Problem:
How many positive integers not exceeding are multiples of or but not
Answer Choices:
A.
B.
C.
D.
E.
Solution:
For integers not exceeding , there are multiples of and multiples of . The total, , counts the multiples of twice, so there are multiples of or . From these we exclude the multiples of and the multiples of , since these are multiples of . However, this excludes the multiples of twice, so we must re-include these. The number of integers satisfying the conditions is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions