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At a certain summer camp, the average age of the boys attending is 11.

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At a certain summer camp, the average age of the boys attending is 11.  [#permalink]

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New post 18 May 2017, 00:14
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At a certain summer camp, the average age of the boys attending is 11.4 years old and the average age of the girls attending is 12.6 years old. If the average age of all the boys and girls attending the camp is 11.8 years old, what percentage of them are boys?

A. 20%
B. 33 1/3%
C. 50%
D. 66 2/3%
E. 80%

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At a certain summer camp, the average age of the boys attending is 11.  [#permalink]

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New post Updated on: 18 May 2017, 04:09
Bunuel wrote:
At a certain summer camp, the average age of the boys attending is 11.4 years old and the average age of the girls attending is 12.6 years old. If the average age of all the boys and girls attending the camp is 11.8 years old, what percentage of them are boys?

A. 20%
B. 33 1/3%
C. 50%
D. 66 2/3%
E. 80%


Let number of Boys be B and Number of girls be G

Average of Boys = 11.4

Average of Girls = 12.6

Total Of all boys and girls = 11.4B + 12.6G = 11.8 (B+G)

i.e. B/G = 0.8/0.4 = 2/1

Boys as percentage of all kids = 2/(1+2) = 2/3 = 66.66%

Answer: Option D

P.S. You could use weighted average method (star method) as well but prefer the equation method which is applicable to all questions of average more easily
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Originally posted by GMATinsight on 18 May 2017, 01:29.
Last edited by GMATinsight on 18 May 2017, 04:09, edited 1 time in total.
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Re: At a certain summer camp, the average age of the boys attending is 11.  [#permalink]

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New post 18 May 2017, 04:06
GMATinsight wrote:
Bunuel wrote:
At a certain summer camp, the average age of the boys attending is 11.4 years old and the average age of the girls attending is 12.6 years old. If the average age of all the boys and girls attending the camp is 11.8 years old, what percentage of them are boys?

A. 20%
B. 33 1/3%
C. 50%
D. 66 2/3%
E. 80%


Let number of Boys be B and Number of girls be G

Average of Boys = 11.4

Average of Girls = 12.6

Total Of all boys and girls = 11.4B + 12.6G = 11.8 (B+G)

i.e. B/G = 0.4/0.8 = 1/2

Boys as percentage of all kids = 1/(1+2) = 1/3 = 33.33%

Answer: Option B

P.S. You could use weighted average method (star method) as well but prefer the equation method which is applicable to all questions of average more easily




11.8 B + 11.8 G = 11.4 B +12.6 G

=> 0.4 B= 0.8 G
=> B = 2 G
=> B/G = 2:1 OR b/TOTAL= 2/3 I.E 66.2/3 %

Please tell em where I am making a mistake
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Re: At a certain summer camp, the average age of the boys attending is 11.  [#permalink]

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New post 18 May 2017, 05:16
Bunuel wrote:
At a certain summer camp, the average age of the boys attending is 11.4 years old and the average age of the girls attending is 12.6 years old. If the average age of all the boys and girls attending the camp is 11.8 years old, what percentage of them are boys?

A. 20%
B. 33 1/3%
C. 50%
D. 66 2/3%
E. 80%



B/ G = (12.6-11.8) / (11.8-11.4)

B/G = 0.8/ 0.4
B/G = 2/1
%age of Boys= 2/ (2+1) *100 = 200/3

Ans D
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Re: At a certain summer camp, the average age of the boys attending is 11.  [#permalink]

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New post 18 May 2017, 05:18
varundixitmro2512 wrote:
GMATinsight wrote:
Bunuel wrote:
At a certain summer camp, the average age of the boys attending is 11.4 years old and the average age of the girls attending is 12.6 years old. If the average age of all the boys and girls attending the camp is 11.8 years old, what percentage of them are boys?

A. 20%
B. 33 1/3%
C. 50%
D. 66 2/3%
E. 80%


Let number of Boys be B and Number of girls be G

Average of Boys = 11.4

Average of Girls = 12.6

Total Of all boys and girls = 11.4B + 12.6G = 11.8 (B+G)

i.e. B/G = 0.4/0.8 = 1/2

Boys as percentage of all kids = 1/(1+2) = 1/3 = 33.33%

Answer: Option B

P.S. You could use weighted average method (star method) as well but prefer the equation method which is applicable to all questions of average more easily




11.8 B + 11.8 G = 11.4 B +12.6 G

=> 0.4 B= 0.8 G
=> B = 2 G
=> B/G = 2:1 OR b/TOTAL= 2/3 I.E 66.2/3 %

Please tell em where I am making a mistake



U r absolutely right.... :-D
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Re: At a certain summer camp, the average age of the boys attending is 11.  [#permalink]

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New post 22 May 2017, 18:28
Bunuel wrote:
At a certain summer camp, the average age of the boys attending is 11.4 years old and the average age of the girls attending is 12.6 years old. If the average age of all the boys and girls attending the camp is 11.8 years old, what percentage of them are boys?

A. 20%
B. 33 1/3%
C. 50%
D. 66 2/3%
E. 80%


We can create the following weighted average equation in which b = the number of boys and g = the number of girls.

(11.4b + 12.6g)/(b + g) = 11.8

11.4b + 12.6g = 11.8b + 11.8g

114b + 126g = 118b + 118g

8g = 4b

2g = b

b/(b+g) x 100 = 2g/(2g+g) x 100 = (2g/3g) x 100 = (2/3) x 100 = 66 2/3%

Answer: D
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Re: At a certain summer camp, the average age of the boys attending is 11. &nbs [#permalink] 22 May 2017, 18:28
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