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A school admin will assign each student in a group of N [#permalink]

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06 May 2006, 20:16

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B

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E

Difficulty:

75% (hard)

Question Stats:

52% (02:44) correct
48% (01:56) wrong based on 126 sessions

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A school admin 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 question stmt asks whether each of the n students can be assigned to the m classroom so that equal number of students are accomodated in the classrooms.
statement 1: 3n students can be accomodated in the m classrooms, which means that 3n is divisible m. This does not necessarily tell us that n should also be divisible by m. Hence the question string can be either yes or no.
statement 2: 13n should be divisible by m, which implies n should be definately divisible by m. hence above stmt can be answered in yes.

Hence 2nd stmt alone is sufficient to answer the question. Hence B

i) Students can be divided evenly only if 3n/m is a positive integer. If n is odd then 3 n = odd x odd = odd. For m=even nos. statement 1 is not possible but for some m odd nos it is. Hence (i) is insufficient.

ii) Same as (i). 13n will be odd for n odd nos. and maybe possible for some m odd nos. Hence (ii) is also insufficient.

Re: A school administrator will assign each student in a group [#permalink]

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22 Jun 2012, 16:36

Can any one provide a much elaborate solution, did not understand the above's....
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Can any one provide a much elaborate solution, did not understand the above's....

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?

Basically the question asks whether \(n\) (# of students) is a multiple of \(m\) (# of classrooms), or whether \(\frac{n}{m}=integer\), because if it is then we would be able to assign students to classrooms so that each classroom has the same number of students assigned to it.

Given: \(3<m<13<n\).

(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 --> \(\frac{3n}{m}=integer\), from this we can not say whether \(\frac{n}{m}=integer\). For example \(n\) indeed might be a multiple of \(m\) (\(n=14\) and \(m=7\)) but also it as well might not be (\(n=14\) and \(m=6\)). Not sufficient.

(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 --> \(\frac{13n}{m}=integer\), now as given that \(3<m<13\) then 13 (prime number) is not a multiple of \(m\), so \(\frac{13n}{m}\) to be an integer the \(n\) must be multiple of \(m\). Sufficient.

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