Problem:
A poll asked a number of people if they liked solving mathematics problems. Exactly answered "yes." What is the fewest possible number of people who could have been asked the question?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
can be written as which is the fraction of people who answered "yes" out of everyone polled. Suppose the total number of people polled is . Then, the number of people who answered "yes" is . Since the number of people must be an integer, must be a multiple of . The smallest such possible integer is .
The problems on this page are the property of the MAA's American Mathematics Competitions