AMC 8 2005 Problem 8

AMC8 2005 年第 8 题

奇偶性★★☆☆☆
Suppose m and n are positive odd integers. Which of the following must also be an odd integer?
假设 m 和 n 都是正奇数,下面哪个一定也是奇数?
  1. A.m+3n
  2. B.3m-n
  3. C.3m2+3n23m^2 + 3n^2
  4. D.(nm+3)2(nm + 3)^2
  5. E.3mn

正确答案 · Correct Answer

E

解析 · Solution

Solution 1

Assume WLOG that mm and nn are both 1. Plugging into each of the choices, we get 4, 2, 6, 16, and 3. The only odd integer is 3mn.

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