OG 154 - inequalities

[crackitpal]

154. Is x negative?

(1) x^3(1-x^2)<0

(2) x^2-1<0

OA is C

I did not understand how can you get the range of x from these equations and then say equation 1 and 2 together are sufficient. Could someone please explain ?

Thanks

[samirpandeyit62]

Is x negative?

(1) x^3(1-x^2)<0

here if x is + ve then x^3 will be +ve & if X^2 > 1 the expr is -ve so

x can be +ve

if x is -ve & x^2 is less than 1 then also the expr is satisfied

INSUFF

(2) x^2-1<0

here also x can be both -ve & +ve i.e -ve when x^2 < 1 & +ve otherwise also x can be 0 (no sign)

INSUFF

combine: x^3(1-x^2)<0 & x^2-1<0 or 1-x^2 > 0

so if 1 - x^2 > 0 i.e it is +ve so x must be -ve to make x^3 -ve

hence x must be -ve C

[crackitpal]

thank you Samir !! 1-x^2>0 was the key !! I really appreciate your skills to explain in very few words. I got it now.