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

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Director
Joined: 03 Jul 2003
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Is the positive integer n equal to the square of an integer? [#permalink]

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13 Dec 2003, 21:52
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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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CEO
Joined: 15 Aug 2003
Posts: 3454

Kudos [?]: 904 [0], given: 781

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13 Dec 2003, 22:51
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.

with A

say n = 36 p =2 , p^2 = 4
say n = 49 p = 7, p^2 = 49
say n = 125 p = 5 , p^2 = 25

A is also sufficient

D

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Manager
Joined: 12 Oct 2003
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Location: USA

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14 Dec 2003, 06:42
B

BG I took the same example. What if n is 18

n = 18
p = 3
n/p = 6
n / (p^2) = 2

but n is not a square of ...

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CEO
Joined: 15 Aug 2003
Posts: 3454

Kudos [?]: 904 [0], given: 781

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14 Dec 2003, 07:41
BG wrote:
What about if N is 18 ?

we consider those #'s that satisfy that condition.

the given statements are facts..use them like facts.

you are trying to prove the statement wrong.

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Director
Joined: 13 Nov 2003
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14 Dec 2003, 10:33
Praet read the question and please note that it is: Is the positive integer n equal to the square of an integer?..From statement 1 we know that for every prime number p if p is a divisor of n then so is p^2..so n could be 4,9 but n could be 18 or 50, for example, which makes statement 1) insufficient since we can not say if n is a square of an integer

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CEO
Joined: 15 Aug 2003
Posts: 3454

Kudos [?]: 904 [0], given: 781

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14 Dec 2003, 11:37
BG wrote:
Praet read the question and please note that it is: Is the positive integer n equal to the square of an integer?..From statement 1 we know that for every prime number p if p is a divisor of n then so is p^2..so n could be 4,9 but n could be 18 or 50, for example, which makes statement 1) insufficient since we can not say if n is a square of an integer

you miss the p^2 part.

let me rephrase.

1. If n is divisible by p, it is divisible by p^2 too.

you have to satisfy the above requirement.

18 is divisible by 2 , but not divisible by 2^2.

so 18 does NOT satisfy the requirement of statement 1.

Do NOT violate the FACT in (1).

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Director
Joined: 13 Nov 2003
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15 Dec 2003, 03:11
Think that 18 is divisible by 3 and 9 also ....

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15 Dec 2003, 03:11
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