Data Sufficiency

greenwich wrote:Is x negative?

(1) x^3(1-x^2)<0
(2) x^2-1<0

Please provide explanation as well.

these are standard inequalities with factored expressions; you should know how to solve these routinely.
the process:
(1) make sure that you have zero on one side of the inequality (this is already done here)
(2) factor the other side
(3) find the zeroes (roots) of the other side
(4) test the regions of the number line between those roots, to see if they satisfy the inequality

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statement (1)
factor --> (x^3)(1-x)(1+x) < 0
roots are -1, 0, 1
test the number line:
<.................FALSE...........(-1)...........TRUE........(0)..........FALSE............(1)............TRUE.............>
there are both negative and non-negative numbers in this solution, so, insufficient.

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statement (2)

factor --> (x-1)(x+1) < 0
roots are -1, 1
test the number line:
<.................FALSE...........(-1).........TRUE............(1)............FALSE.............>
there are both negative and non-negative numbers in this solution, so, insufficient.

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together

look at both of the number lines above, and notice that the only values that are common to both of them are -1 < x < 0.
these are all negative.
sufficient.

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(c)

missrochelle wrote:this number line approach seems so tedious... i.e More than 2 minutes! Is it common on the GMAT these days?

it shouldn't be overly tedious -- it's actually the standard protocol for solving inequalities like this. if it seems tedious or long, that's probably because you haven't practiced it enough yet.
same as with any other algebraic process. the first time you solved a quadratic equation, complete with factoring and rearrangement of terms, you might have had the same thought -- but after solving hundreds of them, you would no longer find this to be the case. therefore, if the problem is just that you haven't solved very many of these, you may want to grab a high school algebra book and get cracking.

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incidentally, it's also the standard way of solving inequalities that contain fractional expressions, too. when you make that number line for a fractional inequality, you need to include two kinds of values as boundary points of the regions:
1) values that are zeros of the corresponding equation (this is the same as what's shown here)
2) values that make the denominators of the fractions equal to zero.

so, for instance, given the equation (x + 2)(x - 3)/(x + 5) < 0, you have to include -2, 3, and -5 on your number line, not just -2 and 3.