题目
If x, y, and z are three different positive integers less than 10, what is the greatest possible value of the expression ?
解析
**问题**:若\(x\)、\(y\)、\(z\)是小于10的三个不同正整数,求表达式\(\frac{x-y}{z}\)的最大可能值。
要让\(\frac{x-y}{z}\)最大,需满足:\(x-y\)尽可能大,且\(z\)尽可能小。
- 若\(y=1\)、\(z=2\)、\(x=9\),则\(\frac{x-y}{z} = \frac{9-1}{2} = 4\);
- 若\(z=1\)、\(y=2\)、\(x=9\),则\(\frac{x-y}{z}\)的最大值为\(\frac{9-2}{1} = 7\)。
答案:B