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Senior Manager
Joined: 08 Jun 2006
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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

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

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

Good job...OA is B
No need to post OE..



Manager
Joined: 18 Nov 2006
Posts: 123

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

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.










