Posted by **Sarah** on Wednesday, August 15, 2012 at 7:26pm.

Which of the following CANNOT be the average ( arithmetic mean) of four positive even integers?

a) 1

b) 2

c) 6

d) 9

e) 17

( please explain or show work. It will help me understand it better! Thanks)

- Math -
**MathMate**, Wednesday, August 15, 2012 at 8:13pm
To give an example, 17 can be thought of as

(6+6+6+6)/4=6

or

(17+17+17+17)/4=17

Since they are not all even, we can adjust by adding 1 to a number, and subtracting 1 from the next, such as:

(18+16+18+16)/4=17

So work in a similar way for all the given choices until you find one that does not satisfy the conditions that

1. all numbers must be positive (i.e. ≥ 1).

2. all numbers must be even

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