Question

一支垒球队打了十场比赛，得分分别为 $1$ ， $2$ ， $3$ ， $4$ ， $5$ ， $6$ ， $7$ ， $8$ ， $9$ 和 $10$ 分。他们恰好在五场比赛中以一分之差输掉。在其他每场比赛中，他们的得分都是对手的两倍。对手总共得了多少分？

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?

$35$

$40$

$45$

$50$

$55$

答案：C

知识点：奇偶性分类讨论

难度评级：1010

小提示：

只有当本队得分为偶数时，才可能是对手得分的两倍

Scoring twice the opponent is only possible when the team’s own score is even

大提示：

五场一分惜败是奇数得分的比赛；每场对手多得一分。

The five one-run losses are the odd-scored games; each opponent scored one more

解答：

只有当本队得分为偶数时，本队得分才可能是对手的两倍。这些比赛的得分为 $2, 4, 6, 8, 10$ ，因而对手得分为 $1 + 2 + 3 + 4 + 5 = 15$ 。

另外五场比赛的本队得分为 $1, 3, 5, 7, 9$ ，且都是一分惜败，所以对手得分为 $2 + 4 + 6 + 8 + 10 = 30$ 。总分为 $15 + 30 = 45$ 。

因此，正确答案是 C。

The team can only score twice as many runs as its opponent when its own score is even. Those games have scores $2, 4, 6, 8, 10,$ so their opponents scored $1 + 2 + 3 + 4 + 5 = 15.$

The other five games had scores $1, 3, 5, 7, 9$ and were one-run losses, so their opponents scored $2 + 4 + 6 + 8 + 10 = 30.$ The total is $15 + 30 = 45.$

Thus, the correct answer is C.

2013 AMC 12A 第 2 题

答案：C

难度评级：1010

小提示：

大提示：

解答：

其他年份的第 2 题