GMAT Prep Integers

[moneyman]

Your thoughts on this one pls

[alescau]

in problems like this you need to consider numbers that differ in behavior.
if x>1, x^2>x, 1/x<1
if x<1, x^2<x, 1/x>1

so, if x>1, 1/x<1. the other ones >1. we do not have an answer choice that has 1/x as the lowest number.

if x<1, x^2 is the lowest. possible choices are I and II.

just consider 2x < 1/x
reorder x^2<1/2
x<1/Sqrt[2]

so, I is satisfied when x<1/Sqrt[2], otherwise II is satisfied.
Answer should be D. I and II only.

[tendays2go]

IMO: A [None]

as for when x>1, say x =4 =>
x^2 = 16
2*x= 8
1/x = 0.25
clearly, 1/x < 2*x < x^2

as for when x<1, say x =1/4 =>
x^2 = 1/16
2*x= 1/2
1/x = 4

clearly, x^2 < 2*x < 1/x

and lastly when x =1 => 1/x = 2*x = x^2

since all these cases are not satisfied in any of the choices, answer should be (A)