Difference between revisions of "2006 AMC 10B Problems/Problem 16"
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== Problem == | == Problem == | ||
| + | Leap Day, February 29, 2004, occured on a Sunday. On what day of the week will Leap Day, February 29, 2020, occur? | ||
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| + | <math> \mathrm{(A) \ } Tuesday \qquad \mathrm{(B) \ } Wednesday \qquad \mathrm{(C) \ } Thursday \qquad \mathrm{(D) \ } Friday \qquad \mathrm{(E) \ } Saturday </math> | ||
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== Solution == | == Solution == | ||
| + | There are <math>365</math> days in a year, plus <math>1</math> extra day if there is a Leap Day, which occurs on years that are multiples of 4 (with a few exceptions that don't affect this problem). | ||
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| + | Therefore, the number of days between Leap Day 2004 and Leap Day 2020 is: | ||
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| + | <math> 16 \cdot 365 + 4 \cdot 1 = 5844 </math> | ||
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| + | Since the days of the week repeat every <math>7</math> days and <math> 5844 \equiv -1 \bmod{7}</math>, the day of the week Leap Day 2020 occurs is the day of the week the day before Leap Day 2004 occurs which is <math>Saturday \Rightarrow E </math> | ||
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== See Also == | == See Also == | ||
*[[2006 AMC 10B Problems]] | *[[2006 AMC 10B Problems]] | ||
Revision as of 15:41, 16 July 2006
Problem
Leap Day, February 29, 2004, occured on a Sunday. On what day of the week will Leap Day, February 29, 2020, occur?
Solution
There are 
days in a year, plus 
extra day if there is a Leap Day, which occurs on years that are multiples of 4 (with a few exceptions that don't affect this problem).
Therefore, the number of days between Leap Day 2004 and Leap Day 2020 is:
Since the days of the week repeat every 
days and 
, the day of the week Leap Day 2020 occurs is the day of the week the day before Leap Day 2004 occurs which is 
