2015 AMC 8
Complete problem set with solutions and individual problem pages
A baseball league consists of two four-team divisions. Each team plays every other team in its division games. Each team plays every team in the other division games with and . Each team plays a game schedule. How many games does a team play within its own division?
- A.
- B.
- C.
- D.
- E.
Solution 1
On one team they play games in their division and games in the other. This gives .
Since we start by trying M=5. This doesn't work because is not divisible by .
Next, does not work because is not divisible by .
We try does work by giving , and thus games in their division.
seems to work, until we realize this gives , but so this will not work.
Solution 2
, giving . Since , we have . Since is , we must have equal to , so .
This gives , as desired. The answer is .
