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  3. In a certain game, each player scores either 2 points or 5 points. If n players

In a certain game, each player scores either 2 points or 5 points. If n players

游客2025-02-23  37
问题 In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive difference between n and m?
选项 A、1
B、3
C、5
D、7
E、9
答案 B
解析 由题意得到：2n+5m=50，即2n=5(10-m)。由于2和5互质，那么n是5的倍数，而(10-m)是2的倍数。m可以是0，2，4，6，8，10，那么相应的n分别是25，20，15，10，5，0。现在要求|m-n|的最小值，那么当m=8，n=5时求得最小值为3。
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