|
|
| Line 1: |
Line 1: |
| − | == Problem ==
| + | #REDIRECT[[2002 AMC 12B Problems/Problem 8]] |
| − | | |
| − | Suppose July of year <math>N</math> has five Mondays. Which of the following must occurs five times in the August of year <math>N</math>? (Note: Both months have <math>31</math> days.)
| |
| − | | |
| − | <math>\textbf{(A)}\ \text{Monday} \qquad \textbf{(B)}\ \text{Tuesday} \qquad \textbf{(C)}\ \text{Wednesday} \qquad \textbf{(D)}\ \text{Thursday} \qquad \textbf{(E)}\ \text{Friday}</math>
| |
| − | | |
| − | ==Solution==
| |
| − | If there are five Mondays, there are only three possibilities for their dates: <math>(1,8,15,22,29)</math>, <math>(2,9,16,23,30)</math>, and <math>(3,10,17,24,31)</math>.
| |
| − | | |
| − | In the first case August starts on a Thursday, and there are five Thursdays, five Fridays, and five Saturdays in August.
| |
| − | | |
| − | In the second case August starts on a Wednesday, and there are five Wednesdays, five Thursdays, and five Fridays in August.
| |
| − | | |
| − | In the third case August starts on a Tuesday, and there are five Tuesdays, five Wednesdays, and five Thursdays in August.
| |
| − | | |
| − | The only day of the week that is guaranteed to appear five times is therefore <math>\boxed{\textbf{(D)}\ \text{Thursday}}</math>.
| |
| − | | |
| − | ==See Also==
| |
| − | {{AMC10 box|year=2002|ab=B|num-b=7|num-a=9}}
| |
| − | | |
| − | [[Category:Introductory Algebra Problems]] | |
