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1 is insufficient. There are many possible values for p:
a. p = 8 makes p/4 = 2, which is prime
b. p = 12 makes p/4 = 3, which is prime again
c. p = 20 makes p/4 = 5, a prime number as well....

2 is insufficient, since there are plenty of numbers divisible by 3: 3, 6, 9,.....

But put them both together to get your answer: p/4 is a prime number, but it will also be divisible by 3 (since p is divisible by 3). The only prime number divisible by 3 is 3 itself, so p/4 = 3, making p - 12.

statement 1: P/4 = prime

with this statement you will get set of values of P such as 8,12...
so this is insufficient

statement 2: p is divisible by 3

you will get set of values such as 3,6,9...
so insufficient

with 1 & 2 together,
you will get p=12 only. so ans is C

Thank you. you guys are the best...........

ST