akhp77 wrote:Statement 1:
Q, R, and S occur at 2 places. So these cannot be even

yeah.

in more detail:

a product of integers will be even if any of the integers is/are even.
the product is odd only if all of the integers are odd.

so, it's impossible for q, r, or s to be even:
* if q were even, then pq, qr, and qs would all be even.
* if r were even, then both qr and rs would be even.
* if s were even, then both rs and qs would be even.

so the only way to satisfy statement (1) is to make 'p' even. (if p were also odd, then none of the products would be even.)

as akhilesh says, this statement gives no clues as to whether p is prime.

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statement 2:

says nothing about p.

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together:

examine statement 2.
you could do this algebraically, as done by akhilesh, or you could just make a list:
15, 21, 27, 33, 39, ...
if you make a list, it becomes pretty clear that all of these numbers are divisible by 3, so none of them will be prime.
therefore, S is the non-prime number.
so, from statement 1, p is even.
from statement 2, p is prime.
sufficient.