**Question**: The mean of four positive integers is 5 . the median of the four integers is 6 . what is the mean of the largest and smallest of the integers?

**Answer**: Let say four numbers are A , B , C , D arranged in ascending order

A – Smallest

D – Largest

Mean = (A + B + C + D)/4

=> 5 = (A + B + C + D)/4

=> A + B + C + D = 20

Median = ( B + C)/2

=> 6 = (B + C)/2

=> B + C = 12

=> A + 12 + D = 20

=> A + D = 8

=> (A + D)/2 = 4

mean of the largest and smallest of the integers = 4

Few example Satisfying all these : ( for understanding)

1 6 6 7

1 5 7 7