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.