act-dog

If Q has 5 factors, we can represent Q = a^4, where a is positive integer more than 1.Let's assume that "a" is not a prime number. Let a = kp, where both k and p are positive integers.

Thus, Q = (kp)4=k4∗p4(kp)4=k4∗p4. Now the number of factors of Q = (4+1)*(4+1) = 25. But as the given condition states that Q has ONLY 5 factors, thus "a" can't have any other factor except 1 and itself. Thus, a = prime number.

Statement I :We can represent Q = (a^2)^2. Thus, we have to prove whether a^2 is a prime number. Take a=2. We can see that it is not a prime number. Thus, this option can't answer a "MUST be true question"

Statement II : Always true as proved above.

Statement III : Again take a =2. Thus, Q = 64. We don't have this as product of 2 primes.

The Answer is, B.