Which is correct?

[colakumarfanta]

X range is -1 <X <1, Q Which of the following must be true?
Answers are:
X ^ 2> X ^ 3,
(X +1 / 2) (X-1 / 2) <0

[frank1]

X ^ 2> X ^ 3,

[saurabhmahajan]

Yeap it should be X ^ 2> X ^ 3

[colakumarfanta]

I guess X ^ 2> X ^ 3 is also not true when X = 0 . Please let me know if I am missing anything ?

[Rahul@gurome]

Solution.
Obviously x^2 > x^3 does not hold for x = 0.
Taking the second statement we have that (X +1 / 2) (X-1 / 2) <0
So we have that either (a) (X +1 / 2)>0 and (X-1 / 2)< 0
Or
(b) (X +1 / 2)<0 and (X-1 / 2)>0. This would mean x<-1/2 and x>1/2 which is not possible and so (b) is automatically rejected.
So we have that (X +1 / 2) (X-1 / 2) <0 implies -1/2<x<1/2 which is possible because given range of x is -1 <x<1.

The second statement is true.

[quantskillsgmat]

first statement doesnt hold always put x=0
for second statement x should be between -1/2 and 1/2.since range of x is between -1 and 1.so it is always true.
quantskillsgmat
wisdommart delhi