[求助]天山数学4-28

lemonees

天山4-28:
A school administrator will assign each student in a group of n students to 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 same number of students assigned to it.
        (2)it is possible to assign each of 13n students to one of m classroom so that each classroom has the same number of students assigned to it.

lemonees

通了。感谢！！！[em08]

diatomss

把n个学生分到m个班里，每人只在一个班。

问分的时候能不能让各班学生人数相等。

-----英文不好，如果我的理解没有错误的话那么：就是求一个n能否被m整除的问题

3<m<13<n

(1)3n能平均分配到m个班里

3n能被m整除，n不一定。比方说m=6,n=20不可以；m=6，n=30可以，所以不充分

(前提就是当3是m的因数而不是n的因数的时候不可以）

(2)13n能平均分配到m个班里

13n能被m整除。这时候注意题中给的限制条件：m<13，所以13不可能是m的一个因数。又因为13是个质数，所以m的每一个因数都得包含在n里面。充分。如果不好理解结合前面的(1)

答案是B

不知道能否讲通