GMAT/留學申請專業顧問 Donz 之資訊交流園地

128.
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 stu\
dents to
one of the m classrooms so that each classroom has the same number of studen\
ts assigned
to it?

     題目就是問 n/m is an integer? (m 是否可以整除 n)

 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.

      3n/m 是整數 --> n/m 不見得是整數

      有可能 m = 3x, n = 7x 除完以後 7/3 化不掉

      但 3n 乘下去之後就可以把 3 化掉了

2)  It is possible to assign each of 13n students to one of m classrooms so
     that each classroom has the same number of students assigned to it.
    
     13n/m = k 是整數 --> n/m 一定是整數

      因為 m 一定不是 13 的倍數 

      n/m 乘上 13 之後 絕對不可能通分 m

      代表 n/m 本來就是整數

    這題是我少數用代數法做題的題目 但不用代數法 實在不好做