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

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

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New post 07 Jun 2010, 02:37
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A
B
C
D
E

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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 four different prime numbers

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/if-k-is-a-pos ... 55987.html
[Reveal] Spoiler: OA

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Kudos [?]: 36 [0], given: 33

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Kudos [?]: 36 [0], given: 33

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Re: If k is a positive integer, is k the square of an integer? [#permalink]

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New post 07 Jun 2010, 02:42
Ohhh....now got the ans....

I mistook B as my ans...because I thought 4 different prime nos....so 4 different numbers...and hence we can infer that it is not a Square...

but the case can be...like squares/cubes of prime numbers.

Simple question, but got confused....hmmm.. :cry:
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Re: If k is a positive integer, is k the square of an integer? [#permalink]

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New post 07 Jun 2010, 02:59
Given k is a positive integer. Prompt - Is k a perfect square?

With this one it's easiest to test it by plugging in.

(1) Pick k = 8 not a perfect square
Pick k = 16, a perfect square
--> INSUFF

(2) Pick k = 2*3*5*7 = 210 ; not a perfect square

Pick \(k = 2^2 * 3^2 * 5^2 * 7^2 = (210)^2\) ; is a perfect square

--> INSUFF

Both (1) and (2)
(210)^2 satisfies (1) and (2) and IS a perfect square.
So does 420 which is not a perfect square
--> INSUFF

Pick E

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Re: If k is a positive integer, is k the square of an integer? [#permalink]

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New post 11 Aug 2017, 02:52
If k is a positive integer, is k the square of an integer?

(1) k is divisible by 4. If \(k=4\) answer is YES, but if \(k=8\) answers is NO. Not sufficient.

(2) k is divisible by exactly four different prime numbers.

We don't know the powers of these primes, so if \(k=2^2*3*5*7\) the answer is NO, but if \(k=(2^2*3*5*7)^2\) the answer is YES (\(k\) equals to square of some integer). Not sufficient.

(1)+(2) Again if \(k=2^2*3*5*7\) the answer is NO, but if \(k=(2^2*3*5*7)^2\) the answer is YES. Not sufficient.

Answer: E.


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Kudos [?]: 124141 [0], given: 12072

Re: If k is a positive integer, is k the square of an integer?   [#permalink] 11 Aug 2017, 02:52
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