If x and y are integers, is x + y even? (1) x + 2y is odd.

[BTGmoderatorDC]

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

(1) x + 2y is odd.
(2) xy is odd.

OA B

Source: GMAT Prep

[Jay@ManhattanReview]

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

(1) x + 2y is odd.
(2) xy is odd.

OA B

Source: GMAT Prep

(x + y) even is even if any one of the two conditions are met: 1. Both x and y are odd, or 2. Both x and y are even.

Let's take each statement one by one.

(1) x + 2y is odd.

1. Since 2y is odd irrespective of whether y is even and odd, we can't get wether y is even or odd. (x + 2y) is odd shows that x is odd. Since we do not know whether y is even or odd, we can't get the answer. Insufficient.

(2) xy is odd.

=> x as well as y is odd. Thus, (x + y) = even. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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[Ian Stewart]

(1) x + 2y is odd.

1. Since 2y is odd irrespective of whether y is even and odd

In case this is confusing for anyone reading, I'm sure this is meant to say "Since 2y is even irrespective of whether y is even or odd".