riteshgupta wrote:

Can any one provide a much elaborate solution, did not understand the above's....

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-school-admin-will-assign-each-student-in-a-group-of-n-127509.html In case of any questions please post there.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:

PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.

What are GMAT Club Tests?

25 extra-hard Quant Tests

Take a Survey about GMAT Prep - Win Prizes!