2015 AMC 8 Problem 24
Attempt Problem 24 of the 2015 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2015 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
24.
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?
Answer: B
Small hint:
Write the schedule equation
Big hint:
Use and the equation modulo
Video solution:
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Written solution:
Each team plays games within its own division and games against the other division, so
Since we have and hence Thus Together with this gives
Reducing modulo gives so Therefore the team plays non-division games and division games.
Thus, B is the correct answer.
Problem 24 in other years
- 1985 AMC 8
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