GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 15 Aug 2018, 11:52

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

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
B
Joined: 28 Jul 2018
Posts: 4
If x and y are integers, is x + y even?  [#permalink]

Show Tags

New post 28 Jul 2018, 21:33
1
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

80% (00:38) correct 20% (01:04) wrong based on 25 sessions

HideShow timer Statistics

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

(1) x + 2y is odd.
(2) xy is odd.
Intern
Intern
avatar
B
Joined: 28 Jul 2018
Posts: 4
Re: If x and y are integers, is x + y even?  [#permalink]

Show Tags

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
RC Moderator
User avatar
G
Status: Perfecting myself for GMAT
Joined: 22 May 2017
Posts: 418
Concentration: Nonprofit
Schools: Haas '21
GPA: 4
WE: Engineering (Computer Software)
GMAT ToolKit User Premium Member CAT Tests
Re: If x and y are integers, is x + y even?  [#permalink]

Show Tags

New post 28 Jul 2018, 21:53
1
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
_________________

If you like my post press kudos +1

New - RC Butler - 2 RC's everyday

Tag me in RC questions if you need help. Please provide your analysis of the question in the post along with the tag.

Intern
Intern
avatar
B
Joined: 27 Oct 2014
Posts: 29
Premium Member
Re: If x and y are integers, is x + y even?  [#permalink]

Show Tags

New post 28 Jul 2018, 21:54
1
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 :)
RC Moderator
User avatar
G
Status: Perfecting myself for GMAT
Joined: 22 May 2017
Posts: 418
Concentration: Nonprofit
Schools: Haas '21
GPA: 4
WE: Engineering (Computer Software)
GMAT ToolKit User Premium Member CAT Tests
Re: If x and y are integers, is x + y even?  [#permalink]

Show Tags

New post 28 Jul 2018, 21:56
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
_________________

If you like my post press kudos +1

New - RC Butler - 2 RC's everyday

Tag me in RC questions if you need help. Please provide your analysis of the question in the post along with the tag.

Intern
Intern
avatar
B
Joined: 28 Jul 2018
Posts: 4
Re: If x and y are integers, is x + y even?  [#permalink]

Show Tags

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)
Re: If x and y are integers, is x + y even? &nbs [#permalink] 28 Jul 2018, 22:03
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.