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

 It is currently 23 May 2019, 10:10

### 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

# Is x the square of an Integer?

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 465
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Is x the square of an Integer?  [#permalink]

### Show Tags

Updated on: 23 May 2013, 05:19
2
16
00:00

Difficulty:

85% (hard)

Question Stats:

53% (02:14) correct 47% (02:12) wrong based on 372 sessions

### HideShow timer Statistics

Is x the square of an integer?

(1) x = 12k + 6, where k is a positive integer
(2) x = 3q + 9, where q is a positive integer

_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Originally posted by enigma123 on 21 Jan 2012, 14:56.
Last edited by Bunuel on 23 May 2013, 05:19, edited 2 times in total.
Math Expert
Joined: 02 Sep 2009
Posts: 55266
Re: Is x the square of an Integer?  [#permalink]

### Show Tags

21 Jan 2012, 15:15
2
2
enigma123 wrote:
Is x the square of an integer?
(1) x = 12k + 6, where k is a positive integer
(2) x = 3q + 9, where q is a positive integer

Guys any idea how to solve this? Unfortunately OA is not given.

Is x the square of an integer?

(1) x = 12k + 6, where k is a positive integer --> $$x=6(2k+1)=2*3(2k+1)$$. Now, $$x$$ to be a perfect square it should have an even power of its primes, but $$2k+1$$ is an odd number and can no way produce 2 for $$x$$. Thus $$x$$ is not a perfect square. Sufficient.

(2) x = 3q + 9, where q is a positive integer --> $$x=3(q+3)$$. If $$q=1$$ then $$x=12$$ and the answer is NO but if $$q=9$$ then $$x=36$$ and the answer is YES (basically if (q+3)=3*any perfect square then x will be a perfect square and if (q+3) is some other type of number then x won't be a perfect square). Not sufficient.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 55266
Re: Is x the square of an Integer?  [#permalink]

### Show Tags

12 Jun 2013, 04:27
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Number Properties: math-number-theory-88376.html

All DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38
All PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59

_________________
Director
Joined: 25 Apr 2012
Posts: 676
Location: India
GPA: 3.21
Re: Is x the square of an Integer?  [#permalink]

### Show Tags

13 Nov 2013, 23:12
1
enigma123 wrote:
Is x the square of an integer?

(1) x = 12k + 6, where k is a positive integer
(2) x = 3q + 9, where q is a positive integer

Hi,

Questions asks whether x=I^2 where I is a Integer.

from St 1 we have that x= 12K+6 or x= 6(2K+1)
Now when can 6*(2k+1) will be square??
2k+1 has to equal to 6 or 24 (6*2*2) or 54 (6*3*3) or 96 (6*4*4) to make 6*(2k+1) as square of integer.

But if 6=2k+1 then k =5/2 which is not an integer and is the case for all the values as well.

Hence St 1 is sufficient and option B,C and E ruled out

St 2 we have x=3q+9 or x=3 (q+3) now Q is a positive integer and for values of q =9, x=36 ie. square of an integer and if q= 1,x=12 ie. not a square of an integer.

Ans A
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Non-Human User
Joined: 09 Sep 2013
Posts: 11004
Re: Is x the square of an Integer?  [#permalink]

### Show Tags

21 Mar 2019, 16:08
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Is x the square of an Integer?   [#permalink] 21 Mar 2019, 16:08
Display posts from previous: Sort by