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A class comprises 40 students and is divided into two sections. In sec

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Bunuel
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A class comprises 40 students and is divided into two sections. In sec [#permalink] A class comprises 40 students and is divided into two sections. In sec   14 Apr 2021, 08:15
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15% (low)

Question Stats:

85% (01:52) correct 15% (02:12) wrong based on 79 sessions
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A class comprises 40 students and is divided into two sections. In section A, the average score in a test was 85. In section B, the average score in the test was 80. If the average score of the class in the test was 82, how many students are in section A?

(A) 12
(B) 14
(C) 16
(D) 20
(E) 22
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C
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Re: A class comprises 40 students and is divided into two sections. In sec [#permalink] A class comprises 40 students and is divided into two sections. In sec   14 Apr 2021, 08:22
Given: A class comprises 40 students and is divided into two sections. In section A, the average score in a test was 85. In section B, the average score in the test was 80.
Asked: If the average score of the class in the test was 82, how many students are in section A?

Let the students in section A be x students.
Students in section B = 40 - x

Average score in the test = 82*40 = 3280 = 85x + 80(40-x) = 3200 + 5x
5x = 80
x = 16


IMO C
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Re: A class comprises 40 students and is divided into two sections. In sec [#permalink] A class comprises 40 students and is divided into two sections. In sec   21 Apr 2021, 07:28
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Bunuel wrote:
A class comprises 40 students and is divided into two sections. In section A, the average score in a test was 85. In section B, the average score in the test was 80. If the average score of the class in the test was 82, how many students are in section A?

(A) 12
(B) 14
(C) 16
(D) 20
(E) 22

Solution:

We can create the equation where x is the number of students in section A:

[85x + 80(40 - x)] / 40 = 82

85x + 3200 - 80x = 3280

5x = 80

x = 16

Answer: C
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A class comprises 40 students and is divided into two sections. In sec [#permalink] A class comprises 40 students and is divided into two sections. In sec   22 Dec 2023, 04:40
Class A avg = 85
Class B avg = 80
Total class avg= 82

Since it's a weighted avg question, and 82 is "closer" to 80, then we know that Class A has less students.

----2x ---------------3x
|-----------|---------------------|
80---------82 -------------------85

A+B = 5X
40=5x
x=40/5=8

Class A (as previously mentioned it's smaller) = 8 (2) = 16 (answer C)
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Re: A class comprises 40 students and is divided into two sections. In sec [#permalink] A class comprises 40 students and is divided into two sections. In sec   22 Dec 2023, 14:02
Simple answer = Total A+B scores / Total A+B number of students = 82
(85A + 80B)/ A+B = 82

85A + 80B = 82A + 82B ==> 3A=2B ==> A= 2B/3

Since A+B = 40 ==> 2B/3 + B = 40 ==> 5B/3= 40, 5B=120
Then B= 24, A= 40-24=16

Answer is 16 (C)
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Re: A class comprises 40 students and is divided into two sections. In sec [#permalink]
22 Dec 2023, 14:02
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