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enigma123
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Is x the square of an Integer? Updated on: 23 May 2013, 05:19
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.
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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
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Is x the square of an Integer? 21 Jan 2012, 15:15
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enigma123
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.

Answer: A.
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Is x the square of an Integer? 12 Jun 2013, 04:27
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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
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Is x the square of an Integer? 13 Nov 2013, 23:12
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enigma123
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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Is x the square of an Integer? 26 Oct 2023, 00:31
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enigma123
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

Question: Is x a perfect square?

For x to be a perfect square, its each prime factor should have an even exponent in the prime factorisation.

(1) x = 12k + 6, where k is a positive integer
x = 6(2k + 1) = 2 * 3 * (2k+1)
(2k+1) is certainly odd. Hence the exponent of 2 in its prime factorization is 1 only.
Hence x cannot be prefect square. Sufficient alone.

(2) x = 3q + 9, where q is a positive integer
x = 3(q + 3)
q could be 1 in which case x is not a perfect square or it could take a value such that we get another 3. Say q could be 24 so that x = 3*27 = 3^4 (and hence 3 has an even exponent)
So here, x is a perfect square. Not sufficient alone

Answer (A)

Check this video on perfect squares: https://anaprep.com/number-properties-f ... ct-square/
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Is x the square of an Integer? 07 Nov 2024, 03:42
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