If \(x, y\) and \(z\) are integers and \(xy + z\) is an odd integer, is \(x\) an even integer?

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If \(x, y\) and \(z\) are integers and \(xy + z\) is an odd integer, is \(x\) an even integer?

(1) \(xy + xz\) is an even integer.
(2) \(y + xz\) is an odd integer.

Answer: A

Source: GMAT Prep
Source: — Data Sufficiency |