sud21 wrote:Integer x is greater than 0, is x a prime number?
1). All the prime factors of x are greater than root x
2). All the prime factors of x are greater than x/2

Hi

I think there is some issue in the problem.

a prime factor of x cannot be b/w root x and x.
please check once.

Regards,
user123321

why you think it's wrong q.?
st(1) implies if x is prime then the only prime factor of x is x itself, and x>sqrt(x). But x as non-prime can have a prime factor equal to srt(x) and/or less (not greater). Ex., x=9, factor=3 and 3=sqrt(9). All other non-primes will contain 2 as a prime as well and will be not suitable here. Hence the answer is Yes, x is prime. Sufficient

st(2) implies if x is prime then x>x/2, which is true. If x is non-prime, then it's possible for prime factors of x to be only less than or equal to x/2. Ex., 3<9/2 or 2=4/2 Sufficient

d

user123321 wrote:

sud21 wrote:Integer x is greater than 0, is x a prime number?
1). All the prime factors of x are greater than root x
2). All the prime factors of x are greater than x/2

Hi

I think there is some issue in the problem.

a prime factor of x cannot be b/w root x and x.
please check once.

Regards,
user123321

user123321 wrote:

sud21 wrote:Integer x is greater than 0, is x a prime number?
1). All the prime factors of x are greater than root x
2). All the prime factors of x are greater than x/2

Hi

I think there is some issue in the problem.

a prime factor of x cannot be b/w root x and x.
please check once.

Regards,
user123321

1.A prime number has two factors one and itself and definitely its greater than sqrt x
15 has one of its prime factors 5 > sqrt x and 3 < sqrt x. INSUFF as the condn holds true for both prime and composite nos

2.Only a prime no can have its prime factors (itself) > x/2. SUFF

IMO B.

@sam, you made a mistake here, as the original question precisely specifies *all prime factors* and you account only for 5 in 15. What about 3?

sam2304 wrote:

user123321 wrote:

sud21 wrote:Integer x is greater than 0, is x a prime number?
1). All the prime factors of x are greater than root x
2). All the prime factors of x are greater than x/2

Hi

I think there is some issue in the problem.

a prime factor of x cannot be b/w root x and x.
please check once.

Regards,
user123321

1.A prime number has two factors one and itself and definitely its greater than sqrt x
15 has one of its prime factors 5 > sqrt x. INSUFF as the condn holds true for both prime and composite nos

2.Only a prime no can have its prime factors (itself) > x/2. SUFF

IMO B.

pemdas wrote:@sam, you made a mistake here, as the original question precisely specifies *all prime factors* and you account only for 5 in 15. What about 3?

sam2304 wrote:

user123321 wrote:

sud21 wrote:Integer x is greater than 0, is x a prime number?
1). All the prime factors of x are greater than root x
2). All the prime factors of x are greater than x/2

Hi

I think there is some issue in the problem.

a prime factor of x cannot be b/w root x and x.
please check once.

Regards,
user123321

1.A prime number has two factors one and itself and definitely its greater than sqrt x
15 has one of its prime factors 5 > sqrt x. INSUFF as the condn holds true for both prime and composite nos

2.Only a prime no can have its prime factors (itself) > x/2. SUFF

IMO B.

Edited it, missed it while typing. But then it breaks the condition right ? The statement is INSUFF.

no Sam, the condition is Sufficient

you are given precisely x>sqrt(x) for all prime factors, which is *true* only for primes

hence D

pemdas wrote:no Sam, the condition is Sufficient

you are given precisely x>sqrt(x) for all prime factors, which is *true* only for primes

hence D

@pemdas: Yea. Got the point. We have to consider only nos which have prime factors > sqrt x, and disprove them if possible. I guess I took it in opposite sense. 15 cannot be considered. Thanks mate. Confusing traps

Statement 1:
All the prime factors of x are greater than root x

Only satisfied by PRIME Numbers.

SUFFICIENT

Statement 2:
All the prime factors of x are greater than x/2

This is also only true for PRIME numbers
SUFFICIENT

else 8/2=4 but it's PRIME factor is 2

Thanks all for correcting :0)

user123321