If x is negative…
We are given that x is negative, and we must determine whether x < -3.
Statement One Alone:
x^2 > 9
Taking the square root of both sides of the inequality in statement one we have:
√x^2 > √9
|x| > 3
x > 3 OR -x > 3
x > 3 OR x < -3
Since we are given that x is negative, we see that x must be less than -3. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:
x^3 < -9
Using the information in statement two we see that x can be less than -3 or not be less than -3.
For example, if x = -4, (-4)^3 = -64, (which fulfills the statement) and -4 is less than -3.
However, if x = -3, (-3)^3 = -27, (which fulfills the statement) but -3 is not less than -3.
Statement two alone is not sufficient to answer the question.