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# A school administrator will assign each student in a group

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VP
Joined: 26 Apr 2004
Posts: 1209
Location: Taiwan

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22 Dec 2004, 10:39
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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.
Director
Joined: 19 Nov 2004
Posts: 556
Location: SF Bay Area, USA

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22 Dec 2004, 15:13
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

So B it is.
CIO
Joined: 09 Mar 2003
Posts: 463

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24 Dec 2004, 01:09
I agree with B.

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.

Same logic will not work in number 1.
24 Dec 2004, 01:09
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