 
Summary: Sponsored by: UGA Math Department and UGA Math Club
Written test, 25 problems / 90 minutes
October 13, 2007
WITH SOLUTIONS
No calculators are allowed on this test. 10 points for a correct answer, 0
points for an incorrect answer, and 2 points for an answer left blank.
Problem 1. How many 2digit numbers are there such that the sum of the digits
plus the product of the digits equals the number itself?
(A) 2 (B)
9 (C) 10 (D) 18 (E) None of the above
Solution. We have
a + b + ab = 10a + b, or ab = 9a
So the last digit must be 9 and the first digit any number between 1 and 9.
Problem 2. Tyler has in his pocket assorted coins (including possibly pennies, nick
els, dimes, quarters, and fiftycent pieces). What is the largest possible amount of
money he can have without being able to make change for a nickel, a dime, a quarter,
a fiftycent piece or a dollar?
(A) $.74 (B) $.69 (C) $.79 (D) $.94 (E)
None of the above
Solution. He can have four pennies, no nickels, four dimes, one quarter, and one
