Skip to main content

2016 AMC 12B Problem 5

Problem 5 of 25EasierNumber TheoryArithmetic

The War of 18121812 started with a declaration of war on Thursday, June 18,18, 1812.1812. The peace treaty to end the war was signed 919919 days later, on December 24,24, 1814.1814. On what day of the week was the treaty signed?

Answer choices

Show solution

Solution

Because 919=7⋅131+2,919=7\cdot131+2, the treaty was signed 131131 full weeks plus 22 days after Thursday. Two days beyond Thursday is Saturday. Thus, the correct answer is B.
AoPS wiki

Tagged: modular arithmetic · date and time

More practice