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

[M7MBA]

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

(1) xy is even

(2) x/y is even

The OA is the option E.

Experts, both statements imply that x and y are even, then x+y is even. Why the correct answer is E. Can you give me some help? Thanks in advanced.

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Hi M7MBA,

We're told that X and Y are positive integers. We're asked if (X+Y) is EVEN. This is a YES/NO question and we can solve it by TESTing VALUES.

1) (X)(Y) is EVEN.

IF....
X=2, Y=1, then the answer to the question is NO.
X=4, Y=2, then the answer to the question is YES.
Fact 1 is INSUFFICIENT

(2) X/Y is EVEN

IF....
X=2, Y=1, then the answer to the question is NO.
X=4, Y=2, then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we already have two pairs of values that 'fit' both Facts and produce different answers (one "YES" and one "NO").
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

[Jeff@TargetTestPrep]

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

[Krabhay]

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.