Problem:
In year , the day of the year is a Tuesday. In year , the day is also a Tuesday. On what day of the week did the day of year occur?
Answer Choices:
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B.
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E.
Solution:
Note that, if a Tuesday is days after a Tuesday, then is a multiple of 7. Next, we need to consider whether any of the years , is a leap year. If is not a leap year, the day of year is days after a Tuesday, and thus is a Monday, since 265 if 6 larger than a multiple of 7 . Thus, year is a leap year and the day of year is another Tuesday (as given), being 266 days after a Tuesday. It follows that year is not a leap year. Therefore, the day of year precedes the given Tuesday in year by days, and therefore is a , since is 5 larger than a multiple of 7 .
The problems on this page are the property of the MAA's American Mathematics Competitions