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

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Manager
Joined: 28 Mar 2009
Posts: 74

Kudos [?]: 368 [0], given: 0

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

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05 Jun 2009, 20:18
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Is x^3 > x^2?

(1) x > 0

(2) x^2 > x

Kudos [?]: 368 [0], given: 0

Director
Joined: 03 Jun 2009
Posts: 782

Kudos [?]: 902 [0], given: 56

Location: New Delhi
WE 1: 5.5 yrs in IT

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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
_________________

Kudos [?]: 902 [0], given: 56

Re: inequalities (I)   [#permalink] 05 Jun 2009, 23:14
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