If positive integers x and y are not both odd, which of the

Question

If positive integers x and y are not both odd, which of the following must be even?

(A) xy
(B) x + y
(C) x - y
(D) x + y -1
(E) 2(x + y) - 1

Bunuel · Answer

SOLUTION

If positive integers x and y are not both odd, which of the following must be even?

(A) xy
(B) x + y
(C) x - y
(D) x + y -1
(E) 2(x + y) - 1

Positive  integers  x and y are NOT both odd, means that either  both x and y are even  or  one is even and the other one is odd . In either case xy must be even.

Answer: A.

kinjiGC · Answer

If x and y are both odd, either one of them is odd or both are even.
In any case xy will always have a factor of 2 and hence even - Option A)

AKG1593 · Answer

Even +/- odd= odd
Even +/- even= even
Odd +/- odd = even

Even * even= even
Even * odd= even
Odd * odd= odd

X & Y could be both even or one odd and one even=> x*y= even always.
Ans.A

Posted from my mobile device

havoc7860 · Answer

I am sorry but i disagree as x and y are not both odd means that either one of them is odd i.e. x or y is odd which implies the one that is not odd is even. so basically x is odd and y is even or x is even and y is odd.

Bunuel · Answer

Nope. x and y are not both odd means that:

(i) Both x and y are even;
OR:
(ii) One of x or y is even, the other odd.

BrentGMATPrepNow · Answer

Given: integers x and y are not both odd

There are two different cases that satisfy this information: 
 Case i : Both numbers are even
 Case ii : One number is even and one number is odd

Let's examine each case individually...

Case i : Both numbers are even 
So it could be the case that x = 2 and y = 2, so let's plug these values into our answer choices

(A) (2)(2) = 4, which is even. Keep. 
(B) 2 + 2 = 4, which is even. Keep.
(C) 2 - 2 = 0, which is even. Keep.
(D) 2 + 2 - 1 = 3, which is odd. ELIMINATE. 
(E) 2(2 + 2) - 1 = 7, which is odd. ELIMINATE.

We're down to A, B and C

Case ii : One number is even and one number is odd 
So it could be the case that x = 1 and y = 2, so let's plug these values into the remaining answer choices
(A) (1)(2) = 2, which is even. Keep.
(B) 1 + 2 = 3, which is odd. ELIMINATE. 
(C) 1 - 2 = -1, which is odd. ELIMINATE.

By the process of elimination, the correct answer is A

Cheers, 
Brent

breezeit · Answer

If both x and y are both even, then shouldn't x + y always equal even (as even + even = even)? In this case, B could be the answer.

I think the question meant that ATLEAST ONE, i.e either x or y, must be odd. In that case, A is a definitive answer.

Thoughts?

Bunuel · Answer

I think this is explained in the solution you quote: Positive  integers  x and y are NOT both odd, means that either   both x and y are even   or   one is even and the other one is odd  .

Option B is not correct because if one is even and the other one is odd, then x + y = even + odd = odd.

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

If positive integers x and y are not both odd, which of the

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If positive integers x and y are not both odd, which of the

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards