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shankar.ashwin
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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
