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.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
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
Small hint:
In days, three weekdays occur one extra time
Big hint:
Monday and Wednesday must either both be extra days or both not be extra days
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
- 2000 AMC 10
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