The solution is not correct- The answer should be c

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 429
Joined: Wed Sep 19, 2012 11:38 pm
Thanked: 6 times
Followed by:4 members

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 » Mon Jul 29, 2013 8:28 am
is x between 0 and 1?
1) x² is less than x
2) x³ is positive
Statement 1: x² < x
Consider the following options for x:
-2, -1, -1/2, 0, 1/2, 1, 2.
Only the value in red satisfies the constraint that x²<x:
(1/2)² < 1/2
1/4 < 1/2.
The implication is that x must be a POSITIVE FRACTION BETWEEN 0 AND 1.
SUFFICIENT.

Statement 2: x³ > 0
Consider the following options for x:
-2, -1, -1/2, 0, 1/2, 1, 2.
Any of the values in red will satisfy the constraint that x³>0.
If x = 1/2, then x is between 0 and 1.
If x = 1, then x is NOT between 0 and 1.
INSUFFICIENT.

The correct answer is A.
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

Master | Next Rank: 500 Posts
Posts: 429
Joined: Wed Sep 19, 2012 11:38 pm
Thanked: 6 times
Followed by:4 members

by [email protected] » Mon Jul 29, 2013 6:15 pm
GMATGuruNY wrote:
is x between 0 and 1?
1) x² is less than x
2) x³ is positive
Statement 1: x² < x
Consider the following options for x:
-2, -1, -1/2, 0, 1/2, 1, 2.
Only the value in red satisfies the constraint that x²<x:
(1/2)² < 1/2
1/4 < 1/2.
The implication is that x must be a POSITIVE FRACTION BETWEEN 0 AND 1.
SUFFICIENT.

Statement 2: x³ > 0
Consider the following options for x:
-2, -1, -1/2, 0, 1/2, 1, 2.
Any of the values in red will satisfy the constraint that x³>0.
If x = 1/2, then x is between 0 and 1.
If x = 1, then x is NOT between 0 and 1.
INSUFFICIENT.

The correct answer is A.
But Mitch they are asking if x is between 0 and 1, nowhere is it mentioned that x is between 0 and -1

GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Tue Jul 30, 2013 8:35 am
Here's some algebraic justification:

On the GMAT, x² ≥ 0, no matter what.

If x > x², then we really have the equation x > x² ≥ 0

0 isn't a valid solution to x > x², so x is positive, and our equation is x > x² > 0.

Dividing the entire equation by x, we get 1 > x > 0 -- since x is positive, division by x doesn't change the signs -- and the first statement is sufficient.