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?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?

Answer:Hence to get same number of students in each classroom,the sufficient condition is that assign 13n students to each classroom.Step-by-step explanation:Given:There are m classrooms and n be the students 3<m<13<n.To Find:Whether it is possible to assign each of n students to one of m classrooms with same no.of students.Solution:This problem is related to p/q form  has to be integer in order to get same no of students assigned to the classroom.As similar as ,n/m ratioSo 1st condition is that,If it is possible to assign the n/m must be integer and n should be multiple of m,when we assign 3n students to m classrooms ,we cannot say that 3n/m= integer so that  n is greater than 13 i.e n=14 and m=6 hence they are not multiple of each other so they will not make same students in each classrooms.Otherwise,n=14 and m=7 they will give same number but this condition is not sufficient condition to assign the student.So 2nd condition is that ,When we assign 13n students to m classrooms, as 13 is prime number and 3<m<13 which implies the 13n/m to be integer so n and m must be multiple of each other.Suppose n=20 and m=5 classroomsthen 13*20=260 ,260/5=52 students in each classroom,