Target question: What is the value of p?ProGMAT wrote:Data Sufficiency:
If p is a positive integer, what is the value of p?
(1) p/4 is a prime number.
(2) p is divisible by 3.
Given: p is a positive integer
Statement 1: p/4 is a prime number
There are several values of p that meet this condition. Here are two:
Case a: p = 8 (since 8/4 = 2, which is a prime number)
Case b: p = 12 (since 12/4 = 3, which is a prime number)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: p is divisible by 3
There are several values of p that meet this condition. Here are two:
Case a: p = 6
Case b: p = 9
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 says that p is divisible by 4 (since p/4 results in an integer)
Statement 2 says that p is divisible by 3
So, we know that p must be divisible by 12.
If p is divisible by 12, some possible values of p are: 12, 24, 36, 48, 60, . . . etc.
HOWEVER, since p/4 must be prime, only one of these possible values of p (p = 12) will yield a prime number (3) when divided by 4. Any other value of p, when divided by 4, will yield a multiple of 3 that is not prime.
So, it MUST be the case that p = 12
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
