AMC 8 1990 Problem 7

AMC8 1990 年第 7 题

表达式与运算★★☆☆☆

When three different numbers from the set

\{ -3, -2, -1, 4, 5 \}

are multiplied, the largest possible product is

从集合

\{-3, -2, -1, 4, 5\}

中取三个不同的数相乘，最大可能的乘积是

A.10
B.20
C.30
D.40
E.60

正确答案 · Correct Answer

解析 · Solution

Solution 1

For the product of 3 real numbers to be positive, either all 3 numbers are positive, or 1 number is positive and 2 numbers are negative.

Since there are only 2 positive numbers, the only way to get a positive product is to select 2 negative numbers and 1 positive number. The product is maximized by selecting the 2 negative numbers with the largest absolute values and the positive number with the largest absolute value. In this case the product would be (-3)(-2)(5) = 30.

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