ratio and proportion

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DJHJA: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Mon Dec 13, 2010 3:14 pm

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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Source: Beat The GMAT — Problem Solving | Mon Dec 13, 2010 9:49 pm

Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

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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DJHJA: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Mon Dec 13, 2010 3:14 pm

by DJHJA » Mon Dec 13, 2010 10:23 pm

omg thanks ur a life saver

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frank1: Legendary Member; Posts: 537; Joined: Fri Jan 22, 2010 10:06 pmFollowed by: 1 member; Thanked: 14 times

by frank1 » Tue Dec 14, 2010 1:00 am

When you see two set of mutually exclusive sets use this method...
it saves time

11/70 clear from it

GMAT score is equally counted as your GPA and 78 clicks can change you life.

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ikaplan: Master | Next Rank: 500 Posts; Posts: 181; Joined: Fri Sep 04, 2009 12:06 pmFollowed by: 1 member; Thanked: 17 times

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!

"Commitment is more than just wishing for the right conditions. Commitment is working with what you have."

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