It is currently 22 Feb 2018, 06:31

# TODAY:

MIT Sloan Releasing 1st Wave of Interview Invites - Join GMATClub CHAT for Live Updates

### 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

# M32-11

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43864

### Show Tags

17 Jul 2017, 04:56
Expert's post
1
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

59% (01:21) correct 41% (00:28) wrong based on 17 sessions

### HideShow timer Statistics

Is $$\frac{x + y}{2}$$ an integer?

(1) $$|x| = \sqrt {y^2}$$

(2) $$xy = 9$$
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 43864

### Show Tags

17 Jul 2017, 04:56
Official Solution:

Is $$\frac{x + y}{2}$$ an integer?

First of all, notice that we are NOT told that $$x$$ and $$y$$ are integers.

(1) $$|x| = \sqrt {y^2}$$

$$|x| = |y|$$. So, $$x=-y$$ or $$x=y$$. If $$x=-y$$, then $$\frac{x + y}{2}=\frac{-y + y}{2}=0=integer$$ but if $$x=y$$, then $$\frac{x + y}{2}=\frac{x + x}{2}=x$$, which will be an integer if $$x$$ is an integer but won't be an integer if $$x$$ is not an integer. Not sufficient.

(2) $$xy = 9$$. If $$x=y=3$$, then $$\frac{x + y}{2}=\frac{3 + 3}{2}=3=integer$$ but if $$x=\frac{1}{3}$$ and $$y=27$$, then $$\frac{x + y}{2} \neq integer$$

(1)+(2) If from (1) $$x=-y$$, then from (2) we'll have $$-x^2=9$$, which is the same as $$x^2=-9$$ but this is not possible (the square of a number cannot be negative). Thus, it must be true that $$x=y$$, so $$x^2=9$$, which gives $$x=y=3$$ or $$x=y=-3$$. In any case $$\frac{x + y}{2}=integer$$. Sufficient.

_________________
Intern
Joined: 20 Nov 2017
Posts: 11

### Show Tags

25 Jan 2018, 13:04
Excellent question... I picked E because i got confused.
Re: M32-11   [#permalink] 25 Jan 2018, 13:04
Display posts from previous: Sort by

# M32-11

Moderators: chetan2u, Bunuel

 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®.