rohan2345 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 number and 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
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
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