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2016 AMC 12B Problem 5

Problem 5 of 25EasierAlgebraNumber Theory

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?

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Solution

Because 919=7131+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.

More practice

Concepts: modular arithmetic · date and time

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