Source: OG-12
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.
I don't get OG's explanation for this one. Can anyone explain how to solve it?
A school administrator...
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Elena89 wrote:Source: OG-12
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.
I don't get OG's explanation for this one. Can anyone explain how to solve it?
The question can be rephrased as "If 3 < m < 13 < n, is n/m an integer?"
(1) The information in statement 1 implies that 3n/m is an integer. Now we have find whether n/m is an integer.
Given that 3 < m < 13 < n, if n = 36 and m = 6, then n/m is an integer.
On the other hand if n = 40 and m = 6, then n/m is not an integer.
Since we don't get a unique answer, so (1) is NOT SUFFICIENT.
(2) According to the statement, 13n/m is an integer.
3 < m < 13 < n implies that m lies between 3 and 13 but is not 13, so 13n/m can be integer only if n/m is an integer.
So, (2) is SUFFICIENT.
The correct answer is B.
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