Difference between revisions of "2010 AMC 12B Problems/Problem 4"
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== Solution == | == Solution == | ||
| − | 31 | + | <math>3 \equiv 7 \pmod {31}</math> 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 <math>\boxed{B}</math>. |
== See also == | == See also == | ||
{{AMC12 box|year=2010|num-b=3|num-a=5|ab=B}} | {{AMC12 box|year=2010|num-b=3|num-a=5|ab=B}} | ||
Revision as of 13:48, 31 May 2011
Problem 4
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
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 
.
See also
| 2010 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 3 |
Followed by Problem 5 |
| 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 12 Problems and Solutions | |
