AMC12 2002 A

AMC12 2002 A · Q6

AMC12 2002 A · Q6. It mainly tests Linear inequalities, Arithmetic misc.

For how many positive integers $m$ does there exist at least one positive integer n such that $m \cdot n \le m + n$?

有多少个正整数 $m$，使得存在至少一个正整数 $n$ 满足 $m \cdot n \le m + n$？

(A) 4 4

(B) 6 6

(D) 12 12

(E) infinitely many 无穷多个

Answer

Correct choice: (E)

正确答案：（E）

Solution

For any $m$ we can pick $n=1$, we get $m \cdot 1 \le m + 1$, therefore the answer is $\boxed{\textbf{(E) } \text{infinitely many}}$.

对任意 $m$，取 $n=1$，则有 $m \cdot 1 \le m + 1$，因此答案是 $\boxed{\textbf{(E) } \text{infinitely many}}$。

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