tricky inequality

[DominicanKing]

If x is positive which of the following could be the correct ordering of 1/x, 2x and x^2
I. x^2 < 2x < 1/x
II. x^2 < 1/x < 2x
III. 2x < x^2 < 1/x

a none
b I only
c III only
d I & II only
e I II and III

[aroon7]

If x is positive which of the following could be the correct ordering of 1/x, 2x and x^2
I. x^2 < 2x < 1/x
II. x^2 < 1/x < 2x
III. 2x < x^2 < 1/x

a none
b I only
c III only
d I & II only
e I II and III

i get B but not confident...
when x is 1/2 I is true
i cant find values which could satisfy other two options

[DominicanKing]

I got B as well, but its not the correct answer according to the GMATPrep software...maybe the we're right and they're wrong

[awesomeusername]

I get B too. But I've been surprised many times...

edit, when x = .99, #2 is true...

[nitinrai]

Here is the solution from Ian (I know its difficult)

https://www.beatthegmat.com/number-prope ... 13538.html

[gaggleofgirls]

You can also solve this by graphing it with the equations:

y = 1/x
y = 2/x
and
y = x^2

When you do (and I will try to come back later and post a picture of the graph, but I have to run now), you will see that there are 4 places where any 2 of the three lines cross, so there are 4 different configurations of which equation is >< the other ones (and the crossing points themselves, where you can see when two of the equations are equal.

Of the 4 possibilities (that don't have = in them) only two of them are in the list, I and II.

-Carrie