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A school administrator will assign each student in a group

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New post 06 Jan 2020, 13:41
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Back to the question ( Simplified version):
If 3<M<13<N, Is it possible that N is DIVISIBLE by M? i.e. is N DIVISIBLE by M?

Statement 1: 3N is DIVISIBLE by M.
Statement 2: 13N is DIVISIBLE by M.


I think it's an easy question now.
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New post 06 Jan 2020, 13:57
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BelalHossain046 wrote:
Back to the question ( Simplified version):
If 3<M<13<N, Is it possible that N is DIVISIBLE by M? i.e. is N DIVISIBLE by M?

Statement 1: 3N is DIVISIBLE by M.
Statement 2: 13N is DIVISIBLE by M.


I think it's an easy question now.


Statement 1: 3N is DIVISIBLE by M
Minimum value N=14, So, 3N=42.
42 is DIVISIBLE by 6 or 7. So, M=6 or M=7.
If M=7, N(=14) is DIVISIBLE by M (YES to MAIN QUESTION)
and, If M=6, N(=14) is NOT DIVISIBLE by M (NO to MAIN QUESTION)
NOT SUFFICIENT.


Statement 2: 13N is DIVISIBLE by M
[13*N][/M]=Completely DIVISIBILITY=Integer
Here, M is less than 13. So, 13 is NOT DIVISIBLE by M [More importantly, 13 & M has NO DIVISIBILITY or REDUCTION/COMMON FACTOR relationship.]
So, N MUST BE DIVISIBLE by M to make [13*N][/M] Completely DIVISIBLE
SUFFICIENT.

My Answer: B
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New post 05 Dec 2012, 01:52
pls, explain why from 13n/m= interger we can have n/m= interger. only by picking numbers we have this conclusion.

why from 13/m=no integer, we can have n/m=integer.

why b is correct. I can get B correct by picking numbers but the reasoning must be clear.
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New post 26 Mar 2013, 10:17
The hardest part of this problem wasn't the math. It was the prompt.

Could someone break it down for me?

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?

"is it possible" to me implied whether we can choose an two values within the problem's given inequality to make n/m an integer, at all which we could for condition 1.
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New post 27 Mar 2013, 08:50
Bunuel wrote:
manimgoindowndown wrote:
The hardest part of this problem wasn't the math. It was the prompt.

Could someone break it down for me?

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?

"is it possible" to me implied whether we can choose an two values within the problem's given inequality to make n/m an integer, at all which we could for condition 1.


There are:
m classrooms where 3 < m < 13 < n.
n students where 3 < m < 13 < n.

We are asked to find whether we can divide equally n students in m classrooms, so whether n/m is an integer.

Does this make sense?



It is possible as you demonstrated in your solutions post to have a situation where premise I will make n/m an integer. However it is also possible that there is a situation where it wont be an integer. I guess I focused on the possibility part. Since its possible I would see I. As correct.
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New post 25 Nov 2013, 14:22
Hi Bunuel!

What about n=24 and m=4?

13*24/4 is an integer, so the divisibility of the classes would still be possible. Awaiting for your reply.
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New post 15 Oct 2015, 09:44
Bunuel wrote:
gwiz87 wrote:
Hi,

I'm new to this forum and I'm hoping someone can help me understand the problem below:

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.

Can you please explain this to me?


Welcome to GMAT Club. Below is a solution for your problem. Please don't hesitate to ask in case of any question.

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.

Answer: B.

Hope its' clear.


I have to start to think like bunuel, amazing! :) So easy if you read it...
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New post 22 Jan 2016, 08:57
gwiz87 wrote:
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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New post 05 May 2016, 20:31
Dear Bunuel,

I am still not clear with the line of reasoning used to prove if n/m is an integer with the given option statements.
For option 1 we are saying that 3n/m could give us an integer and also could not give us an integer basis values of 3<m<13,such as 3*15/5=Integer ,however,3*15/6 is not an integer. Then ,in the second option statement we are considering that since m is greater than 13 then n/m will definitely give us an integer.Why are we changing the thought process for option 2 statement.Even in this case,then 13* 20/5=Integer and 13*21/5 is not an integer.

