Hi vivekvijayan,
This question can be solved with a combination of TESTing Values and Number Properties:
We're told that neither A nor B can equal 0. We're also told that (X+A)(X+B) = 0. We're asked if X = A. This is a YES/NO question.
Before going to the 2 Facts, let's talk about the Number Properties in this prompt:
1) A and B cannot be 0 (so they're either positive or negative values)
2) (X+A)(X+B) = 0, so at least one of the parentheses MUST = 0. Either (X+A) OR (X+B) or BOTH = 0.
Fact 1: X-B = 0
This means that X = B.
Since B cannot = 0, X cannot = 0.
Thus, (X+B) CANNOT = 0
Using the initial Number Properties, we now know that (X+A) MUST = 0.
If X = 1, A = -1, then the answer to the question is NO.
If X = -2, A = 2, then the answer to the question is NO.
If X = 5.5, A = -5.5, then the answer to the question is NO.
X and A have to be "opposites", so they will never equal one another and the answer to the question is ALWAYS NO.
Fact 1 is SUFFICIENT
Fact 2: A = -B
If A = -1, B = 1
We would then have (X - 1)(X + 1) = 0, which has two salutations (1 and -1)
If X = 1, then X does NOT equal A and the answer to the question is NO.
If X = -1, then X DOES equal A and the answer to the question is YES.
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
