06/08/2020 (2011: National Sprint Round, Problem 28)

Q: If the degree measure of an arc of a circle is increased by 20% and the radius of the circle is increased by 25% by what percent does the length of the arc increase?

A: 50%

The arc length is directly proportional to the degree measure and the radius. That means that the arc length increases to 1.25 * 1.20 = 1.5 of the original arc. That means it increases by 1.5 - 1 = .5 = 50%