Hi BlueDragon2010,
This is an example of a Roman Numeral question. Usually, the easiest way to find the correct answer is to prove the OPPOSITE of what is asked, if possible. You might end up using a Number Property to verify that a given statement is true though. This question asks for what MUST BE TRUE? Think about how you can prove that each statement is NOT always true, then you can eliminate it from the answer choices.
Here, we're told that the sum of N consecutive integers = 0.
Roman Numeral III shows up the most often, so we'll start there....
III. The average of the integers is 0
For consecutive integers to sum to 0, the numbers need to "balance" around 0.
eg.
0
-1, 0, 1
-2, -1, 0, 1, 2
-3, -2, -1, 0, 1, 2, 3
Etc.
The average of any of these groups will be 0 because the SUM will be 0 (and the average of any group = SUM/Terms).
Roman Numeral III is ALWAYS TRUE. Eliminate A and B.
Based on our examples (above), you can see that the N terms could be include 1 term, 3 terms, 5 terms, 7 terms, etc. This means that N MUST be Odd. With the remaining 2 Roman Numerals, you can see that:
Roman Numeral I is NOT TRUE
Roman Numeral II IS ALWAYS TRUE
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
