Difference between revisions of "1985 AJHSME Problems/Problem 20"
5849206328x (talk | contribs) (New page: ==Problem== In a certain year, January had exactly four Tuesdays and four Saturdays. On what day did January <math>1</math> fall that year? <math>\text{(A)}\ \text{Monday} \qquad \text{...) |
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<math>\text{(A)}\ \text{Monday} \qquad \text{(B)}\ \text{Tuesday} \qquad \text{(C)}\ \text{Wednesday} \qquad \text{(D)}\ \text{Friday} \qquad \text{(E)}\ \text{Saturday}</math> | <math>\text{(A)}\ \text{Monday} \qquad \text{(B)}\ \text{Tuesday} \qquad \text{(C)}\ \text{Wednesday} \qquad \text{(D)}\ \text{Friday} \qquad \text{(E)}\ \text{Saturday}</math> | ||
| − | == | + | ==Solution== |
January has four full weeks and then three extra consecutive days. Each full week contributes one Tuesday and one Saturday, so the three extra days do not contain a Tuesday and Saturday. Therefore, those three days are Wednesday, Thursday, and Friday. | January has four full weeks and then three extra consecutive days. Each full week contributes one Tuesday and one Saturday, so the three extra days do not contain a Tuesday and Saturday. Therefore, those three days are Wednesday, Thursday, and Friday. | ||
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==See Also== | ==See Also== | ||
| − | [[ | + | {{AJHSME box|year=1985|num-b=19|num-a=21}} |
| + | [[Category:Introductory Number Theory Problems]] | ||
| + | |||
| + | |||
| + | {{MAA Notice}} | ||
Latest revision as of 09:01, 10 June 2024
Problem
In a certain year, January had exactly four Tuesdays and four Saturdays. On what day did January 
fall that year?
Solution
January has four full weeks and then three extra consecutive days. Each full week contributes one Tuesday and one Saturday, so the three extra days do not contain a Tuesday and Saturday. Therefore, those three days are Wednesday, Thursday, and Friday.
Wednesday is the 29th day of January, therefore the 22nd, 15th, 8th, and 1st of January are all Wednesdays, so the answer is 
See Also
| 1985 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 19 |
Followed by Problem 21 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
