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[讨论]GWD15-28 答案是不是錯了?

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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仅供参考: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

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第一个条件不可以,如果有39个人,由9个班那么按条件1就可以平均分,但实际上分不了阿

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