2014 AMC 8

Complete problem set with solutions and individual problem pages

Problem 24 Hard

One day the Beverage Barn sold cans of soda to customers, and every customer bought at least one can of soda. What is the maximum possible median number of cans of soda bought per customer on that day?

Answer:C

In order to maximize the median, we need to make the first half of the numbers as small as possible. Since there are people, the median will be the average of the and largest amount of cans per person. To minimize the first , they would each have one can. Subtracting these cans from the cans gives us cans left to divide among people. Taking gives us and a remainder of . Seeing this, the largest number of cans the th person could have is , which leaves to the rest of the people. The average of and is . Thus our answer is .