Difference between revisions of "2000 AMC 12 Problems/Problem 18"
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== Problem == | == Problem == | ||
| − | In year <math>N</math>, the <math>300^{\text{th}}</math> day of the year is a Tuesday. In year <math>N+1</math>, the <math>200^{\text{th}}</math> day is also a Tuesday. On what day of the week did the <math>100</math><sup>th</sup> day of year <math>N-1</math> occur? | + | <!-- don't remove the following tag, for PoTW on the Wiki front page--><onlyinclude>In year <math>N</math>, the <math>300^{\text{th}}</math> day of the year is a Tuesday. In year <math>N+1</math>, the <math>200^{\text{th}}</math> day is also a Tuesday. On what day of the week did the <math>100</math><sup>th</sup> day of year <math>N-1</math> occur?</onlyinclude>I |
<math>\text {(A)}\ \text{Thursday} \qquad \text {(B)}\ \text{Friday}\qquad \text {(C)}\ \text{Saturday}\qquad \text {(D)}\ \text{Sunday}\qquad \text {(E)}\ \text{Monday}</math> | <math>\text {(A)}\ \text{Thursday} \qquad \text {(B)}\ \text{Friday}\qquad \text {(C)}\ \text{Saturday}\qquad \text {(D)}\ \text{Sunday}\qquad \text {(E)}\ \text{Monday}</math> | ||
Revision as of 12:19, 3 March 2015
- The following problem is from both the 2000 AMC 12 #18 and 2000 AMC 10 #25, so both problems redirect to this page.
Problem
In year 
, the 
day of the year is a Tuesday. In year 
, the 
day is also a Tuesday. On what day of the week did the 
th day of year 
occur?I
Solution
There are either 
or 
days between the first two dates depending upon whether or not year is a leap year. Since 
divides into 
, then it is possible for both dates to be Tuesday; hence year is a leap year and is not a leap year. There are 
days between the date in years 
, which leaves a remainder of 
upon division by . Since we are subtracting days, we count 5 days before Tuesday, which gives us 
.
See also
| 2000 AMC 12 (Problems • Answer Key • Resources) | |
| Preceded by Problem 17 |
Followed by Problem 19 |
| 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 | |
| 2000 AMC 10 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 24 |
Followed by Last Problem | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
