2010 AMC 12B Problems/Problem 4

Problem 4

A month with $31$ 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?

$\textbf{(A)}\ 2 \qquad \textbf{(B)}\ 3 \qquad \textbf{(C)}\ 4 \qquad \textbf{(D)}\ 5 \qquad \textbf{(E)}\ 6$

Solution

31%7 = 3 so the week cannot start with Saturday, Sunday, Tuesday or Wednesday as that would result in an unequal number of Mondays and Wednesdays. Therefore Monday, Thursday and Friday are valid so the answer is (B).

2010 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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2010 AMC 12B Problems/Problem 4

Problem 4

Solution

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