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.
_________________
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
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
close
47% (02:16) correct
