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# If k is a positive integer, is k the square of an integer?

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Director
Joined: 29 Aug 2005
Posts: 808
If k is a positive integer, is k the square of an integer?  [#permalink]

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09 Nov 2008, 03:21
If k is a positive integer, is k the square of an integer?
(1) k is divisible by 4.
(2) k is divisible by exactly 4 different prime numbers.

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Intern
Joined: 30 Oct 2008
Posts: 30
Re: GMAT Set 30 - 18  [#permalink]

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09 Nov 2008, 04:15
E.

Stmnt 1: k=16, k=12. Both are divisible by 4 but may or may not be square of a integer. Not sufficient.
Stmnt 2: k=210=2*3*5*7 which is not square. k=210*210 which is square. Not sufficient.

OA?
Manager
Joined: 30 Sep 2008
Posts: 111
Re: GMAT Set 30 - 18  [#permalink]

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09 Nov 2008, 04:44
mbajingle wrote:
E.

Stmnt 1: k=16, k=12. Both are divisible by 4 but may or may not be square of a integer. Not sufficient.
Stmnt 2: k=210=2*3*5*7 which is not square. k=210*210 which is square. Not sufficient.

OA?

if (1) & (2), k is divisible by 4 and k is divisible by exactly 4 different prime numbers.

we know that only 2 is an even prime number so k can't be divisible by 4, at least 2 is suff. So we can't determine k, does it mean k is not the square of an integer => C?????
Intern
Joined: 30 Oct 2008
Posts: 30
Re: GMAT Set 30 - 18  [#permalink]

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09 Nov 2008, 04:49
lylya4 wrote:
mbajingle wrote:
E.

Stmnt 1: k=16, k=12. Both are divisible by 4 but may or may not be square of a integer. Not sufficient.
Stmnt 2: k=210=2*3*5*7 which is not square. k=210*210 which is square. Not sufficient.

OA?

if (1) & (2), k is divisible by 4 and k is divisible by exactly 4 different prime numbers.

we know that only 2 is an even prime number so k can't be divisible by 4, at least 2 is suff. So we can't determine k, does it mean k is not the square of an integer => C?????

Isn't the question somewhat ambiguous? "exactly 4 different prime numbers" doesn't mean "exactly 4 different factors". Lets wait for the OA.

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This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: GMAT Set 30 - 18 &nbs [#permalink] 09 Nov 2008, 04:49
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# If k is a positive integer, is k the square of an integer?

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