1999 AMC 8 第 9 题

先试着解答 1999 AMC 8 第 9 题,然后核对你的答案与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1999 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

9.

如图,三个花坛互相重叠。花坛 AA 有 500500 株植物,花坛 BB 有 450450 株植物,花坛 CC 有 350350 株植物。花坛 AA 和 BB 共有 5050 株植物,花坛 AA 和 CC 共有 100100 株植物。植物总数是
Three flower beds overlap as shown. Bed AA has 500500 plants, bed BB has 450450 plants, and bed CC has 350350 plants. Beds AA and BB share 5050 plants, while beds AA and CC share 100.100. The total number of plants is
850850
10001000
11501150
13001300
14501450
答案:C
知识点:容斥原理韦恩图
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=15050 + 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。 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=15050 + 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. 500 + 450 + 350 - 150 = 1150. We subtract to get rid of the plants that we counted twice.
Thus, C is the correct answer.
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