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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 -

    To give an example, 17 can be thought of as

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


    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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