Inequalities- Manhattan guide problem

This topic has expert replies
Junior | Next Rank: 30 Posts
Posts: 10
Joined: Wed Sep 25, 2013 9:38 am
is x^3> x^2?
{A} x>0
{B} x^2>x

If x is positive then x^3> x^2, so A is sufficient right? but ans says C.

why should we factor it?

Please explain!
Regards
Premalatha

User avatar
GMAT Instructor
Posts: 905
Joined: Sun Sep 12, 2010 1:38 am
Thanked: 378 times
Followed by:123 members
GMAT Score:760

by Geva@EconomistGMAT » Wed Oct 16, 2013 12:56 pm
Hint: X>0 allows fraction values. Try plugging in x=1/2 - is x^3 still > x^2 then?

0<x<1 fraction values behave in exactly the opposite manner from x>1 values - the higher the power, the SMALLER the fraction.
Geva
Senior Instructor
Master GMAT
1-888-780-GMAT
https://www.mastergmat.com

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Wed Oct 16, 2013 7:24 pm
Is x^3 > x^2 ?

(1) x > 0
(2) x^2 > x
Since x³ > x² only if x≠0, we can rephrase the question stem by dividing by x², which must be a POSITIVE value:
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: x² > 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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3