If X = 1/2

1/x = 2
2x = 1
x^2 = 1/4

So I works.

If

X = 4/5

1/x = 5/4 = 1.25
2x = 8/5 = 1.6
x^2 = 16/25

So II works.

If X > 1 doesn't work

X = 10
1/x = 1/10
2x = 20
X^2 = 100

X = 1

1,2,1

I would go with I and II only?

X is positive. That means you can multiply or divide everything by X, to make life easier.

I. divide by x. x < 2 < 1/(x^2)

Pick any small fraction. 1/4 < 2 < 1/(1/16)



II. Divide by x. x < 1/(x^2) < 2

This one is stickier, because we need to keep 1/(x^2) less than two and greater than 1, but 3/4 will do it here; 3/4 < 1/(9/16) < 2


III. Divide again here. 2< x < 1/(x^2)

Impossible. If x is greater than 2, then 1/x will be less than one, and increasing it by a power will make it yet smaller.


Answer is D, I and II only.