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If 20% of a class averages 80% on a test, 50% of the class averages 60

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If 20% of a class averages 80% on a test, 50% of the class averages 60 [#permalink]

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New post 24 Jan 2016, 05:48
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If 20% of a class averages 80% on a test, 50% of the class averages 60% on the test, and the remainder of the class averages 40% on the test, what is the overall class average?

A. 80%
B. 74%
C. 58%
D. 56%
E. 50%
[Reveal] Spoiler: OA

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Kudos [?]: 135163 [0], given: 12664

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Re: If 20% of a class averages 80% on a test, 50% of the class averages 60 [#permalink]

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New post 25 Jan 2016, 15:43
Hi All,

This question is a Weighted Average question with a series of dependent variables. It can be solved Algebraically or by TESTing VALUES.

We're told that:
1) 20% of a class averages 80% on a test
2) 50% of the class averages 60% on the test
3) the remainder of the class averages 40% on the test

We're asked for the overall class average.

Since the class can be broken down into 3 groups, and the first two groups represent 20% and 50%, the third group represents 30% of the class. While it might be tempting to use 100 students when we TEST VALUES, it will actually be easier to use 10 total students instead...

2 students scored 80%
5 students scored 60%
3 students scored 40%

(2)(80) + 5(60) + 3(40) =
160 + 300 + 120 =
580

580/10 students = 58 --> 58% average

Final Answer:
[Reveal] Spoiler:
C


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Kudos [?]: 3662 [0], given: 173

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If 20% of a class averages 80% on a test, 50% of the class averages 60 [#permalink]

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New post 25 Jan 2016, 20:11
Bunuel wrote:
If 20% of a class averages 80% on a test, 50% of the class averages 60% on the test, and the remainder of the class averages 40% on the test, what is the overall class average?

A. 80%
B. 74%
C. 58%
D. 56%
E. 50%


Apart from the calculations method we can get down to two choices by merely looking at the info..
20%-80%marks..
50%-60% marks..
30%-40%marks..


1)Here once we see the max concentration is 60% and the other two sets are at equidistant from 60% with slight bias towards 40%.
so our answer has to be slightly less than 60..
A and B are straightway out as they are >60.. E too is far off ..
finally we are left with only C and D.. now we are left with only 2 to answer..

2)Lets do it by weighted average..
first take weighted average for outer values..
20%-80%marks..
30%-40%marks..

the difference 80-40=40 is divided into five equal parts (due to ratio 20:30)..
so each part is 8.
since 40% has more weight we will add lesser of 2 parts: 3 parts to it..
40 + 2*8=56..
now we have two set of people..
50%-56%marks..
50%-60% marks..

equal numbers for 60 and 56, so ans (60+56)/2=58
C
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Re: If 20% of a class averages 80% on a test, 50% of the class averages 60 [#permalink]

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New post 10 Oct 2017, 09:05
Total Marks = (20x80)+(50x60)+(30x40) = 5800
Total Class weight = 100

Weighted avg = 5800/100 = 58

Kudos [?]: 4 [0], given: 78

Re: If 20% of a class averages 80% on a test, 50% of the class averages 60   [#permalink] 10 Oct 2017, 09:05
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