If \(x\) and \(y\) are non-zero integers and \(|x| + |y| = 32,\) what is \(xy?\)

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If \(x\) and \(y\) are non-zero integers and \(|x| + |y| = 32,\) what is \(xy?\)

(1) \(-4x - 12y = 0\)

(2) \(|x| - |y| = 16\)

Answer: A

Source: Manhattan GMAT