1987 AMC 8 第 6 题

先试着解答 1987 AMC 8 第 6 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 1987 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。

6.

从集合 {−7,−5,−1,1,3}\{ -7, -5, -1, 1, 3 \} 中选两个数相乘,可能得到的最小乘积是
The smallest product one could obtain by multiplying two numbers in the set {−7,−5,−1,1,3}\{ -7, -5, -1, 1, 3 \} is
−35-35
−21-21
−15-15
−1-1
33
答案:B
知识点:最优化
小提示:
最小的乘积是最负的乘积,来自一个负因数和一个正因数
The smallest product is the most negative one, which comes from one negative and one positive factor
大提示:
把最负的数和最大的正数配对
Pair the most negative number with the largest positive number
解答:
负乘积来自负数乘正数;要最负,就让两个因数的绝对值尽可能大。
最负的乘积是 (−7)(3)=−21(-7)(3) = -21。
所以正确答案是 B。
A negative product comes from multiplying a negative number by a positive number, and it is most negative when both factors are largest in size.
The most negative product is (−7)(3)=−21.(-7)(3) = -21.
Thus, the correct answer is B .
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