AMC 8 1994 Problem 23

AMC8 1994 年第 23 题

逻辑推理（跨域）★★★☆☆

X

Y

and

Z

are different digits, then the largest possible 3-digit sum for the addition problem shown below has the form

若

X

、

Y

和

Z

是不同的数字，则如下所示加法算式的最大可能三位数和的形式为

A.XXY
B.XYZ
C.YYX
D.YYZ
E.ZZY

正确答案 · Correct Answer

解析 · Solution

Solution 1

The sum can be rewritten as 113X + 10Y. To get the largest possible sum, we maximize the hundreds digit,

X

. If X=9, the sum is a 4 -digit number, so we let X=8 and 113(8)+10Y = 904+10Y. To continue maxmimizing this sum, we can let Y=9, a different digit from

X

, and 904+10(9)=994, which has the form

\text{(D)\ YYZ}

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