1986 AMC 8 第 4 题

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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
难度评级:730
小提示:

估算各因数:1.81.8 接近 2240.3+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)=808=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)=808=72,2(40) - 0.2(40) = 80 - 8 = 72, so the product is closest to 74.74.

Thus, the correct answer is C .

第 3 题#3
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