2010 AMC 10B Problem 5
Problem 5 of 25EasierAlgebraNumber Theory
A month with days has the same number of Mondays and Wednesdays. How many of the seven days of the week could be the first day of this month?
Answer choices
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Solution
Note that days leaves a remainder of when divided by
This means that if the month starts on a Saturday, Sunday, Tuesday, or Wednesday, there will be an uneven number of Mondays and Wednesdays.
Then the month can only start on a Monday, Thursday, or Friday.
Thus, B is the correct answer.