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# Is x the square of an Integer?

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Is x the square of an Integer? [#permalink]

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21 Jan 2012, 14:56
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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
[Reveal] Spoiler: OA

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Last edited by Bunuel on 23 May 2013, 05:19, edited 2 times in total.
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Re: Is x the square of an Integer? [#permalink]

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21 Jan 2012, 15:15
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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.

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Re: Is x the square of an Integer? [#permalink]

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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

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Re: Is x the square of an Integer? [#permalink]

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13 Nov 2013, 23:12
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
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Re: Is x the square of an Integer? [#permalink]

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01 Sep 2015, 05:48
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).

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Re: Is x the square of an Integer?   [#permalink] 01 Sep 2015, 05:48
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