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
OG 154 - inequalities
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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
(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
Regards
Samir
Samir
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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.