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Problem Corner Solutions Winter Break 2016/2017

The following are sample problems from the AMATYC Faculty Mathematics League Competition held each year during the national AMATYC conference.. Solutions can be found on our website below and also on www.ohiomatyc.org.


1. The only integer pair with a difference equal to the quotient is (4, 2). Find the sum of the only pair of positive fractions with de- nominator 8 in lowest terms with this property.

  1. 11.0
  2. 11.25
  3. 11.5
  4. 11.75
  5. 12.0


2. The interior angles of an n-gon form an arithmetic sequence with the first term 128° and common
difference 4°. There are two values of n which satisfy this condition. Find their sum.

 

  1. 20
  2. 21
  3. 22
  4. 25
  5. 27


3. For the function f(x), f(1) = 4. Also, f(x)*f(y) = f(x+y) + f(x – y) for all real numbers x and y. Find f(5).

  1. 720
  2. 724
  3. 728
  4. 732
  5. 736