I'm new here, but what I believe you're missing is that because both the absolute value of X, and the square of X are positive, X could be either positive or negative. Therefore, only choice I can always be true.

Hope that helps!

clock60 wrote:hi guys the problem looks like rather trivial [spoiler]but i picked E but oa is A i can`t get why third in not true[/spoiler] can somebody share some ideas?
If |x|<x^2 , which of the following must be true?
I. x^2>1
II. x>0
III. x<-1

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only

clock60, we have got the absolute value of x i.e. |x| which is less than x^2. This is possible only if we multiply the value on itself and the product (x*x=x^2) becomes less than the value itself. Remember FDPs, if we have value less than 1 all products of this value will be less than one of the values in multiplication operation. e.g. 0.1*0.1 = 0.01, 0.2*0.2 = 0.04.

So, pick I or (A) for x^2>1 because then x must be at least greater than 1, x>1.

Hi

In my point of view the answer is E. not only I is correct as night reader said but also III is correct. just put any number less than -1 thr, it come out positive (absolute number which always less than X power 2.

hope it helps

-2 will work. However +2 will work also. X could be negative or positive, therefore X<-1 must NOT always be true.

got it
thanks to all

the answer is A

lets take a number 0.3 in this case the square is less than the number itself hence square has to be greater than one