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03 Feb 2005, 20:11
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If x^1/2 is a +ve integer, is x^1/2 a prime number ?
I. x is divisible by exactly 3 +ve integers.
II. All +ve factors of x are odd.
I. x is divisible by exactly 3 +ve integers.
II. All +ve factors of x are odd.
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03 Feb 2005, 20:22
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1) statement A is enough, X can be 4,9,25,49 so everytime x^1/2 is a prime number like 2,3,5,7
2) statement B is not sufficient, X can be 1 which is not a prime number
1) statement A is enough, X can be 4,9,25,49 so everytime x^1/2 is a prime number like 2,3,5,7
2) statement B is not sufficient, X can be 1 which is not a prime number
03 Feb 2005, 20:40
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A)
The three different factors of X are: 1, SQRT(X) and X. This can only happen for squares of prime numbers and X can't be 1 (non-prime), as it does not have three different factors - it just has one factor.
Yes
Another Fun Fact:
* All perfect squares >1 have odd number of factors
B) 625 had all odd factors, but SQRT(625) is not prime.
25 has all odd factors, but SQRT(25) is prime
No
A)
The three different factors of X are: 1, SQRT(X) and X. This can only happen for squares of prime numbers and X can't be 1 (non-prime), as it does not have three different factors - it just has one factor.
Yes
Another Fun Fact:
* All perfect squares >1 have odd number of factors
B) 625 had all odd factors, but SQRT(625) is not prime.
25 has all odd factors, but SQRT(25) is prime
No
A)
