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# If sqrt(x) is a positive integer, is sqrt(x) a prime number?

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Senior Manager
Joined: 08 Jun 2006
Posts: 335
Location: Washington DC
If sqrt(x) is a positive integer, is sqrt(x) a prime number? [#permalink]

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13 Dec 2006, 12:25
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If sqrt(x) is a positive integer, is sqrt(x) a prime number?
1) all positive factors of x are odd
2) x is divisible by exactly 3 positive integers
Director
Joined: 28 Dec 2005
Posts: 919

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13 Dec 2006, 12:39
I get B.

1) All positive factors are odd:
factors could be multiples of a prime (eg: 15,21 etc) , or a prime - insuff

2) x has only 3 positive factors SUFF. the factors being 1, x and the prime number. If the third number were not prime, there would be more possible factors.
Director
Joined: 06 Sep 2006
Posts: 736

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13 Dec 2006, 14:16
If sqrt(x) is a positive integer, is sqrt(x) a prime number?
1) all positive factors of x are odd
2) x is divisible by exactly 3 positive integers

From 1) x could be any number e.g. 25, 625, So we are not sure if sqrt(x) will be a prime number. INSUFFICIENT.

From 2) According to 2 x is one of these kind: 4,9,25,49,81,121,

So sqrt(x) is a prime number.
Sufficient.

B.
Senior Manager
Joined: 08 Jun 2006
Posts: 335
Location: Washington DC

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13 Dec 2006, 14:49
Good job...OA is B
No need to post OE..
Manager
Joined: 18 Nov 2006
Posts: 123

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15 Dec 2006, 13:28
lesson is: Square of a prime no has exactly 3 factors

condition 1) was present just to confuse..
Senior Manager
Joined: 01 Oct 2006
Posts: 495

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15 Dec 2006, 13:55
Late but B

Few things worth remembering
A prime number has two factor 1 and itself.
A sqaure of a prime number has three factors 1,sqrt,and itself.
15 Dec 2006, 13:55
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