Practice GMAT Data Sufficiency Question
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Is xx^{3} < (x)^{x}?
 x^{2} + 4x + 4 = 0
 x < 0
Correct Answer: D

Evaluate Statement (1) alone.
 The equation in Statement (1) can be factored.
x^{2} + 4x + 4 = 0
(x + 2)(x + 2) = 0
Consequently, x = 2.  With one specific value of x, the inequality can be definitively evaluated:
Is 2(2)^{3} < (2)^{2}?  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.
 The equation in Statement (1) can be factored.

Evaluate Statement (2) alone.
 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)?  Statement (2) enables the question to be definitively answered. Statement (2) is SUFFICIENT.
 With the information in Statement (2), plug in the sign of x:
 Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT, answer D is correct.
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