dassabyasachi14 wrote: But why do we need statement 1) to prove X is an integer? Since statement 2) says that x^3 is an odd no...which makes it evident that x is integer because only integers are classified as even or odd.

Your conclusion is not quite true.
Notice that if x = ∛7, then x³ = 7.
Here, x³ is ODD, but we cannot say that x is odd.

Cheers,
Brent

Hi dassabyasachi14,

When dealing with DS questions, you have to be careful about what you KNOW and what you DON'T KNOW.

In this prompt, we're asked if X is odd. That is a YES/NO question, but we were told NOTHING about X. Maybe it's positive or negative (or 0), maybe it's an integer or maybe it's not. We're responsible to consider all of the possibilities.

1) 2X-1 = odd

This Fact tells us that 2X-1 could equal any odd number, including -3, -1, 1, 3, 5, etc.

IF....
2X-1 = 1, then X=1 and the answer to the question is YES.
2X-1 = 3, then X=2 and the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) X^3 = odd

This Fact tells us that X^3 could equal any odd number, including -3, -1, 1, 3, 5, etc.

IF....
X^3 = 1, then X=1 and the answer to the question is YES.
X^3 = 3, then X= (cube-root of 3) and the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we know...
X will have to be an integer (from Fact 1). Since X^3 is odd AND we're now limited to integers only, then X must NOW be an odd integer. Thus, the answer to the question is ALWAYS YES.
Combined, SUFFICIENT.

Final Answer: C

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