Please clarify my doubt.

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New post 24 Oct 2016, 01:27
Hey guys,

might be a little bit off topic.
But do I have to understand (be able to solve) these very hard questions if I am aiming for a low 600?
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New post 24 Oct 2016, 10:09
AK125 wrote:
Hey guys,

might be a little bit off topic.
But do I have to understand (be able to solve) these very hard questions if I am aiming for a low 600?


No, you absolutely don't. All you need to do with these problems is be able to recognize them. The only reason to recognize them is so you can guess on them and move on quickly, rather than mistaking them for simpler problems and spending too much time trying to solve before giving up.
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New post 25 Oct 2016, 05:19
AK125 wrote:
Hey guys,

might be a little bit off topic.
But do I have to understand (be able to solve) these very hard questions if I am aiming for a low 600?


Hi AK125

You need to understand whether your strength is Quant or Verbal

If your strength is Quant and your verbal section is weak then you must try all ways to get as many questions as possible however if your Strength area is Verbal then such hard questions can be done away with.

Being an instructor I would atleast suggest or motivate you to try to understand such question. After giving it a try even if you fail to solve such questions in actual test then atleast it will help you build concepts and confidence in cracking comparatively easier question

Getting 650 with aspiration of 600 is not a bad idea anyway... ;)
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New post 21 May 2017, 22:05
Bunuel wrote:
gwiz87 wrote:
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.


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.

Answer: B.


Hi Bunuel,

\(3<M<13<N\)

Possible value of M = 4, 5, 6, 7, 8, 9, 10, 11, 12
Possible value of N = 14, 15, 16, 17, 18, 19

I could not understand the solution for statement (2). \(\frac{13N}{M} = integer\) What if M=4, N=14? \(\frac{13(14)}{4} ≠ integer\). Could you help to explain?

Shall we use the value as below?

M= 7___8___9__
N=14__16__18__

\(\frac{13N}{M}=13(\frac{14}{7})=26\)
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New post 21 May 2017, 23:16
hazelnut wrote:
Bunuel wrote:
gwiz87 wrote:
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.


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.

Answer: B.


Hi Bunuel,

\(3<M<13<N\)

Possible value of M = 4, 5, 6, 7, 8, 9, 10, 11, 12
Possible value of N = 14, 15, 16, 17, 18, 19

I could not understand the solution for statement (2). \(\frac{13N}{M} = integer\) What if M=4, N=14? \(\frac{13(14)}{4} ≠ integer\). Could you help to explain?

Shall we use the value as below?

M= 7___8___9__
N=14__16__18__

\(\frac{13N}{M}=13(\frac{14}{7})=26\)


The question asks whether \(\frac{n}{m}=integer\).

(i) From stem we are given that \(3<m<13<n\).
(ii) From (2) we are given that \(\frac{13n}{m}=integer\).

When testing values, we should choose those which satisfy (i) and (ii) and test whether they give definite answer to the question: is \(\frac{n}{m}=integer\). All values that satisfy (i) and (ii) will give an YES answer to the question "is \(\frac{n}{m}=integer\)?".

Does this make sense?
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New post 16 Jun 2017, 08:39
manimgoindowndown wrote:
Bunuel wrote:
manimgoindowndown wrote:
The hardest part of this problem wasn't the math. It was the prompt.

Could someone break it down for me?

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?

"is it possible" to me implied whether we can choose an two values within the problem's given inequality to make n/m an integer, at all which we could for condition 1.


There are:
m classrooms where 3 < m < 13 < n.
n students where 3 < m < 13 < n.

We are asked to find whether we can divide equally n students in m classrooms, so whether n/m is an integer.

