For a set X containing n integers, is the mean even?

(1) n is even.

(2) All of the integers in set X are even.

My Approach:
1) even number of integers, BUT no information pertaining to the spacing between the integers ie. consecutive or evenly spaced.

Insuff

2) integers are multiples of two, BUT no information pertaining to the number of integers ie. even number of integers or odd number of integers

Even number of integers: AM (X) = odd
Odd number of integers: AM (X) = even

Insuff

1) & 2) integers are multiples of two and even number of integers

AM (X) = odd

Suff

What's wrong?