Numbers DS

[shankar.ashwin]

Is x between -1 and 1 ?

(1) x^3 is less than x.
(2) x^3 is less than x^2.

[sl750]

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

[GMATGuruNY]

Is x between -1 and 1 ?

(1) x^3 is less than x.
(2) x^3 is less than x^2.

Plug in values between -1 and 1 and outside this range.
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.