Hi alanforde800Maximus,
This question is based on several Number Properties, so you can get to the solution knowing those NPs, TESTing VALUES or a combination of the two.
From the given range, we know that X is a NEGATIVE FRACTION between -1 and 0. We're asked which of the following MUST be true.
I. X^3 < X^2
(negative)^3 = negative
(negative)^2 = positive
(negative) is always less than a (positive)
Roman Numeral I is ALWAYS TRUE
II. X^5 < 1 - X
(negative)^5 = negative
1 - (negative) = postiive
(negative) is always less than a (positive)
Roman Numeral II is ALWAYS TRUE
III. X^4 < X^2
Both X^4 and X^2 will be positive in these circumstances, so we have to think about what happens when you raise a negative fraction to those two exponents.
(-1/2)^4 = +1/16
(-1/2)^2 = +1/4
1/16 < 1/4
This relationship will hold true for any value from the given range.
Roman Numeral III is ALWAYS TRUE
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
