For all integers \(a\) and \(b,\) the operation \(\theta\) is defined by \(a\theta b=\dfrac{a+b}2.\) If \(x\) and \(y\)

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For all integers \(a\) and \(b,\) the operation \(\theta\) is defined by \(a\theta b=\dfrac{a+b}2.\) If \(x\) and \(y\) are integers, is \(x\theta y\) an integer?

(1) \(x^2=y^2\)

(2) \(x=-y\)

Answer: D

Source: GMAT Prep