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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

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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

by BTGmoderatorLU » Wed Aug 11, 2021 12:41 pm

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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 OA is B
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Re: 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

by Brent@GMATPrepNow » Thu Aug 12, 2021 6:09 am

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BTGmoderatorLU wrote: ↑
Wed Aug 11, 2021 12:41 pm
 Source: Official Guide

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 OA is B
[/quote]Target question: 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

This is a great candidate for rephrasing the target question (more info about rephrasing the target question can be found in this free video:
https://www.gmatprepnow.com/module/gmat- ... cy?id=1100)

In order to be able to assign the same number of students to each classroom, the number of students (n) must be divisible by the number of classrooms (m). In other words, n/m must be an integer.

REPHRASED target question: Is n/m an integer?

Statement 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 to it.

This statement is telling us that the number of students (3n) is divisible by the number of classrooms (m). In other words, 3n/m is an integer.

Does this mean mean that m/n is an integer? No.
Consider these contradictory cases.
case a: m = 4 and n = 20, in which case n/m is an integer.
case b: m = 6 and n = 20, in which case n/m is not an integer.
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 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 to it
This statement tells us that the number of students (13n) is divisible by the number of classrooms (m). In other words, 13n/m is an integer.

The given information tells us that 3 < m < 13 < n. Since m is between 3 and 13, there's no way that 13/m can be an integer. From this, we can conclude that n/m must be an integer.
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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