If x + y is odd, which of the following could be true?

(I) xy is even
(II) xy is odd
(III) x/y is even

Correct answer marked below

I only

II only

III only

I and II

I and III

Correct

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Explanation

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Comments

HannahAug 6

Wait, so if x+y is odd then one of them has to be even and the other odd right? That's the key here. Took me a sec to see why II can't work.

BharathAug 14

yep and that's also why I works, one even factor is enough to make the product even

YaelApr 24

the x/y is even part threw me off. can someone explain how that's possible without giving away the whole thing?

DevanshMay 6

ohh got it, the even one goes on top. sneaky. thanks

ArvindAug 5

solid question. 605-655 feels right, not hard but you have to actually check all three statements instead of assuming.

PabloJul 25

thanks, helpful!

What this question tests

Your command of divisibility, primes, factors, parity, and how the GMAT tests properties of integers.

Forgetting that 1 is not prime, that 0 is divisible by every integer, or that negative numbers flip your assumptions.

If x + y is odd, which of the following could be true?(I) xy is even(II) xy is odd(III) x/y is even