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Students Vs Classrooms

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Students Vs Classrooms

by karthikpandian19 » Tue Nov 22, 2011 2:48 pm
A school administrator will assign each student in a group of n students to one of m classroom. 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 the 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 the m classrooms so that each classroom has the same number of students assigned to it.
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by user123321 » Tue Nov 22, 2011 3:12 pm
karthikpandian19 wrote:A school administrator will assign each student in a group of n students to one of m classroom. 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 the 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 the m classrooms so that each classroom has the same number of students assigned to it.
IMO B
1)given 3n/m = integer and we know that 3<m<13
if 3n is div by above values of m we cannot comment whether n/m = integer or not for above values of m. this is because m can be a multiple of 3
for example if n = 16,m = 6 then 3n/m = integer but not n/m. hence insufficient.

2)given 13n/m = integer and we know that 3<m <13.
if we observe closely 13n will be div by m only when n is div by m(since m cannot be a multiple of 13 because of restriction given in the question). hence we can say that m/n = integer. hence sufficient.

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