Problem:
Which of the following sets of whole numbers has the largest average?
Answer Choices:
A. multiples of between and
B. multiples of between and
C. multiples of between and
D. multiples of between and
E. multiples of between and
Solution:
In a set of whole numbers which are equally spaced, the average of the numbers in the set is the average of the smallest number and the largest number. For example, the average of , and the average of is . In this problem, then, the averages are:
One could "guesstimate" that the set with the "largest" numbers should have the largest average. The numbers and are (overall) larger than the corresponding numbers in the other sets.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions