Difference between revisions of "2006 AMC 10B Problems/Problem 16"
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Leap Day, February 29, 2004, occured on a Sunday. On what day of the week will Leap Day, February 29, 2020, occur? | Leap Day, February 29, 2004, occured on a Sunday. On what day of the week will Leap Day, February 29, 2020, occur? | ||
| − | <math> \mathrm{(A) \ } Tuesday \qquad \mathrm{(B) \ } Wednesday \qquad \mathrm{(C) \ } Thursday \qquad \mathrm{(D) \ } Friday \qquad \mathrm{(E) \ } Saturday </math> | + | <math> \mathrm{(A) \ } \textrm{Tuesday} \qquad \mathrm{(B) \ } \textrm{Wednesday} \qquad \mathrm{(C) \ } \textrm{Thursday} \qquad \mathrm{(D) \ } \textrm{Friday} \qquad \mathrm{(E) \ } \textrm{Saturday} </math> |
== Solution == | == Solution == | ||
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<math> 16 \cdot 365 + 4 \cdot 1 = 5844 </math> | <math> 16 \cdot 365 + 4 \cdot 1 = 5844 </math> | ||
| − | 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>. | + | 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>\textrm{Saturday} \Rightarrow E </math>. |
== See Also == | == See Also == | ||
*[[2006 AMC 10B Problems]] | *[[2006 AMC 10B Problems]] | ||
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| + | *[[2006 AMC 10B Problems/Problem 15|Previous Problem]] | ||
| + | |||
| + | *[[2006 AMC 10B Problems/Problem 17|Next Problem]] | ||
Revision as of 15:02, 2 August 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 
.
