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A college chemistry course is divided into two sections. In section A,

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Bunuel
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A college chemistry course is divided into two sections. In section A, [#permalink] New post   29 Jun 2017, 04:23
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A college chemistry course is divided into two sections. In section A, the average score in the final examination was 92. In section B, the average score in the final examination was 84. If the average score of all 40 students in the course was 89, how many students are in section A?

(A) 15
(B) 18
(C) 20
(D) 22
(E) 25
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Re: A college chemistry course is divided into two sections. In section A, [#permalink] New post   29 Jun 2017, 04:28
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Bunuel wrote:
A college chemistry course is divided into two sections. In section A, the average score in the final examination was 92. In section B, the average score in the final examination was 84. If the average score of all 40 students in the course was 89, how many students are in section A?

(A) 15
(B) 18
(C) 20
(D) 22
(E) 25


A : Average : B
92 : 89 : 84

A : B
89-84 : 92-89
5 : 3
If total Students are 40
Then
A : B
25 : 15
E
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Re: A college chemistry course is divided into two sections. In section A, [#permalink] New post   29 Jun 2017, 08:18
Let x be the number of students in Section A and y the number of students in Section B

We know that
-> the average score in the final examination in Section A is 92
-> the average score in the final examination in Section b is 84

From the question stem we can deduce the following :
\(\frac{(92x + 84y)}{(x+y)} = 89\)
\(92x + 84y = 89x + 89y\)
\(3x = 5y\)
\(\frac{x}{y} = \frac{5}{3}\)

Out of 40 students available, there must be 25 students in Section A
and 15 students in Section B(Option E)
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Re: A college chemistry course is divided into two sections. In section A, [#permalink] New post   29 Jun 2017, 09:04
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Bunuel wrote:
A college chemistry course is divided into two sections. In section A, the average score in the final examination was 92. In section B, the average score in the final examination was 84. If the average score of all 40 students in the course was 89, how many students are in section A?

(A) 15
(B) 18
(C) 20
(D) 22
(E) 25

Breakdown and solve -
Quote:
In section A, the average score in the final examination was 92.

Total Score = \(92a\)
Quote:
In section B, the average score in the final examination was 84.

Total Score = \(84b\)
Quote:
If the average score of all 40 students in the course was 89

Total Score is \(40*89 = 3560\)

So, we have \(92a + 84( 40 - a ) = 3560\)

Or, \(92a + 3360 - 84a = 3560\)

Or, \(8a = 200\)

So, \(a = 25\) , thus \(b = 15\)

There were (E) 25 students in section A.
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Re: A college chemistry course is divided into two sections. In section A, [#permalink] New post   09 Nov 2021, 22:07
Hello from the GMAT Club BumpBot!

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Re: A college chemistry course is divided into two sections. In section A, [#permalink]
09 Nov 2021, 22:07
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