It is currently 23 Sep 2017, 16:51

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x is an integer, is y an integer?

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

Hide Tags

Manager
Manager
avatar
Joined: 10 Feb 2011
Posts: 113

Kudos [?]: 346 [0], given: 10

If x is an integer, is y an integer? [#permalink]

Show Tags

New post 15 Mar 2011, 16:46
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

36% (00:56) correct 64% (00:48) wrong based on 56 sessions

HideShow timer Statistics

If x is an integer, is y an integer?

(1) The average (arithmetic mean) of x and y is an integer.
(2) The average (arithmetic mean) of x, y, and y + 4 is x.
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Sep 2017, 06:44, edited 1 time in total.
Edited the OA.

Kudos [?]: 346 [0], given: 10

Manager
Manager
avatar
Joined: 05 Jan 2011
Posts: 171

Kudos [?]: 181 [0], given: 8

Re: If x is an integer, is y an integer? [#permalink]

Show Tags

New post 15 Mar 2011, 19:16
banksy wrote:
8. (MH) If x is an integer, is y an integer?
(1) The average (arithmetic mean) of x and y is an integer.
(2) The average (arithmetic mean) of x, y, and y + 4 is x.



1. (x + y)/2 is an integer
i.e x + y => integer
Therefore Y is an integer since x is an integer and X+Y is also an integer
eg . x+y=5 IF x=3 then y will be 2 (both integer)
Similarly if x=2.5 y will be 2.5 (both non integer) sufficient

2. x+y+y+4=3x
x-y=4
x is an integer (x-y) is an integer .... therefore y must also be an integer sufficient

Kudos [?]: 181 [0], given: 8

1 KUDOS received
SVP
SVP
avatar
Joined: 16 Nov 2010
Posts: 1605

Kudos [?]: 581 [1], given: 36

Location: United States (IN)
Concentration: Strategy, Technology
Premium Member Reviews Badge
Re: If x is an integer, is y an integer? [#permalink]

Show Tags

New post 15 Mar 2011, 19:36
1
This post received
KUDOS
I think the OA is wrong, it should be D.

From (1), (x+y)/2 = k, where k is an integer, so y = 2k - x, an integer - integer = integer, so (1) is sufficient.

From (2) (x + y + y + 4)/3 = x => x + 2y + 4 = 3x => 2x-2y = 4 => x-y = 2, so y = x + 2, an integer + integer = integer, so (2) is sufficient.

Hence the answer is D.
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 581 [1], given: 36

Manager
Manager
avatar
Joined: 05 Jan 2011
Posts: 171

Kudos [?]: 181 [0], given: 8

Re: If x is an integer, is y an integer? [#permalink]

Show Tags

New post 15 Mar 2011, 20:34
banksy wrote:
8. (MH) If x is an integer, is y an integer?
(1) The average (arithmetic mean) of x and y is an integer.
(2) The average (arithmetic mean) of x, y, and y + 4 is x.



hey,
Please share with us the souce.... OA seems to be wrong

Kudos [?]: 181 [0], given: 8

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124659 [0], given: 12079

Re: If x is an integer, is y an integer? [#permalink]

Show Tags

New post 03 Sep 2017, 06:43
banksy wrote:
If x is an integer, is y an integer?

(1) The average (arithmetic mean) of x and y is an integer.
(2) The average (arithmetic mean) of x, y, and y + 4 is x.


If x is an integer, is y an integer?

(1) The average (arithmetic mean) of x and y is an integer --> \(\frac{x + y}{2}=integer\) --> \(x+y=2*integer=integer\) --> \(y = integer-x=integer-integer=integer\). Sufficient.

(2) The average (arithmetic mean) of x, y, and y + 4 is x --> \(\frac{x + y+y+4}{3}=x\) --> \(y=x-2=integer-integer=integer\). Sufficient.

Answer: D.

Edited the OA, it's D not C.

Similar question to practice from OG: https://gmatclub.com/forum/if-x-is-an-i ... 68098.html
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 124659 [0], given: 12079

Re: If x is an integer, is y an integer?   [#permalink] 03 Sep 2017, 06:43
Display posts from previous: Sort by

If x is an integer, is y an integer?

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


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.