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Troika: Master | Next Rank: 500 Posts; Posts: 136; Joined: Wed Apr 08, 2009 12:09 pmFollowed by: 1 member; Thanked: 4 times

by Troika » Sat Oct 27, 2012 7:06 pm

Is x^3 > x^2?

1. X > 0

2. X^2 > X

OA : C

Source: MGMAT Equations, 4th ed., pg. 187

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Source: Beat The GMAT — Data Sufficiency | Sat Oct 27, 2012 7:06 pm

anuprajan5: Master | Next Rank: 500 Posts; Posts: 279; Joined: Mon Jun 25, 2012 10:56 pmFollowed by: 10 members; Thanked: 60 times

by anuprajan5 » Sat Oct 27, 2012 10:02 pm

Hi Troika,

The answer is C

Statement 1 - X>0

Since the question does not mention as to whether x is an integer, we could take fractions into the fray as well. We know that positive integers raised to a higher power will be greater than to the same integer raised to a lower power. But that does not hold for fractions. Examples:

2^3>2^2
But (1/2)^3<(1/2)^2

Insufficient

Statement 2 - x^2>x

This can hold for both negative and positive integers. But in the case of negative integers, this will not hold for the question.

2^2>2 and 2^3>2^2
(-2)^2>-2 but -2^3<-2^2

[spoiler]Combined, we know that the number is positive and that x^2>x^3. This holds true only for positive integers. Hence C[/spoiler]

Regards
Anup

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