Given n = 3k+2
and t = 5p+3
So nt = 15kp+9k+10p+6.
Since 15kp is divisible by 15, in order to give the remainder when nt is divided by 15, we need information about k and p.
Statement I: n-2 = 3k is divisible by 5. So k is divisible by 5. From this we can conclude that 9k is divisible by 15. But we don't know about p.
So I is not sufficient
Statement II: t =5p+3 is divisible by 3, which means p is divisible by 3 So we can conclude that 10p is divisible by 15. But we don't know about k.
So II is not sufficient
Combining both, we can conclude that both 9k and 10p are divisible by 15, hence the remainder when nt is divided by 15 is 6.
Hence C is the answer
