NP: OG DS 135
a school administrator will assign each student in a group of n students to one of m classrooms, if 3<m<13<, 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 to it
2. 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
How to solve this Q?
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Refer to the following post >> https://www.beatthegmat.com/complicated- ... tml#608062
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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 itsanaa.rizwan wrote:NP: OG DS 135
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 to it
2. 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
NOTE: you were missing a small part of the question, which I added above in green.
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 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 target question with certainty, statement 2 is SUFFICIENT
Answer = B
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I totally get Statement 1 but wha is Statement 2 sufficient?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 target question with certainty, statement 2 is SUFFICIENT
Could you please explain it via a case Scenario like in Statement 1?
Why can we conclude this?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.
Thanks a lot!
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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 (3n) is divisible by the number of classrooms (m).
Implication:
(3n)/m = 3(n/m) = integer.
Case 1: n/m = integer
It's possible that n=16 and m=4, with the result that n/m = 16/4 = 4.
Here, 3(n/m) = 3(16/4) = 12.
Case 2: n/m = k/3, where k is not a multiple of 3
In this case, since n/m = k/3, m must be a multiple of 3.
It's possible that n=14 and m=6, with the result that n/m = 14/6 = 7/3.
Here, 3(n/m) = 3(7/3) = 7.
Since n/m is an integer in Case 1 but not in Case 2, 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 (13n) is divisible by the number of classrooms (m).
Implication:
(13n)/m = 13(n/m) = integer.
Case 3: n/m = integer
It's possible that n=16 and m=4, since 16/4 = 4.
Here, 13(n/m) = 13(16/4) = 52.
Case 4: n/m = k/13, where k is not a multiple of 13
In this case, since n/m = k/13, m must be a multiple of 13.
Not possible, since 3 < m < 13.
Since only Case 3 is possible, n/m = integer.
SUFFICIENT.
The correct answer is B.
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Rephrased Question : If 3 < m < 13 < n, is n/m an integer?
Statement 1) 3n/m is an integer.
if n = 18 and m = 6, then 3n/m is an integer and also n/m is an integer.
On the other hand if n = 20 and m = 6, then 3n/m is an integer but n/m is NOT an integer.
Inconsistent solution therefore
Not sufficient
Statement 2) 13n/m is an integer.
3 < m < 13 < n implies that m lies between 3 and 13 but is not 13, so 13n/m can be integer only if n/m is an integer.
Sufficient
Answer: Option B
Statement 1) 3n/m is an integer.
if n = 18 and m = 6, then 3n/m is an integer and also n/m is an integer.
On the other hand if n = 20 and m = 6, then 3n/m is an integer but n/m is NOT an integer.
Inconsistent solution therefore
Not sufficient
Statement 2) 13n/m is an integer.
3 < m < 13 < n implies that m lies between 3 and 13 but is not 13, so 13n/m can be integer only if n/m is an integer.
Sufficient
Answer: Option B
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