If \(|x| - |y| = |x+y|\) and \(xy\) not equal zero, which of the following must be true?

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A

B

C

D

E

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If \(|x| - |y| = |x+y|\) and \(xy\) not equal zero, which of the following must be true?

A. \(x-y> 0\)
B. \(x-y< 0\)
C. \(x+y> 0\)
D. \(xy>0\)
E. \(xy<0\)

Answer: E

Source: Manhattan GMAT