Question

The Little Twelve Basketball Conference has two divisions, with six teams in each division. Each team plays each of the other teams in its own division twice and every team in the other division once. How many conference games are scheduled?

$80$

$96$

$100$

$108$

$192$

Solution:

Let us focus on one team. This team plays against $5$ other teams twice in its own division, for a total of $2 \cdot 5 = 10$ games.

This team also plays $6$ games with teams from the other division. Therefore, they play a total of $10 + 6 = 16$ games.

There are $12$ teams total, so there are $12 \cdot 16 = 192$ games conducted. Each game, however, involves $2$ teams, so we have to divide by $2.$

This gives us the actual total number of games to be $192 \div 2 = 96.$

Thus, B is the correct answer.

2005 AMC 8 Problem 14

Solution:

Problem 14 in Other Years