Question

如图，三个花坛互相重叠。花坛 $A$ 有 $500$ 株植物，花坛 $B$ 有 $450$ 株植物，花坛 $C$ 有 $350$ 株植物。花坛 $A$ 和 $B$ 共有 $50$ 株植物，花坛 $A$ 和 $C$ 共有 $100$ 株植物。植物总数是

Three flower beds overlap as shown. Bed $A$ has $500$ plants, bed $B$ has $450$ plants, and bed $C$ has $350$ plants. Beds $A$ and $B$ share $50$ plants, while beds $A$ and $C$ share $100.$ The total number of plants is

$850$

$1000$

$1150$

$1300$

$1450$

答案：C

知识点：容斥原理韦恩图

难度评级：1020

小提示：

先把三个花坛的数量相加

Add the three bed counts first

大提示：

减去被重复计算的重叠部分

Subtract the overlaps that were counted twice

解答：

有 $50 + 100 = 150$ 株植物在两个花坛中，且没有植物同时在三个花坛中。

所以植物总数为 $500 + 450 + 350 - 150 = 1150\text{。}$ 减去重叠部分是为了去掉被计算两次的植物。

所以正确答案是 C。

Note there are $50 + 100 = 150$ plants that are in two beds and there are no plants in all three beds.

The total number of plants is then $500 + 450 + 350 - 150 = 1150.$ We subtract to get rid of the plants that we counted twice.

Thus, C is the correct answer.

1999 AMC 8 第 9 题

答案：C

难度评级：1020

小提示：

大提示：

解答：

其他年份的第 9 题