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。A 和 B 共有 $50$ 株植物，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

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。

所以植物总数为减去是为了去掉被计算两次的植物。 $500 + 450 + 350 - 150 = 1150.$

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

解答：

其他年份的第 9 题