DS题:
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
有人可以帮忙讲一下思路吗?我看下来没一点想法
谢谢先~
问题:n能否被m整除
条件(1)3n能被m整除
条件(2)13n能被m整除
分析:m可以取6、9、12,这些都是3的倍数,在上述m值情况下,3n能被m整除是3在发挥因子约分的作用,比如说3×14/6=3×2×7/6=7,但是14/6则不能整除。
而13与m的所有取值并无因子上的联系,所以当13n能被m整除时,发挥因子约分作用的只可能是n,所以n一定能被m整除
谢谢,把题目简化看起来果然一目了然
太感谢了
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