NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 22:08 It is currently 26 Apr 2024, 22:08
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

A school administrator will assign each student in a group

SORT BY:
Date
Kudos
   1   2   3   
Tags:
Difficulty: 805+ Levelx   Divisibility/Multiples/Factorsx   Word Problemsx                                 
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619274 [3]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: A school administrator will assign each student in a group [#permalink] New post   03 Jul 2013, 14:47
3
Kudos
Expert Reply
Quote:
mitmat 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?

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.
.


Hi Bunuel, I could not understand how you inferred whether \frac{n}{m}=integer[/m] from this question stem?

I tried to plug in few values to the question stem to help me understand your line of thought, but I could not. As always, thank you for your great help and support.


The question asks whether we can divide n students into m classes so that each classroom has the same number of students. For example, if there are 20 students and 10 classrooms, then we can assign 2 students to each of the 10 classrooms but if there are 20 students and say 9 classrooms, then we cannot assign (divide) 20 students to 9 classrooms so that each classroom to have the same number of students.

So, we need to determine whether n will be divisible by m, or which is the same whether n/m=integer.

Hope it's clear.
User avatar
B
LucyDang
Manager
Manager
Joined: 24 Mar 2010
Posts: 57
Own Kudos [?]: 384 [4]
Given Kudos: 105
Send PM
GMAT ToolKit User
Re: A school administrator will assign each student in a group [#permalink] New post   25 Jun 2014, 05:05
3
Kudos
1
Bookmarks
Bunuel 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?

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.


Dear Bunuel,

I have concern here.

To explain for (2) 13n/m to be integer, you said that since 13 is prime and 3<m<13 --> 13/m = non-integer --> n/m must be integer, then 13n/m = integer.
So why the same reasoning cannot be applied for (1) as following:
--> (1): 3n/m = integer. Since 3<m<13 and 3 is prime --> 3/m = non-integer --> n/m must be integer, then 3n/m = integer --> sufficient

Please help me to clarify this point. Thank you so much!
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619274 [5]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: A school administrator will assign each student in a group [#permalink] New post   25 Jun 2014, 07:34
3
Kudos
2
Bookmarks
Expert Reply
LucyDang wrote:
Bunuel 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?

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.


Dear Bunuel,

I have concern here.

To explain for (2) 13n/m to be integer, you said that since 13 is prime and 3<m<13 --> 13/m = non-integer --> n/m must be integer, then 13n/m = integer.
So why the same reasoning cannot be applied for (1) as following:
--> (1): 3n/m = integer. Since 3<m<13 and 3 is prime --> 3/m = non-integer --> n/m must be integer, then 3n/m = integer --> sufficient

Please help me to clarify this point. Thank you so much!


Because for (2), m cannot have any factor of 13, thus for \(\frac{13n}{m}\) to be an integer n must be divisible by m.

For (1) m could be a multiple of 3, for example, 6, 9, or 12, and in this case n is not necessary to be divisible by m.
User avatar
reto
Retired Moderator
Joined: 29 Apr 2015
Posts: 717
Own Kudos [?]: 4225 [0]
Given Kudos: 302
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE:Asset Management (Investment Banking)
Send PM
GMAT ToolKit User
Re: A school administrator will assign each student in a group [#permalink] New post   15 Oct 2015, 10:44
Bunuel 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?

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...
User avatar
bhamini1
Intern
Intern
Joined: 16 Jul 2015
Posts: 31
Own Kudos [?]: 12 [0]
Given Kudos: 16
GMAT 1: 560 Q40 V28
GMAT 2: 580 Q37 V32
GMAT 3: 680 Q45 V37
GMAT 4: 690 Q47 V37
Send PM
Re: A school administrator will assign each student in a group [#permalink] New post   05 May 2016, 21:31
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.

Regards,
Bhamini
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11181
Own Kudos [?]: 31970 [1]
Given Kudos: 291
Send PM
Reviews Badge
Re: A school administrator will assign each student in a group [#permalink] New post   05 May 2016, 21:45
1
Kudos
Expert Reply
bhamini1 wrote:
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.

Regards,
Bhamini


Hi,
the statement II tells us that 13N/M is an integer...
But M is less than 13 and 13 is a PRIME number, so there are no common factors of 13 and M..
so ONLY possiblity is that N/M is an integer..
so suff..

