gwd math 15-28

jessicafairy

这一题我有些不明白，哪位可否给我指教以下。谢谢了。

Q28:

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.

jessicafairy

thanks&nbsp;&nbsp; a&nbsp;&nbsp; lot&nbsp; !!!!!!!!

liushuixian

b is the answer

veronica845

I think I made a mistake. (1) should not able to satisfy the question since m can be 6,9 and 12 where they are multiple of 3. Let n=14 (n>13), 3x14/6=7 but 14/6 is not integer. m=9 and m=12 are similar.

From (2), 13n/m = k where none of member of m set can be divided by 13 thus n must be multiple of any member of m set hence (2) alone is sufficient.

What is the correct answer by the way? Thanks.

tomatohuas

 m = {4,5,6,7,8,9,10,11,12} since 3<m<13.

(1)3n/m=k where k is a constant. Since 3 is not a member of m set thus n must be multiple of any member of m set hence n/m must be a constant as well.

(2)Same as above.

My answer to this question is both conditions can satisfy the question individually.