Difference between revisions of "2010 AMC 12B Problems/Problem 4"
m |
|||
| Line 8: | Line 8: | ||
== Solution == | == Solution == | ||
<math>31 \equiv 3 \pmod {7}</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>. | <math>31 \equiv 3 \pmod {7}</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>. | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/uAc9VHtRRPg?t=329 | ||
| + | |||
| + | ~IceMatrix | ||
== 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}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 01:57, 26 September 2020
- The following problem is from both the 2010 AMC 12B #4 and 2010 AMC 10B #5, so both problems redirect to this page.
Contents
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 
.
Video Solution
https://youtu.be/uAc9VHtRRPg?t=329
~IceMatrix
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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
