Summary: Sponsored by: UGA Math Department and UGA Math Club
Ciphering Round / 2 minutes per problem
October 13, 2007
No calculators are allowed on this test. 2 minutes per problem, 10 points
for each correct answer.
Problem 1. The length of a rectangle is increased by 30% and its width is decreased
by 20%. By what percentage does its area increase?
Solution. If the original length and width are and w, respectively, then the
new length is 1.3 and the new width is 0.8w, so the area of the new rectangle is
(1.3 )(0.8w) = 1.04 w. Thus, the area increases by 4%.
Problem 2. When two joggers run around a 1-mile oval track in the same direction,
one passes the other every 30 minutes. When they run in opposite directions, they
pass every 10 minutes. What is the speed of the slower jogger (in mph)?
Answer. 2 mph
Solution. Let x be the speed (in mph) of the faster jogger and y the speed of the
slower jogger. Then we have