If n is positive and less than 1...

Hi LUANDATO,

When dealing with Roman Numeral questions, you can work through the 3 Roman Numerals in any order (and eliminate answers according to your results). For this question though, I'll work through all 3 options in order:

We're told that N is POSITIVE and LESS than 1. This means that 0 < N < 1. We're asked which of the Roman Numerals is true (meaning which is ALWAYS true no matter how many different examples we can come up with). This question can be solved with a mix of logic and TESTing VALUES.

I. N^2 - N < 0

Since N is a POSITIVE FRACTION - and squaring a positive fraction will always lead to a SMALLER fraction - we know that N^2 will always be less than N.
For example, (1/2)^2 = 1/4.
Thus N^2 - N will ALWAYS be less than 0.
Roman Numeral 1 IS always true.

II. N^3 < N

The same logic we used in Roman Numeral 1 applies to Roman Numeral 2. Cubing a positive fraction will ALWAYS lead to a SMALLER fraction, so N^3 will always be less than N.
For example, (1/2)^3 = 1/8
Roman Numeral 2 IS always true.

III. N+1 < 1

We're told that N is POSITIVE, so N+1 will be greater than 1.
Roman Numeral 3 is NOT true.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich