BrentGMATPrepNow wrote:
If A and B are integers, is B even?
(1) 14A – 11B = 7N
(2) 14A – 11B = 2N
Given: A and B are integers Target question: Is B even? Statement 1: 14A – 11B = 7N There are several values of A, B and N that satisfy statement 1. Here are two:
Case a: A = 0, B = 0 and N = 0. In this case, the answer to the target question is
YES, B is evenCase b: A = 0, B = 7 and N = -11. In this case, the answer to the target question is
NO, B is not evenSince we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 14A – 11B = 2NThere are several values of A, B and N that satisfy statement 1. Here are two:
Case a: A = 0, B = 0 and N = 0. In this case, the answer to the target question is
YES, B is evenCase b: A = 1, B = 1 and N = 1.5. In this case, the answer to the target question is
NO, B is not evenSince we can’t answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that 14A – 11B = 7N
Statement 2 tells us that 14A – 11B = 2N
Subtract the bottom equation from the top equation to get: 0 = 5N, which means
N = 0Now plug N = 0 into the top equation to get:
14A – 11B = 7(0)Simplify:
14A – 11B = 0Since 14 is even, we know that
14A must be EVEN.
Also
0 is EVEN.
So our equation becomes:
EVEN – 11B = EVENFrom this we can conclude that 11B must be EVEN, which means
B must be EVENSince we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent