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A Mathematics program was tried out in 2 classes in each of 32

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KarunMendiratta
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A Mathematics program was tried out in 2 classes in each of 32 [#permalink] New post   09 Sep 2021, 10:10
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A Mathematics program was tried out in 2 classes in each of 32 elementary schools which involved 37 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3 classes.

Quantity A
Quantity B
Greatest number of teachers who taught 3 classes
13


A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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C
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A Mathematics program was tried out in 2 classes in each of 32 [#permalink] New post   09 Sep 2021, 12:28
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Total number of classes = 2*32=64
37 teachers taught 64 classess implies that at least 37 classes had 1 teacher, and the remaining 27 classes had 2 or 3 teachers. For any teacher to teach 3 classes, the teacher must sign on to 2 additional classes. Hence, \(27/2\) results in 13

Quantity A: 13
Quantity B: 13

answer is C

KarunMendiratta wrote:
A Mathematics program was tried out in 2 classes in each of 32 elementary schools which involved 37 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3 classes.

Quantity A
Quantity B
Greatest number of teachers who taught 3 classes
13


A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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Re: A Mathematics program was tried out in 2 classes in each of 32 [#permalink] New post   09 Nov 2023, 05:41
motion2020 wrote:
Total number of classes = 2*32=64
37 teachers taught 64 classess implies that at least 37 classes had 1 teacher, and the remaining 27 classes had 2 or 3 teachers. For any teacher to teach 3 classes, the teacher must sign on to 2 additional classes. Hence, \(27/2\) results in 13

Quantity A: 13
Quantity B: 13

answer is C

KarunMendiratta wrote:
A Mathematics program was tried out in 2 classes in each of 32 elementary schools which involved 37 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3 classes.

Quantity A
Quantity B
Greatest number of teachers who taught 3 classes
13


A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given



Carcass, why is he dividing by 2? Is there an alternative way of solving this?

Even I got that 27 classes have teachers who are either teaching 2 classes or 3 classes. So, to maximise teachers teaching 3 classes, we will have to consider that no one is teaching 2 classes, then all 27 teach 3 classes? But this doesn't make too much sense. Please help!!
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Re: A Mathematics program was tried out in 2 classes in each of 32 [#permalink] New post   09 Nov 2023, 06:52
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Each teacher took at least 1 class; that means that 37 classes are taken and remaining classes 64-37= 27 classes are divided among 37 teachers again.

If 1 class is given to each teacher, 27 can be divided among 27 teachers, making no teacher teaching 3 classes.

But if 2 classes are given to any of the 37 teachers, we can distribute the classes among 27/2= 13.5= 13 teachers.
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Re: A Mathematics program was tried out in 2 classes in each of 32 [#permalink]
09 Nov 2023, 06:52
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