Hi prachi18oct,

This question can be solved by TESTing VALUES and/or Number Properties.

We're told that A, B and C are NEGATIVE INTEGERS. We're asked if A^B - C^B < 0. This is a YES/NO question.

Fact 1: B is EVEN

IF....
A = -2
C = -1
B = -2
(-2)^(-2) - (-1)^(-2) = -3/4 so the answer to the question is YES

IF....
A = -1
C = -2
B = -2
(-1)^(-2) - (-2)^(-2) = +3/4 so the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: A < C

IF....
A = -2
C = -1
B = -2
(-2)^(-2) - (-1)^(-2) = -3/4 so the answer to the question is YES

IF....
A = -2
C = -1
B = -1
(-2)^(-1) - (-1)^(-1) = +1/2 so the answer to the question is NO

Combined, we know...
B is EVEN
A < C

Since B is EVEN, A^B and C^B will both be POSITIVE. Since A < C, A is "more negative" than C and will produce a SMALLER positive fraction when raised to the "B power." Thus, we'll end up with....

positive fraction - larger positive fraction....the result will ALWAYS be NEGATIVE and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich