Thanks everyone for your responses.

I figured out my mistake in the few questions I got wrong - in every case it boiled down to one simple problem - failure to consider all scenarios.

eg. If X > Y^2 > Z^4, which of the following can possibly be true?

I. X > Y > Z

II. Z > Y > X

III. X > Z > Y

The correct answer was all three. I could not figure out how II could be true because I did not consider fractions between 0 to 1 for values of Y.

All other questions I missed were of similar nature - failed to consider real numbers or fractions in the solution set. Guess, my math is a bit rusty after all.