SOLUTION: Which of the following can be the average (arithmetic mean) of four consecutive positive even integers? A) 2 B) 3 C) 4 D) 5 E) 6

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Question 547715: Which of the following can be the average (arithmetic mean) of four consecutive positive even integers?
A) 2
B) 3
C) 4
D) 5
E) 6
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = the first integer
Then the 4 consecutive positive integers are: n, n+2, n+4, n+6
Average = a = (n + n+2 + n+4 + n+6)/4
Collect terms:
4a = 4n + 12
a = n + 3 -> a - n = 3
Since n is even, the average, a, must be odd
The two possible choices are B) and D)
If a = 3, that means n = 0. But since 0 is not a positive integer, the answer is D).