求助 OG13 DS (135题) 求解释 答案解析和题目都没怎么看懂啊 万分感谢！

cynthia129

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 classrooms so that each classroom has the same number of students assigned to it.
答案是B

beyondgmatqin

Basically the question asks whether  (# of students) is a multiple of  (# of classrooms), or whether , because if it is then we would be able to assign students to classrooms so that each classroom has the same number of students assigned to it.

Given: .

(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 --> , from this we can not say whether . For example  indeed might be a multiple of  ( and ) but also it as well might not be ( and ). Not sufficient.

(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 --> , now as given that  then 13 (prime number) is not a multiple of , so  to be an integer the  must be multiple of . Sufficient.

Answer: B.

reirayanqing

我想題目應該是說要將n個學生分配到m個教室，然後 3<m<13<n
所以教室的個數是4~12的整數，學生是14人以上
(1) 可以將3n 個學生平均分配到m個教室 (每個教室學生人數一樣)
但是不代表n個學生可以 平均分配到m個教室
ex:  n=14   m=6 , 則3n=42人可以平均分配到6個教室(每個教室7人)
但是14個學生 無法平均分配到6個教室


(2) 可以將13n 個學生平均分配到m個教室
13n 個人可以平均分配到m個教室，即13n/m 可以整除
13是質數，而m不能等於13，
所以n/m 可以整除
表示 n個學生可以 平均分配到m個教室


答案B

cynthia129

灰常感谢啊，祝你蛇年好运！