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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
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
admin
2021-10-21
40
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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