A set of statements is given.
(A) P is a perfect square,
(B) P is greater than 2000.
Which of the given set of statements should be used to decide the solution to problem: Is P a prime number if P>1?

Correct option is C

If statement (A) is true, we know:

​$$P = n^2 \quad \text{for some} \quad n > 1$$

such that P>1.
A prime number is defined as:

$$\text{A number } p \text{ is prime } \iff \text{its only divisors are } 1 \text{ and } p.$$

Any perfect square P = $$n^2$$​, where n>1, is divisible by n (other than 1 and itself), so it cannot be prime.

Thus, if P is a perfect square and P>1 :

​$$P \text{ is not prime}\boxed{\text{Only~A~is~required}}$$​​