Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 19 Jun 2013, 19:31

# Is x^3 > x^2? (1) x > 0 (2) x^2 > x

Author Message
TAGS:
Manager
Joined: 28 Mar 2009
Posts: 84
Followers: 2

Kudos [?]: 6 [0], given: 0

Is x^3 > x^2? (1) x > 0 (2) x^2 > x [#permalink]  05 Jun 2009, 20:18
00:00

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
Is x^3 > x^2?

(1) x > 0

(2) x^2 > x
Director
Joined: 03 Jun 2009
Posts: 806
Location: New Delhi
WE 1: 5.5 yrs in IT
Followers: 48

Kudos [?]: 282 [0], given: 56

Re: inequalities (I) [#permalink]  05 Jun 2009, 23:14
skim wrote:
Is x^3 > x^2?

(1) x > 0

(2) x^2 > x

we need to prove if x^3>x^2
since x^2 will always be a +ve value, dividing x^2 from both sides of the inequality will not change the inequality
=> hence, we need to prove if x > 1

(1) x > 0. Insufficient, as it doesn't confirm if x>1

(2) x^2 > x Insufficient
x can be either +ve or -ve
Case I. when x is +ve
Dividing x from both sides of x^2>x, inequality sign remains unchanged
=> x > 1
Case II. when x is -ve
Dividing x from both sides of x^2>x, inequality sign would be inverted
=> x < 1

(3) Together. Sufficient
from 1st we know x is +ve
based on this from 2nd (Case I) we can conclude that x>1, which is what we wanted to check
_________________
Re: inequalities (I)   [#permalink] 05 Jun 2009, 23:14
Similar topics Replies Last post
Similar
Topics:
Is X>1? 1) x^3>x 2) x^2>x>0 9 19 Mar 2006, 16:39
Is X>3? 1) (x-3)(x-2)(x-1)>0 2) x>1 4 04 Jul 2007, 01:30
Is x>0? 1) x^2+x-2>0 2) x^3<x^2 (A) Statement 1 7 25 Jan 2008, 16:44
6 Is x^3 > x^2? 15 15 Mar 2011, 03:24
Is x^3 > x^2? (1) x > 0 (2) x^2 > x 5 06 May 2012, 19:29
Display posts from previous: Sort by