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A class has 12 boys and x girls. Average score of boys and girls is 82

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A class has 12 boys and x girls. Average score of boys and girls is 82  [#permalink]

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New post 16 Nov 2011, 05:07
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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

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

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Re: A class has 12 boys and x girls. Average score of boys and girls is 82  [#permalink]

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New post 16 Nov 2011, 06:47
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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: A class has 12 boys and x girls. Average score of boys and girls is 82  [#permalink]

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New post 16 Nov 2011, 08:49
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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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Re: A class has 12 boys and x girls. Average score of boys and girls is 82  [#permalink]

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New post 30 Nov 2011, 13:01
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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: A class has 12 boys and x girls. Average score of boys and girls is 82  [#permalink]

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New post 30 Nov 2011, 15:08
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.
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Re: A class has 12 boys and x girls. Average score of boys and girls is 82  [#permalink]

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New post 09 Dec 2016, 21:20
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Re: A class has 12 boys and x girls. Average score of boys and girls is 82  [#permalink]

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New post 09 Feb 2018, 06:44
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Re: A class has 12 boys and x girls. Average score of boys and girls is 82 &nbs [#permalink] 09 Feb 2018, 06:44
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