Does this make sense?



It is possible as you demonstrated in your solutions post to have a situation where premise I will make n/m an integer. However it is also possible that there is a situation where it wont be an integer. I guess I focused on the possibility part. Since its possible I would see I. As correct.


Hello. I had the same doubt as you to this question. According to me, the question simply asks "is it possible?", which means that are there any values of n and m which can solve this problem. Since for Statement (1), we do have possible values, shouldn't the answer be "D"?
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New post 16 Jun 2017, 09:10
bhavikagoyal2009 wrote:
Hello. I had the same doubt as you to this question. According to me, the question simply asks "is it possible?", which means that are there any values of n and m which can solve this problem. Since for Statement (1), we do have possible values, shouldn't the answer be "D"?


The point is that m and n are some specific numbers there. So, what the question means is that CAN we 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?
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New post 28 Jul 2017, 00:23
Here is how I thought about it:

From the stem we learn that we need to divide a certain number of students equally to a certain number of classes. It basically implies that we need n (number of students) to be divisible by m (number of classes). If that wasn't the case, we would have "remainder" students that were to be allocated to some classes (and, thus, we would have uneven number of students in all the classses)

Once we understand that, the problem becomes simple plug-and-play:

3 < m < 13 < n

(1) 3N / M - integer

'Yes' case:
3 * 15 / 5 = 9 (thus, 3N is divisible)
15 / 3 = 5 (thus, N is divisible)

'No' case:
3*16 / 6 = 8 (thus, 3N is divisible)
16 / 6 = 2.66666... (thus, N is not divisible)

NOT SUFFICIENT

(2) 13N / M - integer

'No' case:
13 * 14 / 7 = 26 (thus, 13N is divisible)
13/7 = 1.85... (thus, N is not divisible)

'Yes' case:
doesn't exist as 13 is not divisible by any number in between 3 and 13 (exluding both ends)

B; second statement is sufficient!
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New post 13 Dec 2017, 06:12
gwiz87 wrote:
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.


We are given that each student in a group of n students is going to be assigned to one of m classrooms. We are being asked whether it is possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students.

Thus, we need to determine whether n/m = integer.

Statement One Alone:

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.

Statement one is telling us that 3n is evenly divisible by m. Thus, 3n/m = integer.

However, we still do not have enough information to answer the question. When n = 16 and m = 4, n/m DOES equal an integer; however, when n = 20 and m = 6, n/m DOES NOT equal an integer.

Statement Two Alone:

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 statement is telling us that 13n is divisible by m. Thus, 13n/m = integer.

What is interesting about this statement is that we know that n is greater than 13 and that m is less than 13 and greater than 3. Thus, we know that m could equal any of the following: 4, 5, 6, 7, 8, 9, 10, 11, or 12. We see that none of those values (4 through 12) will divide evenly into 13.

Knowing this, we can say conclusively that m will never divide evenly into 13. Thus, in order for m to divide into 13n, m must divide evenly into n.

Answer: B
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New post 21 Sep 2018, 12:53
gwiz87 wrote:
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.


To assign the same number of students to each classroom, the number of students (n) must be divisible by the number of classrooms (m).

Question rephrased: Is \(\frac{n}{m}\) 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 \(\frac{3n}{m}\) 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 \(\frac{3n}{m} = \frac{3*16}{4} = 12\).
In this case, then \(\frac{n}{m} = \frac{16}{4} = 4\), which is an integer.

m=12:
It's possible that m=12 and n=16, with the result that \(\frac{3n}{m} = \frac{3*16}{12} = 4\).
In this case, \(\frac{n}{m}= \frac{16}{12} = \frac{4}{3}\), 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 \(\frac{13n}{m}\) 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 \(\frac{13n}{m}\) to be an integer, m must divide into n, implying that \(\frac{n}{m}\) is an integer.
SUFFICIENT.


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