M7MBA wrote:If x and y are positive integers, is x + y even?

(1) xy is even

(2) x/y is even

We need to determine whether x + y is even. Remember that if x and y are both even or both odd, then their sum will be even.

Statement One Alone:

xy is even

Statement one alone is not sufficient. If x = even and y = odd, then x + y odd; however, if x is even and y is even, then x + y is even. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

x/y is even

Statement two alone is not sufficient. If x = even and y = odd, then x + y is odd; however, if x is even and y is even, then x + y is even. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

We see that statements one and two provide identical information, so we do not have enough information to answer the question.

Answer: E

x + y will be even only if either both of them are even or both of them are odd.
Statement 1: x + 2y is odd.
2y is a multiple of 2 therefore it can't be odd.
So, x is odd. But we don't know if 'y' is odd or even.
Hence, Insufficient.
Statement 2: 'xy' is odd. This is only possible if 'x' and 'y' both are odd.
Since, 'x' and 'y' are odd, x + y is even. Hence, Sufficient.