abhi758 wrote:
Is x negative?
(1) x^3(1-x^2) < 0
(2) x^2-1 < 0
Hi all,
(1) x^3(1-x^2) < 0
let x=10....==>therefore 10^3(1-100)=-99*10^3<0
satisfying for positive X
now let x= -0.1===> therefore (-0.1)^3(1-0.01)= -0.99*0.1^3<0
satisfying when X is negative...
so X can be positive and negative both so not definite answer.
(2) x^2-1 < 0
this holds for -1<x<1
again not sufficient
now combining
from statement 2 we got 2 things:
==> x^2-1<0....therefore 1-x^2>0-----(1)
==>range of x...-1<x<1-----(2)
now coming to statement 1...
we know 1-x^2>0.....from (1)
therefore for
x^3(1-x^2) < 0....to hold true...x^3 <0....since we know 1-x^2 is positive from (1)
now we have x^3<0....therfeore x<0----(3)
now using (2) and (3)
x belongs to-1<x<0
menas x is negative.hence sufficient
therefore (C)
hope it helps.
SKM
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