Hi Abhijit K,

This DS question is loaded with Number Property rules and you have to be thorough with your thinking to get the correct answer.

First, since s�v³x� < 0 we have to think about what S, V and X COULD be....

Since the product is less than 0, NONE of those variables can equal 0.

s� will always be positive, but S COULD be positive or negative

v³ will be positive IF V is positive.
v³ will be negative IF V is negative

x� will be positive IF X is positive
x� will be negative IF X is negative

So, knowing that s�v³x� < 0, that means....

We don't know whether S is positive or negative
Between V and X, one is positive and one is negative.

(+)(+)(-) = less than 0
(+)(-)(+) = less than 0

Knowing all of this, we can now work on the question itself: Is (S)(V)(X) < 0? This is a YES/NO question.

Fact 1: V < 0

Knowing that V is negative, we also know that X is positive. HOWEVER, we don't know whether S is positive OR negative...

IF....S is positive, we have (+)(-)(+) = negative and the answer to the question is YES.
IF....S is negative, we have (-)(-)(+) = negative and the answer to the question is NO.
Fact 1 is INSUFFICENT

Fact 2: X > 0

Here, we have the same situation that we had in Fact 1. We know that X is positive, so we know that V is negative, but we don't know about S. The same two examples in Fact 1 fit here as well.
Fact 2 is SUFFICIENT.

Combined, we know...
V < 0
X > 0
And all of the deductions that we made form the prompt itself.

We end up with the same 2 examples that we had before - one YES and one NO answer.
Combined, INSUFFICIENT.

Final Answer: E

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

The above solutions are great, so I won't delve into in the solution.
I just want to note that, at the heart of this question lie the following (important) properties:

Two important rules:

ODD exponents preserve the sign of the base.
So, (NEGATIVE)^(ODD integer) = NEGATIVE
and (POSITIVE)^(ODD integer) = POSITIVE

An EVEN exponent always yields a positive result (unless the base = 0)
So, (NEGATIVE)^(EVEN integer) = POSITIVE
and (POSITIVE)^(EVEN integer) = POSITIVE

Cheers,
Brent