Last visit was: 12 Aug 2024, 22:53 It is currently 12 Aug 2024, 22:53
Toolkit
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

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.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Intern
Joined: 28 Jul 2018
Posts: 3
Own Kudos [?]: 24 [22]
Given Kudos: 30
MBA Section Director
Joined: 22 May 2017
Affiliations: GMATClub
Posts: 12760
Own Kudos [?]: 8944 [10]
Given Kudos: 3038
GRE 1: Q168 V154
GPA: 3.4
WE:Engineering (Education)
General Discussion
Intern
Joined: 28 Jul 2018
Posts: 3
Own Kudos [?]: 24 [0]
Given Kudos: 30
Intern
Joined: 27 Oct 2014
Posts: 19
Own Kudos [?]: 45 [1]
Given Kudos: 38
Re: If x and y are integers, is x + y even? [#permalink]
1
Kudos
emanresu1 wrote:
This one (from GMATPrep Exam 5) has me pulling my hair out. According to the OA, only (2) is sufficient. I think (1) is sufficient alone too, however.

My logic for (1):
- x + 2y -> O
- 2y must be even (any integer times 2 is even)
- thus x must be odd
- "x + y" is only odd if either x or y is odd
- thus (1) indicates that "x + y" is odd

emanresu1, 'y' could be even OR odd for 'x' + '2y' to result in an odd integer. Therefore, statement (a) does not give us sufficient information as to whether integer 'y' is indeed an odd integer. Therefore, plugging it into the question stem (x+y) may result in an even OR an odd expression, hence insufficient. Hope that helps
MBA Section Director
Joined: 22 May 2017
Affiliations: GMATClub
Posts: 12760
Own Kudos [?]: 8944 [0]
Given Kudos: 3038
GRE 1: Q168 V154
GPA: 3.4
WE:Engineering (Education)
Re: If x and y are integers, is x + y even? [#permalink]
emanresu1 wrote:
This one (from GMATPrep Exam 5) has me pulling my hair out. According to the OA, only (2) is sufficient. I think (1) is sufficient alone too, however.

My logic for (1):
- x + 2y -> O
- 2y must be even (any integer times 2 is even)
- thus x must be odd
- "x + y" is only odd if either x or y is odd
- thus (1) indicates that "x + y" is odd

If both x and y are odd then x + y becomes even. You only know the even/odd nature of x and y can be either even or odd. Hence statement 1 is insufficient

Example

x = 3 and y = 6 => x + y = 3 + 6 = 9 odd

x = 3 and y = 7 => x + y = 3 + 7 = 10 even
Intern
Joined: 28 Jul 2018
Posts: 3
Own Kudos [?]: 24 [0]
Given Kudos: 30
Re: If x and y are integers, is x + y even? [#permalink]
workout wrote:
To determine whether x + y is even or odd

Statement 1

x + 2y is odd

=> 2y is always even irrespective of even/odd nature of y (any integer multiplied by even results in an even integer)

=> x + 2y = odd

=> x = odd - 2y = odd - even = odd

So, x is odd and y can either be odd or even

if x is odd and y is odd => x + y = odd + odd = even

if x is odd and y is even => x + y = odd + even = odd

As we have two possible cases, statement 1 is insufficient

Statement 2

xy is odd

=> xy is odd if and only if x is odd and y is odd

=> x + y = odd + odd = even

Statement 2 is sufficient

Hence option B

THANK YOU! This Quant pressure has me flubbing even simple things like thinking 7+7 is odd (yes, I really thought that during my practice exam, and thus the ridiculous confusion)
Intern
Joined: 18 Dec 2018
Posts: 34
Own Kudos [?]: 10 [1]
Given Kudos: 0
Re: If x and y are integers, is x + y even? [#permalink]
1
Kudos
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.
Intern
Joined: 12 Jan 2019
Posts: 35
Own Kudos [?]: 17 [1]
Given Kudos: 0
Re: If x and y are integers, is x + y even? [#permalink]
1
Kudos
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.
Non-Human User
Joined: 09 Sep 2013
Posts: 34395
Own Kudos [?]: 862 [0]
Given Kudos: 0
Re: If x and y are integers, is x + y even? [#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.
Re: If x and y are integers, is x + y even? [#permalink]
Moderator:
Math Expert
94906 posts