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Fraction problem

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Fraction problem

by aman88 » Tue Dec 18, 2012 11:13 pm
In a group of people, 3/5 have brown hair and 3/4 of the people with brown hair also have brown eyes, while only one quarter of the people who don't have brown hair have brown eyes. What is the ratio of the number of people with both brown hair and brown eyes to the number with neither?

A. 1/2
B. 9/8
C. 3/2
D. 5/2
E. 9/2

OA C

Can someone please explain this problem to me.

Thanks.
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by puneetkhurana2000 » Tue Dec 18, 2012 11:49 pm
Brown Eyes No Brown Eyes Total
Brown Hair 0.45 0.15 0.60
No Brown Hair 0.10 0.30 0.40

Answer is 0.45/0.30 = 3/2.

Answer C.
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by GMATGuruNY » Wed Dec 19, 2012 8:33 am
aman88 wrote:In a group of people, 3/5 have brown hair and 3/4 of the people with brown hair also have brown eyes, while only one quarter of the people who don't have brown hair have brown eyes. What is the ratio of the number of people with both brown hair and brown eyes to the number with neither?

A. 1/2
B. 9/8
C. 3/2
D. 5/2
E. 9/2

OA C
This is an EITHER/OR group problem.
Everyone EITHER has brown hair OR does not.
Everyone EITHER has brown eyes OR does not.
For an EITHER/OR group problem, use a GROUP GRID to organize the data.

Let BH = brown hair, NBH = no brown hair, BE = brown eyes, NBE = no brown eyes.
Let the total = the LCM of the two denominators in the problem = 5*4 = 20.
______________BH_____NBH_______Total

BE:

NBE:

total:___________________________20
Now let's use the information in the problem to complete the grid step by step.
As soon as we know 2 entries in a row or a column, we can calculate the remaining entry in that row or column.

3/5 have brown hair.
3/4 of the people with brown hair also have brown eyes.:
______________BH_____NBH_______Total

BE:____________9

NBE:___________3

total:_________12_______8_________20
One quarter of the people who don't have brown hair have brown eyes:
_______________BH______NBH_______Total

BE:_____________9________2_________11

NBE:___________3_________6_________9

total:__________12________8_________20
With the grid complete, we can answer the question stem:
(Brown hair and brown eyes) / Neither = 9/6 = 3/2.

The correct answer is C.
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by aman88 » Wed Dec 19, 2012 10:11 am
Thanks a ton, Mr. Hunt! :)
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by gander123 » Wed Dec 19, 2012 2:48 pm
Thanks to Mitch's very valuable advice this prob shouldnt be much of a problem for nearly everyone.

For those interested here's my "PIN-approach" that took perhaps 10-20 seconds:

Plug-in 100 for the whole population:

3/5 have brown hair --> 60 people --> multiply with 3/4 --> 45 have also brown eyes
2/5 do not have brown hair (remainder) --> 40 people --> multiply with 1/4 --> 10 have brown eyes but not brown hair

Try to arrange these figures from the biginning in a tree or arrange them logically. Afterwards go back to the actual question stem:

Divide: 45 / (40-10) = 45/30 = 9/6 = 3/2

HTH aman.

Have fun preparing !

Kind regards,

Tobi
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by sharoonsaleem » Thu Dec 20, 2012 1:19 am
Let the total number of humans be X

3/5*X have brown hair in total

3/4*3/5*X have brown eyes (within brown haired people)

1/4 of people not having brown hair have brown eyes that'd be 1/4*(1-3/5*X)

Let's suppose X is 20 (i chose it coz its divisible by 4 and 5 both)

Brown hair = 12
The brown haired people that have brown eyes - 9
Brown eyed people that dont have brown hair - 2

Therefore the fraction is (9/(20-12-2)) = 9/6 = 3/2
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