GWD-16 Q7

weifanmm

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.

                  

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.

Answer:

感觉不是很理解意思， 有同学能解释一下吗？谢谢。

chriszhx

(1)当n=14,m=6时，3n/m=7,不充分

（2)13n/m integer, 3<m<13 and 13 prime number, n/m must be integer, sufficient.

waitting for NN's confirmation

lixinli

My opinion:

First, let's simplify the question:
m, n are integer,  if 3 < m < 13 < n, is n/m an integer?
1. 3n/m is an integer;
2. 13n/m is an integer;
My answer is D;
Because from 1: if 3n/m is an integer, m<>3, then there must be n/m an integer. 1 is sufficient;
Let's look at 2: if 13n/m is an integer, and m<>13, then n/m must be an integer. 2 is sufficient;
Thus D is correct.
Please correct me if I am wrong.