ratio and proportion

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ratio and proportion

by DJHJA » Mon Dec 13, 2010 9:49 pm
In a class, 10% of the girls have blue eyes, and 20% of the boys have blue eyes.
If the ratio of girls to boys in the class is 3:4, then what is the fraction of students in the class having blues eyes?


the answer is 11/70, however the solution given is;

let 1 represent the total # of students
1-(.1+.2)= .7 ( why is this done??? :? why isnt it .1+.2=.3 as the denominator)

girls(with blue eyes) + boys(with blue eyes) =
(3*.1 )+(4*.2)/ .7 = .3+.8/.7= .11/.7 = 11/70

why is .7 the denominator and not .3.
isnt .3 the total percentage of students with blue eyes?
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by Night reader » Mon Dec 13, 2010 10:07 pm
DJHJA wrote:In a class, 10% of the girls have blue eyes, and 20% of the boys have blue eyes.
If the ratio of girls to boys in the class is 3:4, then what is the fraction of students in the class having blues eyes?


the answer is 11/70, however the solution given is;

let 1 represent the total # of students
1-(.1+.2)= .7 ( why is this done??? :? why isnt it .1+.2=.3 as the denominator)

girls(with blue eyes) + boys(with blue eyes) =
(3*.1 )+(4*.2)/ .7 = .3+.8/.7= .11/.7 = 11/70

why is .7 the denominator and not .3.
isnt .3 the total percentage of students with blue eyes?
girls/boys=3/4 => girls/total=3/7 & boys/total=4/7 <=> 3/7 + 4/7 = 1 (girls+boys over total)

blue eyed boys 20% or 1/5
blue eyed girls 10% or 1/10

how many of all boys are blue eyed => 1/5 * 4/7 = 4/35
how many of all girls are blue eyed => 1/10 * 3/7 = 3/70

how many of all boys and girls are blue eyed => 4/35 + 3/70 = 11/70

many OA explanations may differ in notation and decimal translations; we need to know the method only

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by DJHJA » Mon Dec 13, 2010 10:23 pm
omg thanks ur a life saver

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by frank1 » Tue Dec 14, 2010 1:00 am
When you see two set of mutually exclusive sets use this method...
it saves time
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11/70 clear from it
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by ikaplan » Tue Dec 14, 2010 7:22 am
Double matrix method is one of the most useful techniques I have learned during the GMAT prep period. Frank1, thanks for reminding us to use it!
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