greatest possible numberand the least possible number!!!

apoorva.srivastva wrote:If 37 teachers are to be assigned to 64 classes in such a way that each of teacher
teaches at least one class and at most three classes. What are the greatest possible numberand the least possible number of the teachers who teach three classes?
(A) 14,0
(B) 13, 1
(C) 13, 0
(D) 12, 2
(E) 12, 1

OA is C

explain for the greatest!!

For the greatest, first assign 1 class to each teacher (to satisfy that condition)
We now have 27 classes remaining to assign.
To maximize the number of teachers who get 3 classes, start giving 2 additional classes to each teacher.
We have 27 classes to distribute, and we are giving each teacher 2 additional classes. We can do this 13 (and 1/2 ) times.
We now have 13 teachers with 3 classes.

apoorva.srivastva wrote:If 37 teachers are to be assigned to 64 classes in such a way that each of teacher
teaches at least one class and at most three classes. What are the greatest possible numberand the least possible number of the teachers who teach three classes?
(A) 14,0
(B) 13, 1
(C) 13, 0
(D) 12, 2
(E) 12, 1

OA is C

explain for the greatest!!

Let a, b, and c be the number of teachers who teach exactly one class, two classes, and three classes, respectively. We can create the equations:

a + b + c = 37

and

a + 2b + 3c = 64

Since 64/3 = 21 R 1, we see that c ≤ 21. However, by looking at the answer choices, we can see that c is actually much less than 21. So let’s start with c = 14.

If c = 14, the two equations above reduce to a + b = 23 and a + 2b = 22, respectively. However, we see that this is not possible since the value of a + b can’t be more than the value of a + 2b.

Now let’s try c = 13.

If c = 13, the two equations reduce to a + b = 24 and a + 2b = 25, respectively. We see that this is possible since a = 23 and b = 1 would satisfy both equations.

So 13 is the maximum value of c. Let’s now determine the minimum value of c. If c = 0, then we have a + b = 37 and a + 2b = 64. We see that this is possible since a = 10 and b = 27 would satisfy both equations.

Answer: C