GMAT申友数据充分DS题库-A school administrator will assign each student in a group of n students to one of m classrooms. If-GWD

本题由chris提供

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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

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答案：

某个学校

领导安排n个学生到m个教室，如果3<m<13<n，那么是否这m个教室里每个教室的人数是不是都一样？其实就是问n能不能被m整除。

条件一：如果安排3n个学生到m个教室，那么可以做到每个教室里的人数都一样。

条件二：如果安排13n个学生到m个教室，那么可以做到每个教室里的人数都一样。
解析：

条件一说明3n能够被m整除，那么m可能值有4,5,6,7,8,9,10,11,12，其中6,9,12均是3的倍数，3n/m可约分，导致3n/m的整除与n/m的整除之间没有必然联系。例如，m=6，n=16，3n/m=8，但是n/m=8/3，不能整除，所以（1）不充分；

条件二说明13n能够被m整除，那么m可能值有4,5,6,7,8,9,10,11,12，没有13这个因子，且13是质数，所以13n/m无论m为何值均不能将13约分下去，这就导致了若想13n/m是整数，则n/m必须是整数。所以（2）充分。

选B

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