1966 AMC 12 第 13 题

Question

在

xy

平面中满足

x+y\leq5

的点中，坐标均为正有理数的点共有：

The number of points with positive rational coordinates selected from the set of points in the

xy

-plane such that

x+y\leq5,

is:

9

10

14

15

无限多个

infinite

尝试固定其中一个正有理数坐标

Try fixing one positive rational coordinate

一个区间内有无限多个正有理数

There are infinitely many positive rational numbers in an interval

例如，令

y=1

。此时每个满足

x\leq4

的正有理数都给出一个合格点

(x,1)

，而这样的有理数有无限多个。

因此，正确答案是 E。

For example, set

y=1.

Every positive rational

x\leq4

then gives an allowed point

(x,1),

and there are infinitely many such rationals.

Therefore, the correct answer is E.

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