Is x between -1 and 1 ?
(1) x^3 is less than x.
(2) x^3 is less than x^2.
Numbers DS
This topic has expert replies
-
- Legendary Member
- Posts: 966
- Joined: Sat Jan 02, 2010 8:06 am
- Thanked: 230 times
- Followed by:21 members
- sl750
- Master | Next Rank: 500 Posts
- Posts: 496
- Joined: Tue Jun 07, 2011 5:34 am
- Thanked: 38 times
- Followed by:1 members
Statement 1
x(x^2-1) < 0
Case 1
x>0 and x^2-1<0; x>0 and -1<x<1 ; 0<x<1
Case 2
x<0 and x^2-1>0; x<0 and x>1 or x<-1; x<-1
We have 2 solutions. Insufficient
Statement 2
x^3-x^2<0
x*x(x-1)<0
Case 1
x>0 and x(x-1)<0; x>0 and x<0 and x>1. Not valid
x>0 and x(x-1)<0; x>0 and x>0 and x<1 . 0<x<1
Case 2
x<0 and x(x-1)>0; x<0 and x>0 and x>1. Not valid
x<0 and x(x-1)>0; x<0 and x<0 and x<1. x<0
We have two solutions . Insufficient
Statement 1 and 2
From 1, we have 0<x<1 or x<-1
From 2, we have 0<x<1 or x<0.
Only 0<x<1 is common to both and this lies between -1<x<1. Sufficient
For this problem, I think using numbers would be easier, especially when dealing with statement 2
x(x^2-1) < 0
Case 1
x>0 and x^2-1<0; x>0 and -1<x<1 ; 0<x<1
Case 2
x<0 and x^2-1>0; x<0 and x>1 or x<-1; x<-1
We have 2 solutions. Insufficient
Statement 2
x^3-x^2<0
x*x(x-1)<0
Case 1
x>0 and x(x-1)<0; x>0 and x<0 and x>1. Not valid
x>0 and x(x-1)<0; x>0 and x>0 and x<1 . 0<x<1
Case 2
x<0 and x(x-1)>0; x<0 and x>0 and x>1. Not valid
x<0 and x(x-1)>0; x<0 and x<0 and x<1. x<0
We have two solutions . Insufficient
Statement 1 and 2
From 1, we have 0<x<1 or x<-1
From 2, we have 0<x<1 or x<0.
Only 0<x<1 is common to both and this lies between -1<x<1. Sufficient
For this problem, I think using numbers would be easier, especially when dealing with statement 2
- GMATGuruNY
- 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
Plug in values between -1 and 1 and outside this range.shankar.ashwin wrote:Is x between -1 and 1 ?
(1) x^3 is less than x.
(2) x^3 is less than x^2.
x = 1/2 and x = -2 satisfy both statements.
Since x = 1/2 is between -1 and 1 and x=-2 is not between -1 and 1, both statements combined are INSUFFICIENT.
The correct answer is E.
Algebra would probably take longer.
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
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