Sponsored by: UGA Math Department and UGA Math Club Written test, 25 problems / 90 minutes 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 2-digit 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 fifty-cent 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 fifty-cent 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 Collections: Mathematics