Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "1985 AJHSME Problems/Problem 20"

(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{...)
(No difference)

Revision as of 18:56, 13 January 2009

Problem

In a certain year, January had exactly four Tuesdays and four Saturdays. On what day did January $1$ fall that year?

$\text{(A)}\ \text{Monday} \qquad \text{(B)}\ \text{Tuesday} \qquad \text{(C)}\ \text{Wednesday} \qquad \text{(D)}\ \text{Friday} \qquad \text{(E)}\ \text{Saturday}$

Solutions

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 $\boxed{\text{C}}$

See Also

1985 AJHSME Problems

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1985_AJHSME_Problems/Problem_20&oldid=29548"