Given, $\frac{x^{2}}{y^{3}}$ is an even integer
i.e let us assume $\frac{x^{2}}{y^{3}} = 2k$ [Where $k$ is an integer]
$x^{2} = 2k * y^{3} = even \ * anything = even $
So, $x = even$
Now, from here we can easily conclude, $xy = even * anything = even$ [as $y$ can be even or odd ]
Correct Ans : Option D