A set of five different positive integers has an average (arithmetic mean) of 11. What is the largest possible number in this set?
(A) 45
(B) 40
(C) 35
(D) 44
(E) 46
A set of five different positive integers has an average (arithmetic mean) of 11. What is the largest possible number in this set?
(A) 45
(B) 40
(C) 35
(D) 44
(E) 46

## Solution

If the set of five different positive integers has an average of 11 the five integers must sum to $5 \times 11$ or 55. The four smallest possible integers are 1, 2,3, and 4. The largest possible integer in the set is $55-(1+2+3+4)=45$.

ANSwER: (A)