2013 AMC 10A Problem 4
Problem 4 of 25EasierNumber Theory
A softball team played ten games, scoring and runs. They lost by one run in exactly five games. In each of their other games, they scored twice as many runs as their opponent. How many total runs did their opponents score?
Answer choices
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Solution
Note that if they scored twice as many runs as their opponents, then they scored an even number of runs.
This means in the games where they scored and runs, their opponents scored and runs respectively.
This sums to
In the other games, their opponents scored and runs.
This sums to
The total number of runs is then Thus, C is the correct answer.