AMC12 2013 A

AMC12 2013 A · Q2

AMC12 2013 A · Q2. It mainly tests Averages (mean), Casework.

A softball team played ten games, scoring 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 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?

一个垒球队打了十场比赛，得分为 1, 2, 3, 4, 5, 6, 7, 8, 9, 和 10 分。他们恰好有五场比赛以一分之差输掉。在其他比赛中，他们的得分是对手的两倍。对手总共得了多少分？

(A) 35 35

(B) 40 40

(D) 50 50

(E) 55 55

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): The softball team could only have scored twice as many runs as their opponent when they scored an even number of runs. In those games their opponents scored $\frac{2}{2}+\frac{4}{2}+\frac{6}{2}+\frac{8}{2}+\frac{10}{2}=15$ runs. In the games the softball team lost, their opponents scored $(1+1)+(3+1)+(5+1)+(7+1)+(9+1)=30$ runs. The total number of runs scored by their opponents was $15+30=45$ runs.

答案（C）：垒球队只有在自己得分为偶数时，才可能得到对手两倍的得分。在那些比赛中，对手得分为 $\frac{2}{2}+\frac{4}{2}+\frac{6}{2}+\frac{8}{2}+\frac{10}{2}=15$ 分。在垒球队输掉的比赛中，对手得分为 $(1+1)+(3+1)+(5+1)+(7+1)+(9+1)=30$ 分。对手总得分为 $15+30=45$ 分。

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