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.

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

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

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.

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

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.

This is #128 from the OG 12. Solution & Take-away are attached.

-Patrick

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!

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

this is a very difficult question finding it tough to understand

How do you know if m should divide n OR n should divide m?

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.

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 .

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?