Problem Solving

This question is from GMAT prep 1 exam:

If x> y^2 > z^4 which of the following statements could be true?

I. x>y>z
II. z>y>x
III. x>z>y

I only
I and II only
I and III only
II and III only
I, II and III

Please provide your answer explanations. OA to follow after couple of threads. Thanks.

I would go with I and II and III

I could be true

5 > 2 ^ 2 > 1 ^ 4 (x= 5, y=2,z=1 i.e x>y>z)

II could be true

1/5 > 1/4 ^ 2 > 1/2 ^ 4 (x=1/5,y=1/4,z=1/2 i.e z>y>x)

III could be true

100 > (-4) ^ 2 > (-3) ^ 4 (x=100,y=-4,z=-3 so x>z>y)

Hmm,

I think that you are overlooking the fact that the exponents are not a part of the 3 choices.

Therefore, it is down to picking numbers:

I. x>y>z if x=5, y=2, z=1, then both equations can be satisfied, yes
II. z>y>x if x=-1/4, y=-1/2, z cannot be greater than y, no
III. x>z>y if x=1/2, y=1/4, z=1/3, yes

C?

I would tend to differ on that just beacuse of the fact that it says could be true and not must be true. Then we would try to work on disproving the choices if possible to confirm that it is true for all cases.

I guess the OA will clarify this!

All 3 could be true.

This is a could be true question and not Must be true

the OA is E - all 3 are correct.

I chose option C (only 1 and 3 correct) but i think i overlooked the words "could be".

Thanks everyone for your inputs.