Made Easy Booklet

Question

$x$ and $y$ are integers and if $\frac{x^2}  {y^3}$ is an even integer then which of the following must be an even integer?

• A. $x - y$ 
• B.  $y + 1$
• C. $\frac{x^2}{y^4}$ 
• D. $xy$

 

Comments

If $\frac{x^2}{y^3}$ is even integer then x must be even, we can't comment on y. so anything multiple of even is even, so D must be correct.

Answer 1

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