If \(x\) and \(y\) are positive integers and \(x^y=y^x+1,\) which of the following must be odd?

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If \(x\) and \(y\) are positive integers and \(x^y=y^x+1,\) which of the following must be odd?

A. \(xy\)
B. \(x + y - 1\)
C. \(x + 2y\)
D. \(3x - y\)
E. \(xy + 2\)

Answer: D

Source: GMAT Club Tests
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