The average (arithmetic mean) of five consecutive integers is an odd n...
Since we are talking about consecutive integers, what is good for one set should be good for every set of consecutive integers. Let's take 1,2,3,4,5.
I. The largest of the integers is even. (Incorrect)
II. The sum of the integers is odd. (Correct)
III. The difference between the largest and smallest of the integers is an even number. (Correct)
Since II and III are correct, answer should be E.
This can be solved mathematically be considering a series of integers n-2, n-1, n, n+1, n+2
Since the average of an odd number of consecutive terms is the middle number, n must be odd.
I. The largest of the integers is even. (incorrect)
II. The sum of the integers is odd. (Sum of integers is 5n; odd integer * odd integer = odd integer, therefore correct)
III. The difference between the largest and smallest of the integers is an even number. (difference between largest and smallest number will be 4. therefore, correct)