Orla M wrote:If P is a positive integer, what is P?
1) p/4 is a prime number
2) p is divisible by 3
Target question:
What is p?
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, (in which case p/4 = 2)
Case b:
p = 12, (in which case p/4 = 3)
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 = 3
Case b:
p = 6
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
From statement 2, we know that p = 3k (for some integer k)
From statement 1, we know that p/4 is a prime number, which means 3k/4 is a prime number.
This means that 3k/4 is also an integer.
Since 3 is not divisible by 4, we can see that k must be divisible by 4. In other words k/4 is an integer.
So, we know that (3)(k/4) is an integer (which is also prime)
For (3)(k/4) to be prime, k/4 must equal 1, which means k
must equal 4.
Since p = 3k (from statement 2), we can now be certain that
p = 3(4) = 12
Since we can now answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
