Problem:
How many positive integers not exceeding 2001 are multiples of 3 or 4 but not 5 ?
Answer Choices:
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Solution:
For integers not exceeding 2001, there are multiples of 3 and multiples of 4. The total, 1167 , counts the multiples of 12 twice, so there are multiples of 3 or 4 . From these we exclude the multiples of 15 and the 100 multiples of 20 , since these are multiples of 5 . However, this excludes the multiples of 60 twice, so we must re-include these. The number of integers satisfying the conditions is .
The problems on this page are the property of the MAA's American Mathematics Competitions