OG 11th edition Q 154- Have I oversimplified the problem?

Nidhs wrote:In the following question, can someone please tell me if my reasoning is correct or if i have oversimplified the problem;

Is x negative?
(1) x^3(1-x^2)<0
(2) x^2-1<0

My answer is also c, as given the book...but my reasoning to it is the following;
acc to me st1 says- x^3<0 or (1-x^2)<0,
either x^3<0 could be true or (1-x^2)<0 could be true but not both as the value needs to be negative. As we don't know which one is true INSUFFICIENT

St2 x^2-1<0 but we don't know if x is positive or negative; so INSUFFICIENT

Combining 1 and 2 says that (1-x^2)is not less than 0. Hence, x^3<0 must be correct.

Do I have the right approach for solving this?

Nidhs wrote:In the following question, can someone please tell me if my reasoning is correct or if i have oversimplified the problem;

Is x negative?
(1) x^3(1-x^2)<0
(2) x^2-1<0

from one

the expression can be -ve if:

a) x is -ve given that /x/< 1 or
b) x +ve and /x/>1...........insuff

from 2

x^2 < 1 x can be +ve or -ve fraction. or 0........insuff

both

x is not 0 , /x/<1 and thus option (a) from one is valid...C