请教OG12 数学128题

foofie

128. 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.

答案选b，认为（1）不sufficient。并且解释是：
(1) Given that 3n is divisible by m, then n is
divisible by m if m = n = 9 (note that 3n = 27
and m = 9, so 3n is divisible by m) and n is
not divisible by m if m = 9 and n = 12 (note
that 3n = 36 and m = 9, so 3n is divisible by
m); NOT suffi cient.

可是这题不是很明确说了n是大于13的吗？怎么可能是9或者12呢。这个答案的解释看不懂。

我的理解是这个也是充分的。如果说3n可以被m整除，即m是3n的因数，m大于3，所以m不能是3的因数，所以m是因数。。请问我这样的理解有什么不对呢？

fly12404

A錯在
3<M<13
其中6 因子有3 , 2
舉個例子
IF N=14 , M=6  , 14X3=42 , 42可被6整除
BUT 14無法被6整除
IF N=18 , M=6 ,18X3=54 54跟18都可被6整除
有兩種結果  故A選項錯嚕

OG解答我通常不理會  至少他給的ANS是對的

foofie

多谢！