oks wrote:If A is a prime number, what is the value of A?
1) 0 < A < 10.
2) (A � 2) is divisible by 3.

Target question: What is the value of A?

Given: A is a prime number

Statement 1: 0 < A < 10
Let'sTEST some values.
There are several values of A that satisfy statement 1. Here are two:
Case a: A = 2
Case b: A = 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: (A - 2) is divisible by 3
There are several values of A that satisfy statement 2 Here are two:
Case a: A = 5. Notice that A - 2 = 5 - 2 = 3, and 3 is divisible by 3. In this case, the answer to the target question is A = 5
Case b: A = 11. Notice that A - 2 = 11 - 2 = 9, and 9 is divisible by 3. In this case, the answer to the target question is A = 11
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
--------------ASIDE---------------------------
IMPORTANT: If integer N is divisible by integer d, then it must be the case that we can write N = dk for some integer k.
For example, we know that 12 is divisible by 3, because we can write 12 = 3(4)
This means that 0 is divisible by all non-negative integers.
For example, we know that 0 is divisible by 3, because we can write 0 = 3(0)
---------------ONTO THE QUESTION----------------
There are two values of A that satisfy BOTH statements:
Case a: A = 5. Notice that A - 2 = 5 - 2 = 3, and 3 is divisible by 3. In this case, the answer to the target question is A = 5
Case b: A = 2. Notice that A - 2 = 2 - 2 = 0, and 0 is divisible by 3. In this case, the answer to the target question is A = 2
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent