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Is x^3 > x^2 ?

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Source: — Data Sufficiency |

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by Anurag@Gurome » Wed Dec 12, 2012 10:56 pm
vinni.k wrote:Is x^3 > x^2 ?

(1) x > 0
(2) x^2 > x

Answer is C

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Vinni
(1) x > 0
If x = 2, then x^3 = 8, x^2 = 4. Here x^3 > x^2.
If x = 1/2, then x^3 = 1/8 = 0.125 and x^2 = 1/4 = 0.25. Here x^3 < x^2.
No definite answer; NOT sufficient.

(2) x² > x
If x = 2, then x² = 4 and x^3 = 8. Here x^3 > x^2.
If x = -2, then x² = 4 and x^3 = -8. Here x^3 < x^2.
No definite answer; NOT sufficient.

Combining (1) and (2), x² > x > 0, which clearly implies that x^3 > x²; SUFFICIENT.

The correct answer is C.
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by puneetkhurana2000 » Wed Dec 12, 2012 10:58 pm
Trying some numbers will help.

Statement 1) x > 0

X X^2 X^3
1 1 1 No
2 4 8 Yes
1/2 1/4 1/8 No

Not Sufficient!!!

Statement 2) x^2 > x

X X^2 X^3
2 4 8 Yes
-2 4 -8 No

Not Sufficient!!!

Together with x > 0 and x^2 > x ,means x > 1

Sufficient!!!

Answer C
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by GMATGuruNY » Thu Dec 13, 2012 7:54 am
vinni.k wrote:Is x^3 > x^2 ?

(1) x > 0
(2) x^2 > x

Answer is C

Thanks & Regards
Vinni
Since both statements imply that x≠0, we can rephrase the question stem by dividing by x²:
x³/x² > x²/x²
x > 1.
Question rephrased: Is x>1?

Statement 1: x>0
Since it's possible that x=1/2 or that x=2, INSUFFICIENT.

Statement 2: x^2 > x
Since it's possible that x = ±2, INSUFFICIENT.

Statements combined:
No positive value less than or equal to 1 will satisfy both statements.
Thus, x>1.
SUFFICIENT.

The correct answer is C.
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