[讨论]GWD15-28 答案是不是錯了?

mingmings

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

cherryser

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

zdytiffany

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