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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