1986 AMC 8 第 4 题

先试着解答 1986 AMC 8 第 4 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 1986 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。

4.

乘积 (1.8)(40.3+0.07)(1.8)(40.3 + 0.07) 最接近
The product (1.8)(40.3+0.07)(1.8)(40.3 + 0.07) is closest to
77
4242
7474
8484
737737
答案:C
知识点:估算
小提示:
估算各因数:1.81.8 接近 22,40.3+0.0740.3 + 0.07 接近 4040
Round each factor: 1.81.8 is near 22 and 40.3+0.0740.3 + 0.07 is near 4040
大提示:
先估算 2×402 \times 40,再因为 1.8<21.8 \lt 2 稍微向下调整
Estimate 2×402 \times 40 and adjust slightly downward since 1.8<21.8 \lt 2
解答:
第二个因数 40.3+0.07=40.3740.3 + 0.07 = 40.37 约为 4040,而 1.81.8 约为 22。快速估算为 2(40)−0.2(40)=80−8=722(40) - 0.2(40) = 80 - 8 = 72,所以乘积最接近 7474。
所以正确答案是 C。
The second factor 40.3+0.07=40.3740.3 + 0.07 = 40.37 is about 40,40, and 1.81.8 is about 2.2. A quick estimate is 2(40)−0.2(40)=80−8=72,2(40) - 0.2(40) = 80 - 8 = 72, so the product is closest to 74.74.
Thus, the correct answer is C .
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