请教 OG 12 DS128

wadsoda

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
请教大家。谢谢了。

zcooles

这道题问的是n个人能不能平均分进m个教室 就是n能不能被m整除

1 说3n可以被m整除 举个例子 当 n=30 m=5 时可以 n整除m成立 当 n=15 m=9 时也可以 但n整除m不成立 因为原题条件 m大于3 所以m可能为3的倍数 所以3n中的3 帮助n 分担了m 中的因子 使得3n可被m整除

2 13n可被m整除 原题条件m小于13 而且13是质数 不会被小于它的数整除 所以 13n被m整除 完全因为n可以被m整除

所以B单独充分

wadsoda

非常感谢，明白了。我对题目中的 is it possible to assign each of the n students to one of the m classrooms特别糊涂，n=30 m=5不就是一种possible吗？

yidiyuehans

楼主，题中能举出反例就可以

m=6,n=20 时， 3n=60 可以被6整除，20不能被6整除

wadsoda

谢谢楼上了。