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.
GMAT Prep Integers
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tendays2go
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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)
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)
