2016 AMC 12B Problem 5

Attempt Problem 5 of the 2016 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2016 AMC 12B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

5.

The War of 1812 started with a declaration of war on Thursday, June 18, 1812. The peace treaty to end the war was signed 919919 days later, on December 24, 1814. On what day of the week was the treaty signed?

Friday

Saturday

Sunday

Monday

Tuesday

Answer: B
Concepts:modular arithmeticdate and time
Difficulty rating: 1200
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.

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