It is currently 24 Mar 2018, 20:40

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x is an integer, is y an integer?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 10 Feb 2011
Posts: 111
If x is an integer, is y an integer? [#permalink]

### Show Tags

15 Mar 2011, 16:46
00:00

Difficulty:

55% (hard)

Question Stats:

39% (00:57) correct 61% (00:47) wrong based on 61 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.
Manager
Joined: 05 Jan 2011
Posts: 155
Re: If x is an integer, is y an integer? [#permalink]

### Show Tags

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
TOEFL Forum Moderator
Joined: 16 Nov 2010
Posts: 1505
Location: United States (IN)
Concentration: Strategy, Technology
Re: If x is an integer, is y an integer? [#permalink]

### Show Tags

15 Mar 2011, 19:36
1
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.

_________________

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

GMAT Club Premium Membership - big benefits and savings

Manager
Joined: 05 Jan 2011
Posts: 155
Re: If x is an integer, is y an integer? [#permalink]

### Show Tags

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
Math Expert
Joined: 02 Sep 2009
Posts: 44423
Re: If x is an integer, is y an integer? [#permalink]

### Show Tags

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.

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