This is my reasoning. I believe its E. perhaps Bunuel can tell the OA.

If X and Y are positive integers and X*Y is divisible by prime number P. Is P an even number?

(1) X²∗Y² is an even number

(2) X*P = 6

Statement 1

X²∗Y² is an even number

Inferences →

One among X and Y can be even. That means either X is even or Y is even. In this case, we can't deduce whether P is even or ODD. or→

Both X and Y can be even in this case we must have P, which is a prime number, an even integer = 2.

So from this statement, we get both YES and NO. Thus, this statement is not sufficient.

Statement 1

X*P = 2 X 3 = 3 X 2 =

1 X 6 = 6 X 1Remeber the one in red is not posisble as 1 is not a prime number. So again here we have YES and NO.

Let us see If by combination we can get anything.

By Combination we know that X and P are opposite. That means If one is odd then other is Even and Vice Versa.

A lot depend on Y now.

If X is Odd then P is Even(=2), but notice that when X is odd Y has to be even in order to maintain XY → Even.

If X is even then P will depend now on Y, but notice here that Y has no constraint now, the constraint is dismissed. Y can be Even or Odd. Thus, P can be even(=2) or odd(any prime number such as 3, 5, 7, 11, 13____).

I think the answer should be E.

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