Last visit was: 19 Jul 2024, 17:04 It is currently 19 Jul 2024, 17:04
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94421
Own Kudos [?]: 642363 [30]
Given Kudos: 86332
Send PM
Math Expert
Joined: 02 Sep 2009
Posts: 94421
Own Kudos [?]: 642363 [4]
Given Kudos: 86332
Send PM
Director
Director
Joined: 03 Feb 2013
Posts: 793
Own Kudos [?]: 2604 [1]
Given Kudos: 567
Location: India
Concentration: Operations, Strategy
GMAT 1: 760 Q49 V44
GPA: 3.88
WE:Engineering (Computer Software)
Send PM
Manager
Manager
Joined: 20 Dec 2013
Posts: 183
Own Kudos [?]: 291 [2]
Given Kudos: 35
Location: India
Send PM
Re: If positive integers x and y are not both odd, which of the [#permalink]
1
Kudos
1
Bookmarks
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
avatar
Intern
Intern
Joined: 21 Oct 2012
Posts: 27
Own Kudos [?]: 63 [0]
Given Kudos: 19
Location: United States
Concentration: Marketing, Operations
GMAT 1: 650 Q44 V35
GMAT 2: 600 Q47 V26
GMAT 3: 660 Q43 V38
GPA: 3.6
WE:Information Technology (Computer Software)
Send PM
Re: If positive integers x and y are not both odd, which of the [#permalink]
Bunuel wrote:
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.


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.
Math Expert
Joined: 02 Sep 2009
Posts: 94421
Own Kudos [?]: 642363 [1]
Given Kudos: 86332
Send PM
Re: If positive integers x and y are not both odd, which of the [#permalink]
1
Kudos
Expert Reply
havoc7860 wrote:
Bunuel wrote:
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.


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.


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.
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30837 [1]
Given Kudos: 799
Location: Canada
Send PM
Re: If positive integers x and y are not both odd, which of the [#permalink]
1
Kudos
Expert Reply
Top Contributor
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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


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
Intern
Intern
Joined: 16 Aug 2020
Posts: 8
Own Kudos [?]: 0 [0]
Given Kudos: 37
Send PM
If positive integers x and y are not both odd, which of the [#permalink]
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 wrote:
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.
Math Expert
Joined: 02 Sep 2009
Posts: 94421
Own Kudos [?]: 642363 [0]
Given Kudos: 86332
Send PM
Re: If positive integers x and y are not both odd, which of the [#permalink]
Expert Reply
breezeit wrote:
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 wrote:
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.


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.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34033
Own Kudos [?]: 853 [0]
Given Kudos: 0
Send PM
Re: If positive integers x and y are not both odd, which of the [#permalink]
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.
GMAT Club Bot
Re: If positive integers x and y are not both odd, which of the [#permalink]
Moderator:
Math Expert
94421 posts