Is x negative? : GMAT Data Sufficiency (DS)

Is x negative?

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Is x negative? [#permalink]

17 Feb 2013, 12:16

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Question Stats:

53% (02:41) correct

46% (01:06) wrong

based on 32 sessions

Is x negative?

(1) At least one of x and x^2 is greater than x^3.
(2) At least one of x^2 and x^3 is greater than x.

[Reveal] Spoiler: OA

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Re: Is x negative? At least one of x and x^2 is greater x^3 [#permalink]

17 Feb 2013, 14:50

If x > 1, then it is always true that x < x^2 < x^3.

If 0 < x < 1, then it is always true that x^3 < x^2 < x.

From the above, you can see that neither statement is sufficient alone, since in each case, x can be positive. Notice from the above that if x is positive, x^2 is never the largest of the three expressions x, x^2 and x^3. Since Statement 1 guarantees that x^3 is not the largest of the three expressions, and Statement 2 guarantees that x is not the largest of the three expressions, then using both statements, the only possibility is that x^2 is the largest of the three expressions. Since that can't happen when x is positive, x must be negative, and the answer is C.
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Re: Is x negative? At least one of x and x^2 is greater x^3 [#permalink] 17 Feb 2013, 14:50

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Is x negative?

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