GWD 数学 question:

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Q7:

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.

I selected D, but the answer says it is B. Why? Is the answer wrong?

[此贴子已经被作者于2008-8-16 14:43:12编辑过]

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I finally figure it out myself:

3 < m < 13 < n, n=mx? 

(1)3n=ma => n=m(a/3). if m is a mutiple of 3, m can be 6, 9, 12. we don't know if a will be a mutiple of 3 as well, so we don't know if (a/3) will be an intiger, so we don't know if n can be a mutiple of m. insufficient.   

(2)13n=mb. if m is a mutiple of 13, there is no such m <13. so b must be a multiple of 13, say b=13x so 13n=m(13x), then n=mx, sufficient.