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The average (arithmetic mean) of all scores on a certain algebra test

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The average (arithmetic mean) of all scores on a certain algebra test  [#permalink]

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New post 27 Dec 2015, 09:13
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Question Stats:

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The average (arithmetic mean) of all scores on a certain algebra test was 90. If the average of the 8 male students’ grades was 87, and the average of the female students’ grades was 92, how many female students took the test?

A. 8
B. 9
C. 10
D. 11
E. 12

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Re: The average (arithmetic mean) of all scores on a certain algebra test  [#permalink]

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New post 01 Jan 2016, 10:38
The average (arithmetic mean) of all scores on a certain algebra test was 90. If the average of the 8 male students’ grades was 87, and the average of the female students’ grades was 92, how many female students took the test?


(x+8)90=87*8 + 92x
24=2x
x=12

E. 12
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Re: The average (arithmetic mean) of all scores on a certain algebra test  [#permalink]

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New post 03 Jan 2016, 06:03
Total Marks of male = M
Total Marks of female = F
Number of males = 8
Number of females = f

Given: (M+F)/(8+f) = 90 -------------1
Also given, M/8 = 87 Thus M = 696 ---------2
Also, F/f = 92 thus F = 92 F - --------3

Put 2 and 3 in 1: we get
(696+92f)/(8+f) = 90
solving this we get f = 12

Ans: E
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Re: The average (arithmetic mean) of all scores on a certain algebra test  [#permalink]

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New post 05 Jan 2016, 19:50
2
Hi All,

Weighted Average questions can be solved in a variety of ways - Algebraically, Tactically or Conceptually. Here's a conceptual approach to this question...

We're given a few facts to work with:
1) The average of all scores on a certain algebra test was 90.
2) The average of the 8 male students’ grades was 87
3) The average of the female students’ grades was 92

We're asked how many female students took the Test.

For the sake of ease, we can assume that each male scored 87 on the Test. Since the average score was 90, each of those 'male scores' brought the average DOWN by 3 points....

90 - 87 = 3

Since there were 8 males, that is a total of (8)(3) = 24 points that have to be 'made up for' by the female scores.

If we assume that each female scored 92, then each of those individual scores 'makes up for' 2 of the points....

92 - 90 = 2

We need an answer that will counter the 24 points that we 'dropped'...

24/2 = 12 female test takers needed

Final Answer:

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Re: The average (arithmetic mean) of all scores on a certain algebra test  [#permalink]

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New post 02 Sep 2018, 04:18
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Re: The average (arithmetic mean) of all scores on a certain algebra test &nbs [#permalink] 02 Sep 2018, 04:18
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