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题库 / OG2017Q-PS-87
If x and y are integers such that 2 < x ≤ 8 and 2 < y ≤ 9, what is the maximum value of ~$1 \over x$~ - ~$x \over y$~ ?
-3~$1 \over 8$~
0
~$1 \over 4$~
~$5 \over 18$~
2
题目分析：
~$\frac{1}{x}-\frac{x}{y}$~最大，需要满足~$\frac{1}{x}$~最大且~$\frac{x}{y}$~最小，x=3 时，~$\frac{1}{x}$~最大。~$\frac{x}{y}$~最小，应满足，x=3,y=9.（分子最小，分母最大）.x=3 可以同时满足~$\frac{1}{x}$~最大，~$\frac{x}{y}$~最小。所以，x=3,y=9 时，~$\frac{1}{x}-\frac{x}{y}$~最大值，最大值= ~$\frac{1}{3}-\frac{3}{9}=0$~
综上：答案就是 B。
审题：If x and y are integers And 2 < x ≤ 8（只看了后面一个条件）
不需通分，观察。
留心X和Y是整数这一条件。
X不能等于2
Because x and y are both positive, the maximum value of (1/x-x/y) will occur when the
value of 1/x is maximum and the value of x/y is minimum. The value of 1/x is maximum
when the value of x is minimum or when x = 3. The value of x/y is minimum when the
value of x is minimum (or when x = 3) and the value of y is maximum (or when
y = 9). Thus, the maximum value of (1/x-x/y) is 1/3-3/9=0 .
The correct answer is B.
X不能=2
x=3,y=9时是最大值，0
x不等于2