Difference between revisions of "2002 AMC 10B Problems/Problem 8"
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==Solution== | ==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>. |
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| + | In the first case August starts on a Thursday, and there are five Thursdays, five Fridays, and five Saturdays in August. | ||
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| + | In the second case August starts on a Wednesday, and there are five Wednesdays, five Thursdays, and five Fridays in August. | ||
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| + | In the third case August starts on a Tuesday, and there are five Tuesdays, five Wednesdays, and five Thursdays in August. | ||
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| + | The only day of the week that is guaranteed to appear five times is therefore <math>\boxed{\textbf{(D)}\ \text{Thursday}}</math>. | ||
==See Also== | ==See Also== | ||
Revision as of 22:04, 28 January 2009
Problem
Suppose July of year 
has five Mondays. Which of the following must occurs five times in the August of year ? (Note: Both months have 
days.)
Solution
If there are five Mondays, there are only three possibilities for their dates: 
, 
, and 
.
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 
.
See Also
| 2002 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 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 | ||
