Math Olympiad #28 Solutions

1. The largest value occurs when A = 40 and B = 39, namely (40 x 39) / (40 - 39) = 1560

2. The slow clock must lose the equivalent of 12 hours in 720 minutes before it will again show the correct time.  Since the clock loses 1 minute every hour, it will lose 720 minutes in 720 hours.

3. 60

4. 16 cubes have 3 red faces

5. In 1 minute, Alice can do 1/60 of the job, and Betty can do 1/30 of the job.  Working together, they can do 1/60 + 1/30 = 1/20 of the job in one minute.  The entire job will require 20 minutes.