2016 AMC 12B Problems/Problem 5

Problem

The War of $1812$ started with a declaration of war on Thursday, June $18$ , $1812$ . The peace treaty to end the war was signed $919$ days later, on December $24$ , $1814$ . On what day of the week was the treaty signed?

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

Solution

By: dragonfly

To find what day of the week it is in $919$ days, we have to divide $919$ by $7$ to see the remainder, and then add the remainder to the current day. We get that $\frac{919}{7}$ has a remainder of 2, so we increase the current day by $2$ to get $\boxed{\textbf{(B)}\ \text{Saturday}}$ .

Note that the dates themselves (and thus leap years) can be ignored, as we only need the number of days that passed to figure out the day of the week.

2016 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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All AMC 12 Problems and Solutions

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2016 AMC 12B Problems/Problem 5

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