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

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

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