jmc

Question

In a set of five consecutive integers, the largest integer is less than twice the average of the five integers. What is the smallest integer that could be in the set?

Accepted Answer

Let the integers be n, n+1, n+2, n+3 and n+4. Their average is n+2, so we have n+4<2(n+2) n+4<2n+4 0<n.Thus n is at least 1.