Jeff Miller

GMAT OFFICIAL GUIDE DS – If x is negative…

If x is negative…

Solution:

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.

Answer: A

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