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

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Joined: 02 Sep 2009
Posts: 49915
The average (arithmetic mean) score of a class was 70. If the boys’ av  [#permalink]

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25 Sep 2018, 04:48
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Difficulty:

45% (medium)

Question Stats:

67% (00:54) correct 33% (02:07) wrong based on 18 sessions

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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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Re: The average (arithmetic mean) score of a class was 70. If the boys’ av  [#permalink]

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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]

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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.

Re: The average (arithmetic mean) score of a class was 70. If the boys’ av &nbs [#permalink] 25 Sep 2018, 05:02
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