NEW HERE? LEARN MORE
closeclose
It is currently 28 Sep 2023, 11:05
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel

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

9 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
avatar
B
emanresu1
Intern
Intern
Joined: 28 Jul 2018
Posts: 3
If x and y are integers, is x + y even? [#permalink] New post  28 Jul 2018, 21:33
2
Kudos
17
Bookmarks
Quiz Dashboard Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
00:00
A
B
C
D
E

Difficulty:

5% (low)

Question Stats:

84% (01:01) correct 16% (01:15) wrong based on 403 sessions

Hide Show timer Statistics

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

(1) x + 2y is odd.
(2) xy is odd.
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.
Quiz Dashboard Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
Most Helpful Reply
User avatar
L
Nikhil
MBA Section Director
Joined: 22 May 2017
Affiliations: GMATClub
Posts: 12440
GRE 1: Q168 V154
GPA: 3.4
WE:Engineering (Education)
GMAT ToolKit User Reviews Badge CAT Tests
Re: If x and y are integers, is x + y even? [#permalink] New post  28 Jul 2018, 21:53
5
Kudos
5
Bookmarks
Expert Reply
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
_________________
GMATClub Podcast - All episodes
Signature Read More
General Discussion
avatar
B
emanresu1
Intern
Intern
Joined: 28 Jul 2018
Posts: 3
Re: If x and y are integers, is x + y even? [#permalink] New post  28 Jul 2018, 21:38
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
avatar
B
bionication
Intern
Intern
Joined: 27 Oct 2014
Posts: 28
Re: If x and y are integers, is x + y even? [#permalink] New post  28 Jul 2018, 21:54
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 :)
User avatar
L
Nikhil
MBA Section Director
Joined: 22 May 2017
Affiliations: GMATClub
Posts: 12440
GRE 1: Q168 V154
GPA: 3.4
WE:Engineering (Education)
GMAT ToolKit User Reviews Badge CAT Tests
Re: If x and y are integers, is x + y even? [#permalink] New post  28 Jul 2018, 21:56
Expert Reply
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
_________________
GMATClub Podcast - All episodes
Signature Read More
avatar
B
emanresu1
Intern
Intern
Joined: 28 Jul 2018
Posts: 3
Re: If x and y are integers, is x + y even? [#permalink] New post  28 Jul 2018, 22:03
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)
User avatar
Krabhay
Intern
Intern
Joined: 18 Dec 2018
Posts: 36
Re: If x and y are integers, is x + y even? [#permalink] New post  18 Dec 2018, 22:16
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.
avatar
B
meenakshimiyer
Intern
Intern
Joined: 12 Jan 2019
Posts: 39
Re: If x and y are integers, is x + y even? [#permalink] New post  12 Jan 2019, 22:28
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.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 29509
Re: If x and y are integers, is x + y even? [#permalink] New post  28 Aug 2022, 08:52
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources
Signature Read More
GMAT Club Bot
gmatclubot
Re: If x and y are integers, is x + y even? [#permalink]
28 Aug 2022, 08:52
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderator:
Bunuel
Math Expert
89499 posts

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions