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

 It is currently 17 Aug 2018, 10:11

### 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

# M13-13

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47967

### Show Tags

16 Sep 2014, 00:49
2
00:00

Difficulty:

55% (hard)

Question Stats:

48% (00:45) correct 52% (00:48) wrong based on 108 sessions

### HideShow timer Statistics

Is $$(x - y)*(x + y)$$ an even integer?

(1) $$x$$ and $$y$$ are integers

(2) $$x + y$$ is even

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 47967

### Show Tags

16 Sep 2014, 00:49
Official Solution:

(1) $$x$$ and $$y$$ are integers. If $$x=y=1$$, then the answer is YES but if $$x=1$$ and $$y=0$$, then the answer is NO. Not sufficient.

(2) $$x+y$$ is even. If $$x=y=1$$ then the answer is YES but if $$x=1.8$$ and $$y=0.2$$, then the answer is NO, since in this case $$(x-y)*(x+y)$$ is not an integer at all. Not sufficient.

(1)+(2) Since from (1) $$x$$ and $$y$$ are integers and from (2) $$x+y$$ is even then either $$x$$ and $$y$$ are both even or both odd. In either case $$(x-y)*(x+y)$$ is even. Sufficient.

_________________
Intern
Joined: 05 Oct 2013
Posts: 37
Location: United States
Concentration: General Management, Strategy
WE: Design (Transportation)

### Show Tags

13 Dec 2014, 02:11
Bunuel wrote:
Official Solution:

(1) $$x$$ and $$y$$ are integers. If $$x=y=1$$, then the answer is YES but if $$x=1$$ and $$y=0$$, then the answer is NO. Not sufficient.

(2) $$x+y$$ is even. If $$x=y=1$$ then the answer is YES but if $$x=1.8$$ and $$y=0.2$$, then the answer is NO, since in this case $$(x-y)*(x+y)$$ is not an integer at all. Not sufficient.

(1)+(2) Since from (1) $$x$$ and $$y$$ are integers and from (2) $$x+y$$ is even then either $$x$$ and $$y$$ are both even or both odd. In either case $$(x-y)*(x+y)$$ is even. Sufficient.

Can you please explain how x=y=1 gives the equation an even integer... Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 47967

### Show Tags

13 Dec 2014, 05:50
Arnav180 wrote:
Bunuel wrote:
Official Solution:

(1) $$x$$ and $$y$$ are integers. If $$x=y=1$$, then the answer is YES but if $$x=1$$ and $$y=0$$, then the answer is NO. Not sufficient.

(2) $$x+y$$ is even. If $$x=y=1$$ then the answer is YES but if $$x=1.8$$ and $$y=0.2$$, then the answer is NO, since in this case $$(x-y)*(x+y)$$ is not an integer at all. Not sufficient.

(1)+(2) Since from (1) $$x$$ and $$y$$ are integers and from (2) $$x+y$$ is even then either $$x$$ and $$y$$ are both even or both odd. In either case $$(x-y)*(x+y)$$ is even. Sufficient.

Can you please explain how x=y=1 gives the equation an even integer... Thanks

If x = y = 1, then (x - y)*(x + y) = 0 = even (recall that 0 is an even integer).
_________________
Intern
Joined: 02 Feb 2016
Posts: 2

### Show Tags

24 Feb 2016, 18:59
I think this is a poor-quality question and I don't agree with the explanation. If X and Y are both 5 and 5 this doesn't work
Math Expert
Joined: 02 Sep 2009
Posts: 47967

### Show Tags

24 Feb 2016, 23:49
Binglai wrote:
I think this is a poor-quality question and I don't agree with the explanation. If X and Y are both 5 and 5 this doesn't work

I think you should brush up basics. 0 is an even integer.
_________________
Manager
Joined: 22 Feb 2016
Posts: 97
Location: India
Concentration: Economics, Healthcare
GMAT 1: 690 Q42 V47
GMAT 2: 710 Q47 V39
GPA: 3.57

### Show Tags

21 Nov 2016, 07:09
What is the source of the question. It is the perfect glimpse of what trips us at GMAT.
Math Expert
Joined: 02 Sep 2009
Posts: 47967

### Show Tags

21 Nov 2016, 09:09
AmritaSarkar89 wrote:
What is the source of the question. It is the perfect glimpse of what trips us at GMAT.

Source: GMAT Club's Tests.
_________________
Intern
Joined: 15 Aug 2016
Posts: 1

### Show Tags

21 Sep 2017, 05:44
This is very good question. My first answer is B as I thought that A and B both must be odd or even and should be enough to answer the question. However, I missed the point that X and Y can be decimal.
Intern
Joined: 08 Jul 2016
Posts: 38
Location: Singapore
GMAT 1: 570 Q43 V25
GMAT 2: 640 Q42 V36
WE: Underwriter (Insurance)

### Show Tags

18 Feb 2018, 13:31
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 23 Mar 2018
Posts: 10
GMAT 1: 750 Q48 V44

### Show Tags

11 Jun 2018, 00:52
Why are we not considering negative values of x and y?
Math Expert
Joined: 02 Sep 2009
Posts: 47967

### Show Tags

11 Jun 2018, 05:41
verysecretive3 wrote:
Why are we not considering negative values of x and y?

The solution shows that the answer is C not mentioning negative or positive nature of x or y. So, (1)+(2) is sufficient no matter whether you consider positive or negative variables.
_________________
Manager
Joined: 16 May 2016
Posts: 130
Location: India
Concentration: Marketing, Healthcare
GPA: 3
WE: Analyst (Computer Software)

### Show Tags

24 Jun 2018, 06:50
Bunuel wrote:
Is $$(x - y)*(x + y)$$ an even integer?

(1) $$x$$ and $$y$$ are integers

(2) $$x + y$$ is even

I got this wrong since I considered possibility where X and Y can be negative, such as, X=-2 and Y = 4.
Why we are not considering negative number scenarios
_________________

Not Giving UP! Kudos if you like the question

Math Expert
Joined: 02 Sep 2009
Posts: 47967

### Show Tags

24 Jun 2018, 10:05
Cbirole wrote:
Bunuel wrote:
Is $$(x - y)*(x + y)$$ an even integer?

(1) $$x$$ and $$y$$ are integers

(2) $$x + y$$ is even

I got this wrong since I considered possibility where X and Y can be negative, such as, X=-2 and Y = 4.
Why we are not considering negative number scenarios

(1)+(2) is sufficient no matter whether you consider positive or negative variables.

If x = -2 and y = 4, then (x - y)*(x + y) = -6*2 = -12 = even. The same answer as we got in the solution above.
_________________
Re: M13-13 &nbs [#permalink] 24 Jun 2018, 10:05
Display posts from previous: Sort by

# M13-13

Moderators: chetan2u, Bunuel

# Events & Promotions

 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®.