But statement I tells us that 3N/M is an integer...
and M is between 3 and 13, so there can be common factors between 3 and M like 3 and 6 and they can be co-primes 3 and 5..
so BOTH possiblity that N/M is an integer and not an integer exist..
so insuff..
avatar
AK125
Intern
Intern
Joined: 09 Apr 2016
Posts: 28
Own Kudos [?]: 21 [0]
Given Kudos: 600
Send PM
Re: A school administrator will assign each student in a group [#permalink] New post   24 Oct 2016, 02:27
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?
User avatar
G
ccooley
Manhattan Prep Instructor
Joined: 04 Dec 2015
Posts: 935
Own Kudos [?]: 1541 [0]
Given Kudos: 115
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Send PM
Re: A school administrator will assign each student in a group [#permalink] New post   24 Oct 2016, 11:09
Expert Reply
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.
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5962
Own Kudos [?]: 13391 [0]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: A school administrator will assign each student in a group [#permalink] New post   25 Oct 2016, 06:19
Expert Reply
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... ;)
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5962
Own Kudos [?]: 13391 [4]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: A school administrator will assign each student in a group [#permalink] New post   25 Oct 2016, 06:27
1
Kudos
3
Bookmarks
Expert Reply
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?


Here is an effort to make the calculation of question a little easy for you

Quote:
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.


It will be possible to assign each student in classrooms equally only if No. of Students (N) is a factor of No. of classrooms (M)
i.g. 20 students can be assigned in 5 room because 5 is factor of 20 but 20 students can't be assigned in 6 room because 6 is not a factor of 20

Question REPHRASED: Is N/M=Integer???

Statement 1: 3N/M is an Integer
Now I wish to prove this statement insufficient therefore I take two cases
Case 1: N=20 and M=5, such that 3N/M is an Integer And also N/M is and Integer
Case 2: N=20 and M=6, such that 3N/M is an Integer BUT N/M is NOT and Integer
NOT SUFFICIENT

[P.S. I could prove this statement Insufficient because I could take denominator as multiple of 3 in order to use the coefficient of N given in numerator]


Statement 2: 13N/M is an Integer
Now I wish to prove this statement insufficient BUT since M<13 and 13 is a prime Number so I can't choose the value for denominator which can have any factor of 13 so for 13N/M to be an Integer N/M must also be an Integer
SUFFICIENT

Answer: option B
User avatar
L
BillyZ
Current Student
Joined: 14 Nov 2016
Posts: 1174
Own Kudos [?]: 20719 [0]
Given Kudos: 926
Location: Malaysia
Concentration: General Management, Strategy
Schools: Sloan '23 (D) Tuck '23 (D) Darden '23 (D) Ross '23 (D) Kellogg '23 (D) Wharton '23 (D) Booth '23 (D) Fuqua '24 (A) Harvard '24 (D) Stanford '24 (D)
GMAT 1: 750 Q51 V40 (Online)
GPA: 3.53
Send PM
GMAT ToolKit User Reviews Badge
Re: A school administrator will assign each student in a group [#permalink] New post   21 May 2017, 23:05
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__

\(\frac{13N}{M}=13(\frac{14}{7})=26\)
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619274 [0]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: A school administrator will assign each student in a group [#permalink] New post   22 May 2017, 00:16
Expert Reply
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?
avatar
B
bhavikagoyal2009
Intern
Intern
Joined: 29 Apr 2017
Posts: 15
Own Kudos [?]: 4 [0]
Given Kudos: 19
Schools: Yale '20 (I)
GMAT 1: 640 Q49 V27
GMAT 2: 730 Q51 V37
Send PM
Reviews Badge
Re: A school administrator will assign each student in a group [#permalink] New post   16 Jun 2017, 09:39
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"?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619274 [0]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: A school administrator will assign each student in a group [#permalink] New post   16 Jun 2017, 10:10
Expert Reply
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?
avatar
B
pruekv
Intern
Intern
Joined: 05 Oct 2019
Posts: 7
Own Kudos [?]: 1 [0]
Given Kudos: 50
Send PM
Re: A school administrator will assign each student in a group [#permalink] New post   19 Apr 2020, 04:26
Hi Bunuel

The wording, "is it possible?", is a little confusing for me. In statement (1) it is also "possible" for n/m to be an integer such as n=15 and m=5. Can you explain how wording, "is it possible?", in the question should be interpreted?

Thank you!
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619274 [1]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: A school administrator will assign each student in a group [#permalink] New post   19 Apr 2020, 04:49
1
Kudos
Expert Reply
pruekv wrote:
Hi Bunuel

The wording, "is it possible?", is a little confusing for me. In statement (1) it is also "possible" for n/m to be an integer such as n=15 and m=5. Can you explain how wording, "is it possible?", in the question should be interpreted?

Thank you!


I think this is explained many times on previous pages. "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?" means whether we CAN divide equally n students in m classrooms, so whether n/m is an integer.
avatar
S
nyadavalwar
Intern
Intern
Joined: 24 Nov 2019
Posts: 23
Own Kudos [?]: 30 [2]
Given Kudos: 12
Send PM
Re: A school administrator will assign each student in a group [#permalink] New post   24 Apr 2020, 12:30
2
Kudos
WoundedTiger wrote:
kelleygrad05 wrote:
I actually worked this problem out

I picked numbers for statement 1 and found it to be insufficient where:

N=15, M=5

3n/m = 45/5=15 ---> 15/5=3 -----> n is divisible by m or n/m is an integer


and N=15, M=9

3n/m = 45/9=5 ---> 15/9=1.3333 -----> n is NOT divisible by m or n/m is NOT an integer


For statement 2 I picked numbers:


N=14

13N = 182

M=4 no M=5 no M=6 no

I got lazy at that point and said 182 is an even number and isn't divisible by 4 or 6, probably nothing will work and chose answer E although unsure.

