I understand the reasoning for (2) being sufficient but can someone explain why (1) is insufficient?
prob #129
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.
(1) - FROM OG
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 sufficient
I don't get this logic since n cannot equal 12?? and n cannot equal 9 either?( both due to 3<m<13<n )
Also, shouldn't N be divisible by M because the when factoring 3N, 3 is not divisible by any number between 4 and 12 ( again due to 3<m<13<n) and therefore N should be divisible by M to make 13n/m an integer?
best,
c
prob #129
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.
(1) - FROM OG
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 sufficient
I don't get this logic since n cannot equal 12?? and n cannot equal 9 either?( both due to 3<m<13<n )
Also, shouldn't N be divisible by M because the when factoring 3N, 3 is not divisible by any number between 4 and 12 ( again due to 3<m<13<n) and therefore N should be divisible by M to make 13n/m an integer?
best,
c
