Hi kamalakarthi,
As Brent pointed out, you have to be very careful when a variable is in the denominator of a fraction - that variable COULD be positive OR negative and you're responsible to deal with both possibilities.
This DS question is perfect for TESTing VALUES:
We're told that X cannot = 0. We're asked if XY > 0. This is a YES/NO question.
The question itself is based on a series of Number Properties:
If X and Y are BOTH Negative, then the answer is YES.
If X and Y are BOTH Positive, then the answer is YES.
If either X or Y = 0, then the answer is NO.
If X and Y have DIFFERENT signs, then the answer is NO.
Fact 1: X > 0
If....
X = 1, Y = 2, then the answer to the question is YES.
X = 1, Y = -2, then the answer to the question is NO.
Fact 1 is INSUFFICIENT.
Fact 2: 1/X < Y
If....
X = 1, Y = 2, then the answer to the question is YES.
X = -1, Y = 2, then the answer to the question is NO.
Fact 2 is INSUFFICIENT
Combined, we know....
X is positive
1/X < Y
Since X is positive, 1/(positive) = positive AND we can now deduce that positive < Y.
X and Y MUST both be positive, so the answer to the question is ALWAYS YES.
Combined, SUFFICIENT.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
