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A school administrator will assign each student in a group

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A school administrator will assign each student in a group

by doclkk » Wed Aug 05, 2009 8:09 am
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.

OA (B)

I guess - I'm not even understanding what this question is asking?

Can someone help?

Thanks
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by karan81 » Wed Aug 05, 2009 8:30 am
The question is asking if m is a factor of n.
Taking statements 1 and 2 together we know that m is a factor of n.
3 and 13 both don't have common factors, so for m to be a factor of both 3n and 13n, m has to be a factor of n.
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Re: A school administrator will assign each student in a gro

by mohitsharda » Wed Aug 05, 2009 8:33 am
doclkk 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.

OA (B)
I guess - I'm not even understanding what this question is asking?

Can someone help?

Thanks
Hi,

The question actually says that you have a total of n students and m rooms. Now you have to assign room to every student.
Also, it is given that 3<m<13<n which basically means that the total number of students are more than 13. The rooms available are between 3 and 13, both excluded.
Now, the question is whether you can allot the rooms in such a way that the number of students in each room are the same.

In other words, it basically means that will m be a factor of n, because only then can we have a situation in which we have an equal number of students in each room.

Now, consider statement 1

according to this m is a factor of 3n.
eg.1: m=6, n =20
3n=60 => each class will have 10 students.
but consider m and n only, we can not distribute them in such a way that we have equal number of students in each room. So, not possible.
eg.2: m=5, n =20
3n=60 => have 12 students in each room.
m and n => have 4 in each room. So, possible.

Hence this is an insufficient condition

Now, take statement 2,
here, m is a factor of 13n
Also, remember m<13,
So this condition implies that m is a factor of n and hence, we will always have a way to distribute equal number of students in each room.
Hence, this is sufficient

So... answer is (B)

Hope this helps
MS
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by drabblejhu » Wed Sep 16, 2009 9:00 pm
Thanks, MS for your explanation. Very helpful.

Toughest part of these DS problems is picking numbers to test (comparable to inequalities). General principle I've gleaned from doing a lot of number testing problems: try to go for pick numbers that will give you insufficient (yes and no to original question).

Pick possible values for Sufficient and Insufficient--that is, pick a pair n and m so that m IS a factor of n AND a pair where m is NOT a factor.

Other thing that makes this problem tricky is you have three criteria to remember for each statement: 1) n > 13, 2) 3 < m < 13, and m = factor of 3n. Need to make sure satisfy all three criteria before you can even use the number pairs.

In this case, easier to start with the number pairs m and n, then makes sure they fit--otherwise, you can get a bit tangled in the criteria. At least I do...

Hopefully this helps! J
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by palvarez » Sat Oct 24, 2009 4:52 pm
drabblejhu wrote:Thanks, MS for your explanation. Very helpful.

Toughest part of these DS problems is picking numbers to test (comparable to inequalities).
The strategy of "Picking numbers" is helpful when you don't have a better alternative.

In this case, there is a better alternative.

We can rephrase the question thus:

Q: 3 < m < 13 < n, does m | n ?

(1) m | 3n

(2) m | 13 n

( '|' is a sign from number theory books, it indicates the verb "divides)


(1) given m | 3n, m | n only when gcd(3,m) = 1.

In this case, when m = 6, 9, 12, gcd(3,m) <> 1

Insufficient

(2) m | 13n ==> m | n when gcd (13,m ) = 1

note that m < 13 and the latter is prime, therefore (13,m) = 1.

Sufficient.


Lessons to learn:

(1) GMAT tries to complicate things by setting up a word problem.

(2) the chance of getting right with picking numbers is 50-50 under pressure.
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by varundaga05 » Thu May 27, 2010 4:59 pm
Hi,

using GCD was not clear. why we are using GCD.
Can you please explain a bit further with some other example or just elaborate a bit more
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by liferocks » Thu May 27, 2010 5:10 pm
varundaga05 wrote:Hi,

using GCD was not clear. why we are using GCD.
Can you please explain a bit further with some other example or just elaborate a bit more
by GCD what is meant that if m=3kn where k is any integer,n will be divisible by m if 3 is not divisible by n i.e they are co-prime or gcd(3,m)=1.
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by Patrick_GMATFix » Fri May 28, 2010 12:54 pm
This is #128 from the OG 12. Solution & Take-away are attached.

