AMC 8 1991 Problem 8

AMC8 1991 年第 8 题

表达式与运算★★☆☆☆

What is the largest quotient that can be formed using two numbers chosen from the set

\{ -24, -3, -2, 1, 2, 8 \}

从集合

\{-24, -3, -2, 1, 2, 8\}

中选两个数，能形成的最大商是多少？

正确答案 · Correct Answer

解析 · Solution

Solution 1

Let the two chosen numbers be

a

and

b

. To maximize the quotient, we first have either a,b>0 or a,b<0, and from there we maximize |a| and minimize |b|.

For the case a,b<0, we have a=-24 and b=-2, which gives us (-24)/(-2)=12. For the case a,b>0, we have a=8 and b=1, which gives us 8/1=8.

Since 12>8, our answer is

\text{D}

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