2010 AMC 10B Problem 5
Attempt Problem 5 of the 2010 AMC 10B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2010 AMC 10B solutions, or check the answer key.
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5.
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: B
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.
Problem 5 in Other Years
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