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

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If 37 teachers are to be assigned to 64 classes in such a way that  [#permalink]

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New post 18 Sep 2019, 06:22
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A
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C
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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

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If 37 teachers are to be assigned to 64 classes in such a way that  [#permalink]

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New post 18 Sep 2019, 06:57
Approach
Given Info: 37 Teachers, 64 Classes.
Condition 1: each teacher to teach at least 1 class.
Condition 2: each teacher can teach and at max 3 classes.
To find:
Greatest possible number and the least possible number of the teachers who teach three classes?

Greatest possible number
- first 37 classes to all 37 teachers (condition 1)
- next(64-37) 27 classes to be covered - since each teacher can teach at max 3, so to maximize number next 13 teachers can teach 2 classes - covering next 26 classes and remaining one by individual. (condition 2 satisfies)
So greatest possible is 13

least possible number
- first 37 classes to all 37 teachers (condition 1)
- next 27 classes by 27 teachers each. Hence least possible number of teacher who teach 3 classes is 0

Answer: (13, 0) Option C

Hope it is correct. Although i marked it wrong in first attempt.
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Re: If 37 teachers are to be assigned to 64 classes in such a way that  [#permalink]

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New post 18 Sep 2019, 07:25
answers is c and approach is as mentioned above
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Re: If 37 teachers are to be assigned to 64 classes in such a way that  [#permalink]

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New post 23 Sep 2019, 09:37
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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Re: If 37 teachers are to be assigned to 64 classes in such a way that  [#permalink]

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New post 28 Sep 2019, 00:38
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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Re: If 37 teachers are to be assigned to 64 classes in such a way that   [#permalink] 28 Sep 2019, 00:38
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