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In a high school class, the average score on a test among girls was 92

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In a high school class, the average score on a test among girls was 92  [#permalink]

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New post 25 Oct 2018, 03:59
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D
E

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Question Stats:

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In a high school class, the average score on a test among girls was 92.6, while the average score among boys was 83.0. The average score for the class was 89. If there are 16 students in the class, which of the following represents the relationship between the number of girls (g) and boys (b) in the class?


A. g+4=b

B. g+2=b

C. g=b

D. g - 2=b

E. g - 4=b

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Re: In a high school class, the average score on a test among girls was 92  [#permalink]

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New post 25 Oct 2018, 04:39
Bunuel wrote:
In a high school class, the average score on a test among girls was 92.6, while the average score among boys was 83.0. The average score for the class was 89. If there are 16 students in the class, which of the following represents the relationship between the number of girls (g) and boys (b) in the class?


A. g+4=b

B. g+2=b

C. g=b

D. g - 2=b

E. g - 4=b


Average of Girls = 92.6
Number of girls = g
i.e. Total score of all girls = 92.6*g

Average of Boys = 83
Number of girls = b
i.e. Total score of all girls = 83*b

Also, b+g = 16

And, total of entire class = 89*(b+g) = 92.6g + 83b

i.e. 6b = 3.6g
i.e. b = (3/5)g

b+g = 16
i.e. (3/5)g + g = 16
i.e. g = 10
and b = 6

i.e. b = g-4

Answer: Option E
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Re: In a high school class, the average score on a test among girls was 92  [#permalink]

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New post 30 Oct 2018, 11:25
Bunuel wrote:
In a high school class, the average score on a test among girls was 92.6, while the average score among boys was 83.0. The average score for the class was 89. If there are 16 students in the class, which of the following represents the relationship between the number of girls (g) and boys (b) in the class?


A. g+4=b

B. g+2=b

C. g=b

D. g - 2=b

E. g - 4=b


Since the overall class average (89) is closer to the girls’ average (92.6) than it’s to the boys’ average (83), there must be more girls than boys. This narrows to choice D or E as the correct answer. If choice D is the correct answer, then we have:

b + g = 16

g - 2 + g = 16

2g = 18

g = 9

So b = 16 - 9 = 7. Now let’s check the overall class average by calculating the weighted average:

Average = (9 x 92.6 + 7 x 83)/16 = 1414.4/16 = 88.4

Answer choice D does not yield the given overall class average of 89. So the correct answer must be E.

Answer: E
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Re: In a high school class, the average score on a test among girls was 92  [#permalink]

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New post 30 Oct 2018, 11:32
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G/B = Avg score of class- Avg of boy score/ avg score of girl - Avg score of class
= 89-83/ 92.6-89
= 6/3.6
= 5/3
Total 16 student so 10 girl and 6 boys.

G-4= B
Option E
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Re: In a high school class, the average score on a test among girls was 92   [#permalink] 30 Oct 2018, 11:32
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