Question

一名篮球运动员在一场比赛中投进了 $5$ 个球。每次进球得 $2$ 分或 $3$ 分。该运动员总得分可能有多少种不同的数值？

A basketball player made $5$ baskets during a game. Each basket was worth either $2$ or $3$ points. How many different numbers could represent the total points scored by the player?

$2$

$3$

$4$

$5$

$6$

答案：E

知识点：区间内整数计数

难度评级：920

小提示：

总分最小时全是 $2$ 分球，最大时全是 $3$ 分球。

The total is smallest with all $2$ -point baskets and largest with all $3$ -point baskets

大提示：

$5 \cdot 2$ 和 $5 \cdot 3$ 之间的每个整数都能达到。

Every integer between $5 \cdot 2$ and $5 \cdot 3$ is attainable

解答：

总分从 $5 \cdot 2 = 10$ （全是两分球）到 $5 \cdot 3 = 15$ （全是三分球）。每把一个两分球换成三分球，总分正好增加 $1$ ，所以中间的每个整数都会出现。

可能的总分是 $10, 11, 12, 13, 14, 15$ ，共有 $6$ 个值。

因此，正确答案是 E。

The total ranges from $5 \cdot 2 = 10$ (all two-pointers) to $5 \cdot 3 = 15$ (all three-pointers). Swapping one two-pointer for a three-pointer raises the total by exactly $1,$ so every integer in between occurs.

The possible totals are $10, 11, 12, 13, 14, 15,$ which is $6$ values.

Thus, the correct answer is E.

2008 AMC 12B 第 1 题

答案：E

难度评级：920

小提示：

大提示：

解答：

其他年份的第 1 题