Problem Solving

3, k, 2, 8, m, 3

The arithmetic mean of the list of numbers above is 4. If k and m are integers k ≠ m, what is the median of the list?

A. 2
B. 2.5
C. 3
D. 3.5
D. 4

The OA is C.

Hi, I need some help,

List = {2,3,3,8,k,m}

Given that mean is more than 4

which implies 2+3+3+ 8+ k+m >4*6 --> k+m> 8

and we know k ≠ m,

therefore

k=1, m=8 median = 3 { 1,2,3,3,8,8}

k=5, m =10 median = 4 {2,3,3,5,8,10}

Thanks in advance!