Statement 1

X is prime so third side may or may not be integer

Statement 2

Y is a odd no is again not a sufficient condition to answer the question

Now when we combine both of the above mentioned condition we have

X ={ 2,3,5,7....

Y= { 1,3,5,7,....

Clearly of third side to be an integer it has to satisfy.

√(X^2+Y^2)

And by Euclid's formula for this to happen either of x or y has to be even.

On our set we have only one even term 2 which cannot be paired with any other no to yield an integer as third line

So combine both condition we have reached the conclusion that third side is not an integer.

https://en.m.wikipedia.org/wiki/Pythagorean_tripleSo IMO C is the correct answer.