Difference between revisions of "2010 AMC 10B Problems/Problem 5"
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| − | B. 3 | + | == Problem== |
| + | A month with <math>31</math> 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? | ||
| + | |||
| + | <math>\textbf{(A)}\ 2 \qquad \textbf{(B)}\ 3 \qquad \textbf{(C)}\ 4 \qquad \textbf{(D)}\ 5 \qquad \textbf{(E)}\ 6</math> | ||
| + | |||
| + | ==Solution== | ||
| + | In this month there are four weeks and three remaining days. As long as the last three days and the first four days have the same number of Mondays and Wednesdays, then it works. The number of days the month can start on is <math>\boxed{\textbf{(B)}\ 3}</math> | ||
| + | |||
| + | ==See Also== | ||
| + | {{AMC10 box|year=2010|ab=B|num-b=4|num-a=6}} | ||
Revision as of 01:02, 26 November 2011
Problem
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?
Solution
In this month there are four weeks and three remaining days. As long as the last three days and the first four days have the same number of Mondays and Wednesdays, then it works. The number of days the month can start on is 
See Also
| 2010 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
