Problem:
In the population of a town was a perfect square. Ten years later, after an increase of people, the population was more than a perfect square. Now, in , with an increase of another people, the population is once again a perfect square. Which of the following is closest to the percent growth of the town's population during this twenty-year period?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let , and be the populations of the town in , , and , respectively. Then , so . Therefore , and so either and , or and . These give or . Note that if , then , which is not a perfect square. Thus , , and . The percent growth from to was .
The problems on this page are the property of the MAA's American Mathematics Competitions