imc

Question

When 15 is appended to a list of integers, the mean is increased by 2. When 1 is appended to the enlarged list, the mean of the enlarged list is decreased by 1. How many integers were in the original list?

Accepted Answer

Let x be the sum of the integers and y be the number of elements in the list. Then we get the equations x+15y+1=xy+2 and x+15+1y+1+1=x+16y+2=xy+2-1=xy+1. With a lot of algebra, the solution is found to be y= 4.