arjtryarjtry wrote:

. How many prime factors does positive integer N have?

(1) N/5 is a prime number.

(2) 3N^2 has two different prime number.

A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.

B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.

C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.

D. Each Statement ALONE is sufficient..

E. Statements (1) and (2) TOGETHER are NOT sufficient..

(1) - N/5 is a prime number.

from this, we know that 5 is a factor of N

two options

i) N has only one prime factor (N/5 can be = 5 (if N = 25),

ii) N has only two prime factor (N/5 = another prime number (if N <> 25)

therefore insuff

(2) 3N^2 has two different prime number

two different options

i) N^2 has only one prime factor (3 not a factor of N)

i) N^2 has only two prime factors (3 is a factor of N)

combining the two,

we still dont know how many factors are there.

therefore E

PS : N = 25 (N^2 = 625) and N = 15 (N^2 = 225) both satisfy the above conditions.