Hi j_shreyans,
This DS question can be solved in a couple of different ways. For example, you can TEST VALUES or use Number Properties. Since this question is based so heavily on Number Properties, I'm going to focus on that approach:
We're asked if N is negative. This is a YES/NO question.
Here are some Number Properties worth knowing for this question (you can prove all of these rules by TESTing VALUES):
If X > 1, then X < X^2 < X^3
If X < -1, then X^3 < X < X^2
IF X = -1, 0 OR 1, then X = X^2 = X^3
If 0< X< 1, then X^3 < X^2 < X
If -1 < X < 0, then X < X^3 < X^2
Fact 1: X or X^2 (or both) are greater than X^3.
Using the above Number Properties:
We COULD have X < - 1, and the answer to the question would be YES.
We COULD have 0 < X < 1 and the answer to the question would be NO.
We COUDL have -1 < X < 0 and the answer to the question would be YES.
Fact 1 is INSUFFICIENT
Fact 2: X^2 or X^3 (or both) are greater than X.
Again, using the above Number Properties:
We COULD have X < - 1, and the answer to the question would be YES.
We COULD have 1 < X and the answer to the question would be NO.
We COULD have -1 < X < 0 and the answer to the question would be YES.
Fact 2 is INSUFFICIENT
Combined, we have some "overlap":
We COULD have X < - 1, and the answer to the question would be YES.
We COULD have -1 < X < 0 and the answer to the question would be YES.
Combined, the answer is ALWAYS YES. Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
