2015 AMC 8 Problems/Problem 24

Big balck men

Solution 1

On one team they play $3N$ games in their division and $4M$ games in the other. This gives $3N+4M=76$ .

Since $M>4$ we start by trying M=5. This doesn't work because $56$ is not divisible by $3$ .

Next, $M=6$ does not work because $52$ is not divisible by $3$ .

We try $M=7$ does work by giving $N=16$ , $~M=7$ and thus $3\times 16=\boxed{\textbf{(B)}~48}$ games in their division.

$M=10$ seems to work, until we realize this gives $N=12$ , but $N>2M$ so this will not work.

2015 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 23	Followed by Problem 25
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