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# A class has 12 boys and x girls. Average score of boys and

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A class has 12 boys and x girls. Average score of boys and [#permalink]  16 Nov 2011, 06:07
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88% (02:28) correct 11% (00:39) wrong based on 42 sessions
here's an easy question of averages, but let's try to see innovative ways of solving this.

A class has 12 boys and x girls. Average score of boys and girls is 82 and 92 respectively. the average of the whole class is 86, what is the value of x?
a) 6
b) 7
c) 8
d) 10
e) 12

[Reveal] Spoiler:
method one (weighted averages).
ratio of boys:girls = 92-86 : 86-82 = 3:2
i.e. 12 boys, 8 girls.

method two.
each boy scored 4 less than the average OR together scored 12*4 less than the total sum.
each girl scored 6 more than the average OR together scored 6x more than the sum.
6x = 12*4 OR x = 8
[Reveal] Spoiler: OA

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Re: an easy average question, but let's think out of the box [#permalink]  16 Nov 2011, 07:47
12(82)+92x/12+x=86

984+92x/12+x=86

984+92x=86(12+x)

984+92x=1032+86x

X's one side, numbers one side we get,
92x - 86x=1032-984

6x=48
hence, x=8

any faster solutions are appreciated. and kidos if u liked my solution
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Re: an easy average question, but let's think out of the box [#permalink]  16 Nov 2011, 09:28
its 8

solved with the same as the approach you would find above
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Re: an easy average question, but let's think out of the box [#permalink]  16 Nov 2011, 09:49
manalq8 wrote:
12(82)+92x/12+x=86

984+92x/12+x=86

984+92x=86(12+x)

984+92x=1032+86x

X's one side, numbers one side we get,
92x - 86x=1032-984

6x=48
hence, x=8

any faster solutions are appreciated. and kidos if u liked my solution

Agreed with the approach...But you dont have to actually calculate the large numbers...

After you have got : 12(82)+92x/12+x=86

12*82 + 92x = 12*86 + 86x
12(86-82) = (92-86)x
12*4=6x
x=8

I have seen this many a times...You DONT have to do lengthy calculations in 95% of problems. They almost always are divisible by one another which ultimately leads you to a quicker solution.

If you come at a point where you need to do a big calculation, substitute options.
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Kudos [?]: 467 [1] , given: 48

Re: an easy average question, but let's think out of the box [#permalink]  17 Nov 2011, 15:28
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manalq8 wrote:
any faster solutions are appreciated. and kidos if u liked my solution

yes, there is a faster way; see the spoiler in the original post.
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Re: an easy average question, but let's think out of the box [#permalink]  30 Nov 2011, 14:01
It can be solved by weighted averages. 82 is 4 away from 86 and 92 is 6 away from 86. 4/6=2/3. The amount of women must be 2/3 of the amount of men. 2/3 of 12 is 8.
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Re: an easy average question, but let's think out of the box [#permalink]  30 Nov 2011, 16:08
Agree this is a very simple question just takes time to do. Getting one of these at the beginning could really hinder your timing later.
Re: an easy average question, but let's think out of the box   [#permalink] 30 Nov 2011, 16:08
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