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On a particular exam, the boys in a history class averaged 86 points and the girls in the class averaged 80 points. If the overall class average was 82 points, what was the ratio of boys to girls in the class?

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30 Jun 2015, 06:07

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On a particular exam, the boys in a history class averaged 86 points and the girls in the class averaged 80 points. If the overall class average was 82 points, what was the ratio of boys to girls in the class?

A. 1:4 B. 1:3 C. 1:2 D. 2:1 E. 3:1

Solution -

Given that Boys average is 86 and Girls average is 80 points. Total average is 82 points.

(86B+80G)/(B+G) = 82 --> 4B=2G --> B/G = 1/2. ANS C.
_________________

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30 Jun 2015, 07:13

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Bunuel wrote:

On a particular exam, the boys in a history class averaged 86 points and the girls in the class averaged 80 points. If the overall class average was 82 points, what was the ratio of boys to girls in the class?

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30 Jun 2015, 10:03

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Bunuel wrote:

On a particular exam, the boys in a history class averaged 86 points and the girls in the class averaged 80 points. If the overall class average was 82 points, what was the ratio of boys to girls in the class?

A. 1:4 B. 1:3 C. 1:2 D. 2:1 E. 3:1

Kudos for a correct solution.

Solution: We can use the X method to solve similar questions

On a particular exam, the boys in a history class averaged 86 points and the girls in the class averaged 80 points. If the overall class average was 82 points, what was the ratio of boys to girls in the class?

The boys in the class scored 4 points higher on average than the entire class. The boys have a + 4 differential. Similarly, the girls scored 2 points lower on average than the class. They have a - 2 differential. You need to balance out the differentials:

b*(+4) + g*(-2) = 0

If b = 1 and g = 2, the equation will be true. Thus, the ratio of boys to girls is 1:2.

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10 Dec 2016, 10:26

Here is my solution for this one--> Sum(Boys scores)=\(86*B\) Sum(Girls scores)=\(80*G\) Total -> \(86*B+80*G = 82*B+82*G\) Hence \(4B=2G => \frac{B}{G}=\frac{1}{2}\)

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07 Aug 2017, 09:26

ashokk138 wrote:

Bunuel wrote:

On a particular exam, the boys in a history class averaged 86 points and the girls in the class averaged 80 points. If the overall class average was 82 points, what was the ratio of boys to girls in the class?

A. 1:4 B. 1:3 C. 1:2 D. 2:1 E. 3:1

Kudos for a correct solution.

Solution: We can use the X method to solve similar questions

B...................G 86................80

..........82........

2..................4

Hence, Boys: Girls => 2: 4 => 1:2

Option C

I have come across this - "X - method" in several posts on this forum. Is there a theory/article describing this? Seems like a sure shot approach to weighted averages. Can someone point me to the resource, please?

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