-Patrick
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by bluephish » Sun Jun 05, 2011 5:10 pm
best explanation is here:

https://www.urch.com/forums/gmat-data-su ... one-m.html

13n is divisible by m; m is less than 13 so m cannot be divisible by 3; n MUST be divisible by m!
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by cans » Sun Jun 05, 2011 8:54 pm
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.
m classrooms and n students. To have same no. of students in each classroom, n/m should be integer.
a)3n/m is integer. insufficient. n=14,m=6 then 3n/m is integer where as n/m is not. n=15,m=5 both 3n/m and n/m are integers.
b)13n/m is integer. as m<13 and 13 is prime number, thus m!=13 and thus n/m should be integer.
Sufficient
IMO B
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by aftableo2006 » Mon Jun 06, 2011 8:46 pm
this is a very difficult question finding it tough to understand
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by siddhans » Wed Jun 08, 2011 9:41 pm
How do you know if m should divide n OR n should divide m?
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by Geva@EconomistGMAT » Wed Jun 08, 2011 10:01 pm
siddhans wrote:How do you know if m should divide n OR n should divide m?
Putting aside the fact that you need to assign n students to m classrooms (so divide n by m), there is also the fact that n is greater than m (3 < m < 13 < n) and in fact is the greatest number. If the question was phrased so that n must divide m, the result would always be a fraction (dividing a small positive number by a greater positive number will always yield a fraction), and the answer to the question stem would be "no" regardless of what the statements say. In a DS question, the question stem is never sufficient to answer the question alone - you will always need the statement(s) to have any hope of answering the question.
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by siddhans » Wed Jun 08, 2011 10:12 pm
mohitsharda wrote:
doclkk 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.

OA (B)
I guess - I'm not even understanding what this question is asking?

Can someone help?

Thanks
Hi,

The question actually says that you have a total of n students and m rooms. Now you have to assign room to every student.
Also, it is given that 3<m<13<n which basically means that the total number of students are more than 13. The rooms available are between 3 and 13, both excluded.
Now, the question is whether you can allot the rooms in such a way that the number of students in each room are the same.

In other words, it basically means that will m be a factor of n, because only then can we have a situation in which we have an equal number of students in each room.

Now, consider statement 1

according to this m is a factor of 3n.
eg.1: m=6, n =20
3n=60 => each class will have 10 students.
but consider m and n only, we can not distribute them in such a way that we have equal number of students in each room. So, not possible.
eg.2: m=5, n =20
3n=60 => have 12 students in each room.
m and n => have 4 in each room. So, possible.

Hence this is an insufficient condition

Now, take statement 2,
here, m is a factor of 13n
Also, remember m<13,
So this condition implies that m is a factor of n and hence, we will always have a way to distribute equal number of students in each room.
Hence, this is sufficient

So... answer is (B)

Hope this helps
How can 3/m be an integer in 1st case? Lets say m = 4 (since we are given 3<m<13)

so 3/4 is not an integer .
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by siddhans » Wed Jun 08, 2011 10:29 pm
Geva@MasterGMAT wrote:
siddhans wrote:How do you know if m should divide n OR n should divide m?
Putting aside the fact that you need to assign n students to m classrooms (so divide n by m), there is also the fact that n is greater than m (3 < m < 13 < n) and in fact is the greatest number. If the question was phrased so that n must divide m, the result would always be a fraction (dividing a small positive number by a greater positive number will always yield a fraction), and the answer to the question stem would be "no" regardless of what the statements say. In a DS question, the question stem is never sufficient to answer the question alone - you will always need the statement(s) to have any hope of answering the question.
Okay, also how in some of the exmples they have chosen n to be < 13. Dont we need to always choose n>13 to test statement 1 and 2? since 3<m<13<n which implies n is always greater than 13?
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