AMC 8 1987 Problem 8

AMC8 1987 年第 8 题

表达式与运算★★☆☆☆

If the letters are replaced by digits so that the given addition problem is correct, then the number of digits (not necessarily different) in the sum of the three whole numbers is

若字母被数字替换使得给定的加法算式正确，则三个整数的和的位数（数字不必不同）为

A.4
B.5
C.6
D.9
E. $\text{depends on the values of A and B}$ / 取决于 $A$ 和 $B$ 的值

正确答案 · Correct Answer

解析 · Solution

Solution 1

The smallest possible sum occurs if A=B=1, so it is 9876+132+11=10019. The largest possible sum occurs if A=B=9, so it is 9876+932+91=10899. Therefore, the sum is between 10019 and 10899, so it has 5 digits.

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