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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

  

Source: Alexeev, Valery - Department of Mathematics, University of Georgia

 

Collections: Mathematics