If 37 teachers are to be assigned to 64 classes in such a way that

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

given data:
1)64 classes
2)37 teachers

to find the maximum number of teachers who can teach 3 classes and to find the least number of teachers who can teach 3 classes

to find least number is easy: out of 64 classes distribute 37 classes to 37 teachers and the remaining 27 classes can be taught by the 27 teachers again hence least number is 0

Now we can safely eliminate options 2,4 and 5
low lets check for option 1:
if 14 teachers teach 3 classes then 14*3=42 classes are over , remaining classes are (64-42)=22
remaining teachers are (37-14)=23 which is more than required
hence option 3 is the correct option!
IMO C

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