Question

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)

Answer 1

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