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A school administrator will assign each student in a group [#permalink]
22 Dec 2004, 09:39

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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.

The stem looks like this:
3 < m < 13
n <13
and Is n= mK1?

1) 3n = mK2
=> n = m/3 *K2
If m/3 is an integer, it will satisfy the question stem.
m/3 will be an integer only if m=6,9,,12. For the other, it won't
So not an answer as it varies.

2) 13n= mK3
=> n = m/13 *K2
If m/13 is an integer, it will satisfy the question stem.
Since m<13, m/13 will never be an integer.
So this will never provide an answer

If there are less than 13 classrooms, but 13n could be divided amongst them, then the number of students would have do be divisible by the number of classrooms. If it weren't, then the number 13 would have to be divisible by the number of classroom, which isn't possible since there are less than 13 classrooms. So we know that n must be divisible by m.

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