BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Inequalities

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 am
Location: India
Thanked: 64 times
Followed by:6 members
GMAT Score:760

by harsh.champ » Fri Feb 05, 2010 10:17 am
zudecj wrote:Is x^3 >x^2?

(1) x>0
(2)x^2>x
_______________
x^3 > x^2
=> (x^2)(x-1)>0
Now,square of a number is always greater than 0.Hence,x>1.

Statement 1 : x>0 insufficient
Statement 2 : x^2>x
=>x(x-1)>0 ,So x>1 or x<0.
Hence,alone insufficient.

Combining both the statements,we can arrive at the answer.
Top
Newbie | Next Rank: 10 Posts
Posts: 5
Joined: Fri Feb 05, 2010 10:07 am

by zudecj » Fri Feb 05, 2010 10:32 am
=>x(x-1)>0 ,So x>1 or x<0.
Here is were i got confused -
Isnt x(x-1)>0 => x>0 or x-1>0?
leading to x>0 or x>1 ?
Top
User avatar
Legendary Member
Posts: 1560
Joined: Tue Nov 17, 2009 2:38 am
Thanked: 137 times
Followed by:5 members

by thephoenix » Fri Feb 05, 2010 10:47 am
zudecj wrote:Is x^3 >x^2?

(1) x>0
(2)x^2>x
try by plugging no.

s1)x>0
let x=.5 , 1 ,2

fpr 0.5
x^3<x^2
for 1
x^3=x^2
for x=2
x^3>x^2
insuff

s2)x^2>x
letx=-1,2

for -1
x^3<x^2
for 2
x^3>X^2

insuff

comb
x>0 and X^2>x--->x>1
for all x>1 value
x^3>x^2

suff
Top
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

by sanju09 » Sat Feb 06, 2010 3:27 am
zudecj wrote:Is x^3 >x^2?

(1) x>0
(2)x^2>x
(1) If x is positive, x^3 may or may not be greater than x^2. See

If x = 3, x^3 = 27, x^2 = 9, and x^3 > x^2.

But, if x = 1/3, x^3 = 1/27, x^2 = 1/9, and x^3 < x^2.

Insufficient

(2) If the square of a number is greater than the number, then the number could be either negative or more than 1. If x is negative, x^3 is always less than x^2. And, if x is more than 1, then x^3 is always greater than x^2.

Insufficient

Blend (1) and (2)

If x is positive and the square of x is greater than x, then x is definitely more than 1 and x^3 is always greater than x^2.

Sufficient

[spoiler]C[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Post new topic Post Reply
• Page 1 of 1