Upon re-examining it, I see 7 would have worked. However I agree if you can express this algebraically as you did and the OG's answers did, it does become much simpler than picking these vast arrays of numbers.

My problem with your logic (and the OG's) is that finding statement 2 sufficient is based solely on the fact that 13 is a prime number, is 3 not also a prime? What condition allows you to draw this conclusion for the statement that 13n/m = integer that you can't for 3n/m = integer?



Hi kellygrad05,

For St 2 , we are given that 13N/M= Integer and that 3<M<13<N. Now since M, N are integers, we get Value of M can be from (4,5,6...12) and N can be any no greater than 13.Out of the possible values for M, not a single number can divide 13 because it is prime and its only divisor will be 1 and 13. Then for 13N/M to be an integer N has to be a multiple of M or else 13N/M cannot be an Integer which will contradict the given statement itself.

for St1, we are given that 3N/M =Integer and from Q. stem we get 3<M<13<N. Now In possible values of M that can make 3/M in fraction form will be 6,9 and 12 which will result in 3/M value as 1/2,1/3 and 1/4 respectively.

Now if N=15, and M=3 we get 3N/M =15 as integer and N/M also as Integer(Y).
If N=16 and M=3, we get 3N/M=16 as Integer but N/M is not an Integer(N) and hence not sufficient.

Therefore from St 1 we can get 2 ans and hence not sufficient.

Thanks
Mridul




"In 13n/m if you put n=15 and m=5, the you get an integer I think , and it both values satisfies the condition given in the question
avatar
B
theleopride
Intern
Intern
Joined: 12 May 2019
Posts: 45
Own Kudos [?]: 8 [0]
Given Kudos: 56
Location: India
Concentration: Finance, Technology
WE:Operations (Telecommunications)
Send PM
Re: A school administrator will assign each student in a group [#permalink] New post   19 May 2020, 03:42
Bunuel 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?

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 cannot 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.


Bunuel : Statement 2 is not sufficient since n/m may or may not be an integer. If n= 20, m=4 then 13*20/4 gives an integer. The answer to the question is 'Yes'. If, m=4 and n = 21, 13 * 21/4 is not an integer, the answer is a 'No' . Therefore we are getting a 'Yes' and a 'No', so the statement is NOT sufficient. So, we have to combine both statements and check. Please correct me if I am wrong.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619274 [0]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: A school administrator will assign each student in a group [#permalink] New post   19 May 2020, 05:29
Expert Reply
theleopride wrote:
Bunuel 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?

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 cannot 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.


Bunuel : Statement 2 is not sufficient since n/m may or may not be an integer. If n= 20, m=4 then 13*20/4 gives an integer. The answer to the question is 'Yes'. If, m=4 and n = 21, 13 * 21/4 is not an integer, the answer is a 'No' . Therefore we are getting a 'Yes' and a 'No', so the statement is NOT sufficient. So, we have to combine both statements and check. Please correct me if I am wrong.


m = 4 and n = 21 does not satisfy the second statement, so these values are not valid. B is correct.
avatar
B
theleopride
Intern
Intern
Joined: 12 May 2019
Posts: 45
Own Kudos [?]: 8 [0]
Given Kudos: 56
Location: India
Concentration: Finance, Technology
WE:Operations (Telecommunications)
Send PM
Re: A school administrator will assign each student in a group [#permalink] New post   19 May 2020, 05:39
Bunuel 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?

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 cannot 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.


Bunuel : Statement 2 is not sufficient since n/m may or may not be an integer. If n= 20, m=4 then 13*20/4 gives an integer. The answer to the question is 'Yes'. If, m=4 and n = 21, 13 * 21/4 is not an integer, the answer is a 'No' . Therefore we are getting a 'Yes' and a 'No', so the statement is NOT sufficient. So, we have to combine both statements and check. Please correct me if I am wrong.[/quote]

m = 4 and n = 21 does not satisfy the second statement, so these values are not valid. B is correct.[/quote]

In that case, I am thinking since the second statement says 'it is possible', it means n/m must be an integer.

In that case statement 1 should be sufficient, because it says 'it is possible', which means, n/m has to be an integer. Where am I going wrong?
GMAT Club Bot
gmatclubot
Re: A school administrator will assign each student in a group [#permalink]
19 May 2020, 05:39
   1   2   3   
Moderator:
Bunuel
Math Expert
92948 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions