AbeNeedsAnswers wrote:If x is negative, is x < -3?

(1) x^2 > 9
(2) x^3 < -9

A

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.

Statement Two Alone:

x^3 < -9

Using the information in statement two, we see that x can be less than -3 or not 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.

Answer: A