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GWD 15-28 A school administrator will assign each student in a group of n students tp one of m classrooms. If 3<m<13<n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it? (1) It is possible to assign each of 3n students to one of m classrooms so that each classroom has the samr number of students assigned to it. (2) It is possible to assign each of 13n students to one of m classrooms so that each classroom has the samr number of students assigned to it. 為何答案是B? 第一條件也可成立啊? 假設n=14，m=7，3n就是42，42可以被7整除，不是嗎? 請指點  | 
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发表于 2006-12-24 07:36:00
楼主
：不管条件说是多少倍的n个学生能平均分配到m个教室，最终都是希望得到n是m的倍数这一关系，就选项来说：（1）3n能被m整除，但不能保证n就能被m整除，例如：n=20，m=6时，3n=60，3n/m=10,但n明显不能整除m；（2）由于3<m<13,所以13不能被m整除，但13n却能被m整除，因此n是m的倍数，故n个学生能平均分配到m个教室