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The average (arithmetic mean) score of a class was 70. If the boys’ av

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Bunuel
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The average (arithmetic mean) score of a class was 70. If the boys’ av [#permalink] New post   25 Sep 2018, 04:48
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The average (arithmetic mean) score of a class was 70. If the boys’ average was 65 and that of girls’ was 80, what could be the number of boys and girls, respectively, in the class?


(A) 8; 9
(B) 18; 27
(C) 9; 18
(D) 18; 9
(E) 5; 2
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D
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Re: The average (arithmetic mean) score of a class was 70. If the boys’ av [#permalink] New post   25 Sep 2018, 04:55
Bunuel wrote:
The average (arithmetic mean) score of a class was 70. If the boys’ average was 65 and that of girls’ was 80, what could be the number of boys and girls, respectively, in the class?


(A) 8; 9
(B) 18; 27
(C) 9; 18
(D) 18; 9
(E) 5; 2



Let the number of boys and girls be B and G respectively.

Using weighted average formula, we will get \(\frac{65B + 80G}{B + G} = 70\)

\(65B + 80G = 70B + 70G\) -> \(10G = 5B\) -> \(\frac{G}{B} = \frac{5}{10} = \frac{1}{2}\) -> \(B = 2G\)

Therefore, a possibility for the number of boys and girls is 18;9(Option D)
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Re: The average (arithmetic mean) score of a class was 70. If the boys’ av [#permalink] New post   25 Sep 2018, 05:02
Bunuel wrote:
The average (arithmetic mean) score of a class was 70. If the boys’ average was 65 and that of girls’ was 80, what could be the number of boys and girls, respectively, in the class?


(A) 8; 9
(B) 18; 27
(C) 9; 18
(D) 18; 9
(E) 5; 2



using Allegation Method:

70 - 65 = 5
80 - 70 = 10

Ratio: 10: 5 = 2 : 1 = 18 : 9.

The Best answer is D.
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Re: The average (arithmetic mean) score of a class was 70. If the boys’ av [#permalink] New post   13 Feb 2021, 07:18
I kinda guessed this. Since the Average (70) is more closer to Boys Average(65), this implies there are more boys.

In the answer choice, option D and E has tells us that Boys ratio is more, I calculated E and the average was around 60s.. eliminated it and chose D.
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The average (arithmetic mean) score of a class was 70. If the boys av [#permalink] New post   16 Dec 2022, 06:38
So I get that 18 and 9 are the answers. But if we calculated it and got that B=2G, doesn't it mean that we have 2 girls for every one boy? Kindly clarify why it seems that boys are 18 and girls are 9. Thanks
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The average (arithmetic mean) score of a class was 70. If the boys av [#permalink]
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