2016 AMC 12B Problem 5

Below is the professionally curated solution for Problem 5 of the 2016 AMC 12B, 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 of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:modular arithmeticdate and time

Difficulty rating: 1200

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

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.

Problem 5 in Other Years