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

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

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24 Jun 2009, 01:57
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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 $$p^2$$.
(2)$$\sqrt{n}$$is an integer.
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Lahoosaher

Senior Manager
Joined: 16 Jan 2009
Posts: 355
Concentration: Technology, Marketing
GMAT 1: 700 Q50 V34
GPA: 3
WE: Sales (Telecommunications)
Re: DS : square of an integer [#permalink]

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24 Jun 2009, 14:54
Could someone please try this one.
OA is
[Reveal] Spoiler:
B

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Lahoosaher

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Re: DS : square of an integer [#permalink]

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24 Jun 2009, 18:34
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 .
(2)is an integer.

(1) INSUFF - because if n=8, then n is divisible by 2 as well as $$2^2$$. But 8 is NOT the square of an integer.
If n=16, then n is divisible by 2 as well as $$2^2$$. 16 is the suqare of an integer.

(2) SUFF. If \sqrt{n} is an integer, then n MUST be an integer. Try this for any number.
Eg- \sqrt{36} = 6, But \sqrt{1/4} = 1/2 which is not an integer

So B it is.
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Re: DS : square of an integer [#permalink]

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24 Jun 2009, 23:01
Explanation is right. Only 2 is sufficient.
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Re: DS : square of an integer [#permalink]

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25 Jun 2009, 20:52
B.
Agree with the above explanation.
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Re: DS : square of an integer [#permalink]

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26 Jun 2009, 09:22
amolsk11 wrote:
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 $$p^2$$.
(2)$$\sqrt{n}$$is an integer.

1. n= p*k and n = p^2*K where k is some integer

for n=p*k
when k=p implies n is a square of an integer but for k not equal to p n is not square of an integer

for n=p^2*k

when k=1 imples n is a square otherwise not.

2. $$\sqrt{n}$$is an integer

imples $$\sqrt{n}$$=k ;k=some integer

implies n=k^2

Sufficient

Re: DS : square of an integer   [#permalink] 26 Jun 2009, 09:22
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