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

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Intern
Joined: 14 Jun 2005
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If k is a positive integer, is k the square of an integer? [#permalink]  23 Sep 2005, 21:43
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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.
Senior Manager
Joined: 30 Oct 2004
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IMO (B) is suff to prove K is NOT a square of an integer.
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-Vikram

Senior Manager
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Re: DS [#permalink]  24 Sep 2005, 08:37
tingle wrote:
(2) k is divisible by exactly 4 different prime numbers.

Not sure what this means ? - k divisible by 2, 3, 5, 7 for example,
then it is also divisible by 6,15,35, 4, 9, 25, 49 etc. what is "exactly" ?
Senior Manager
Joined: 13 Jan 2005
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I think its a E. May be I am reading too much into it.

A - Not suff (K could be 16 or 8)
B - K= Eg.: 2^a X 3^b X 5^c X 7 ^d

If a=b=c=d=1, then K is exactly divisble by 4 diff prime numbers. K cannot be a square
But a=b=c=d=2 then K is still divisible by 4 diff prime numbers. K can be a square in this case

Hence B not suff

C - not suff as well a=2, but doesn't say much abt b, c, and d

Hence E.

GA
Current Student
Joined: 28 Dec 2004
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B for me

Prime^even power is always perfect square...

Prime^odd power not a perfect square...

(II) tells that there are only 4 prime factors

which I read as they only appear once! which means Prime^1 is not going to lead to a perfect square...

if I read exactly (II) incorrectly, and there can be more than one appeareance of prime factors then E is the right answer..
Intern
Joined: 27 Aug 2005
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The rule states that, for all the perfect squares, the number of prime factors are always odd..

and for all the non perfect square numbers, the number of prime factors are always even.

My answer is (B) because we get to know that K is not a perfect square number
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