xy| + \(\sqrt{\left(xy\right)^2}\)

A. -x
B. -2y
C. x + y
D. -2xy
E. y
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Re: If xy < 0 and yz > 0, what is the following equation?

by Max@Math Revolution » Wed Feb 26, 2020 12:45 am
=>

Since xy < 0 and y/z > 0, x and y have different signs, and y and z have the same sign. Then we have xy < 0, yz > 0 and xz < 0.
|xy-yz| - \(\sqrt{\left(yz-xz\right)^2}\) + |xy| + \(\sqrt{\left(xz\right)^2}\)
= |xy – yz| - |yz – xz| + |xy| + |xz|
= -(xy - yz) – (yz - xz) – xy – xz, since xy - yz < 0, yz - xz >0, xy < 0 and xz < 0
= -xy + yz – yz + xz – xy – xz
= -2xy

Therefore, D is the answer.
Answer: D
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