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.
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OG 18, question-390
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vaibhav101
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To assign the same number of students to each classroom, the number of students (n) must be divisible by the number of classrooms (m).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.
Question rephrased: 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 assigned to it.
In other words, the number of students here (3n) is divisible by the number of classrooms (m), implying that 3n/m is an integer.
Since we need to determine whether m will always divide into n, plug in EXTREME values for m.
m=4:
It's possible that m=4 and n=16, with the result that 3n/m = (3*16)/4 = 12.
In this case, then n/m = 16/4 = 4, which is an integer.
m=12:
It's possible that m=12 and n=16, with the result that 3n/m = (3*16)/12 = 4.
In this case, n/m = 16/12 = 4/3, which is NOT an integer.
INSUFFICIENT.
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 assigned to it.
In other words, the number of students here (13n) is divisible by the number of classrooms (m), implying that 13n/m is an integer.
It is not possible that m divides into 13, since the only factors of 13 are 1 and 13, and m must be BETWEEN 3 and 13.
Thus, for 13n/m to be an integer, m must divide into n, implying that n/m is an integer.
SUFFICIENT.
The correct answer is B.
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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 itA 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.
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. In fact, we can't even reduce the 13/m to simpler terms. 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
For even more information on rephrasing the target question, you can read this article I wrote for BTG: https://www.beatthegmat.com/mba/2014/06/ ... t-question
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
