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

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Manager
Joined: 28 Feb 2010
Posts: 166
WE 1: 3 (Mining Operations)
If k is a positive integer, is k the square of an integer? [#permalink]

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07 Jun 2010, 01:37
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(N/A)

Question Stats:

83% (01:02) correct 17% (00:00) wrong based on 6 sessions

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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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Regards,
Invincible...
"The way to succeed is to double your error rate."
"Most people who succeed in the face of seemingly impossible conditions are people who simply don't know how to quit."

Manager
Joined: 28 Feb 2010
Posts: 166
WE 1: 3 (Mining Operations)
Re: If k is a positive integer, is k the square of an integer? [#permalink]

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07 Jun 2010, 01:42
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..
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Regards,
Invincible...
"The way to succeed is to double your error rate."
"Most people who succeed in the face of seemingly impossible conditions are people who simply don't know how to quit."

Manager
Joined: 03 May 2010
Posts: 86
WE 1: 2 yrs - Oilfield Service
Re: If k is a positive integer, is k the square of an integer? [#permalink]

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07 Jun 2010, 01:59
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
Math Expert
Joined: 02 Sep 2009
Posts: 43808
Re: If k is a positive integer, is k the square of an integer? [#permalink]

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11 Aug 2017, 01:52
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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/if-k-is-a-pos ... 55987.html
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Re: If k is a positive integer, is k the square of an integer?   [#permalink] 11 Aug 2017, 01:52
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