# Practice GMAT Data Sufficiency Question

Is x|x|3 < (|x|)x?
1. x2 + 4x + 4 = 0
2. x < 0
 A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
1. Evaluate Statement (1) alone.
1. The equation in Statement (1) can be factored.
x2 + 4x + 4 = 0
(x + 2)(x + 2) = 0
Consequently, x = -2.
2. With one specific value of x, the inequality can be definitively evaluated:
Is -2|(-2)|3 < (|-2|)-2?
3. Since this will give a definitive answer, the data are sufficient. (Note: Although the answer to the question here is yes, it does not need to be yes in order for sufficiency to exist. In other words, if the answer to our question were always no, that would be sufficient.) Statement (1) is SUFFICIENT.
2. Evaluate Statement (2) alone.
1. With the information in Statement (2), plug in the sign of x:
is (negative)(|negative|)3 < (|negative|)negative?
Simplified:
Is (negative)(positive)3 < (positive)(negative)?
Since a positive number raised to an odd exponent is always positive and (negative)(positive) = negative, we can simplify further:
Is (negative) < (positive)(negative)?
Since a positive number raised to a negative number is simply a smaller positive number, we can simplify further:
Is (negative) < (positive)?
2. Statement (2) enables the question to be definitively answered. Statement (2) is SUFFICIENT.
3. Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT, answer D is correct.