(問題) 天山04-28

[flyflyy]

A school administrator will assign each student in a group of n students to one of m classmates. 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 classrooms so that each classroom has the same number of students assigned to it.

答案為b.請問為什麼1不行阿??!! 感恩~~

[scujean]

這題在問N可否被m整除
cd’s ans
條件一其實就是3N能被M整除。因爲3<M<13<N，舉例說明，有9個教室，18個學生（18=3*6），18能被9整除，但是6不能被9整除，不充分；
條件二其實就是13N能被M整除。因爲3<M<13<N，13N能被M整除，所以N肯定是M的倍數。也就是說N能被M整除，單獨充分。
所以選B