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# Is the positive integer n equal to the square of an integer?

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Manager
Joined: 04 Dec 2008
Posts: 104

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Is the positive integer n equal to the square of an integer? [#permalink]

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06 Aug 2009, 07:35
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Difficulty:

(N/A)

Question Stats:

33% (01:06) correct 67% (01:45) wrong based on 6 sessions

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Is the positive integer n equal to the square of an integer?
(1) For every prime number p, if p is a divisor of n, then so is p2.
(2) sqrt root (n) is an integer.

I got this correct. But I'm still not sure about Stmt 1. Pls. Explain. Thks!

Kudos [?]: 225 [0], given: 2

Senior Manager
Joined: 20 Mar 2008
Posts: 452

Kudos [?]: 133 [0], given: 5

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06 Aug 2009, 09:51
I think the answer is (B.) Is that what the OA is?

Regarding St. 1:

Let n = 27.
It's divisible by 3 (p) as well as 3^2 (p^2) but it's not a square of an integer. So the st.1 is insuff.

Kudos [?]: 133 [0], given: 5

Manager
Joined: 18 Jul 2009
Posts: 167

Kudos [?]: 115 [0], given: 37

Location: India
Schools: South Asian B-schools

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06 Aug 2009, 23:44
Statement 1 : For every prime number p, if p is a divisor of n, then so is p2

this means nothing but P^2 is a factor of n

consider a number 252 = 4x7x(3^2)....here prime number 3 sqr is a factor if 252 ..but that doesnt mean all other powers of factor of 252 will be even for him to qualify as a sqr....

hence insufficient
_________________

Bhushan S.
If you like my post....Consider it for Kudos

Kudos [?]: 115 [0], given: 37

Intern
Joined: 11 Jul 2009
Posts: 36

Kudos [?]: 49 [0], given: 3

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07 Aug 2009, 06:44
If it (1) is insufficient, then here's my explanation:

"for every prime number p, if p is a divisor of n, then so is 2p." --> basically said to me that n/p = integer and n/(2p) = integer.

I tried prime numbers 2 & 3.

for 2:
n is positive, so I picked n = 4 for prime divisor 2. 4/2 = 2. 4/(2*2) = 1. Both integers. and n = 4, which is equal to 2^2. This works.

for 3:
I picked n = 6 to be divisible by 3 and 2(3). 6/3 = 2. 6/(2*3) = 1. BUT, n =6 and this is ≠ to the square of any integer.

Dunno if this is 100% correct, but this is how I arrived at my conclusion (B).

(please give kudos if I'm right...thanks!)

Kudos [?]: 49 [0], given: 3

Re: Prime & Square   [#permalink] 07 Aug 2009, 06:44
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