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In a group of people, 3/5 have brown hair and 3/4 of the people with

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In a group of people, 3/5 have brown hair and 3/4 of the people with  [#permalink]

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New post 21 Jun 2019, 00:36
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Question Stats:

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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

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Re: In a group of people, 3/5 have brown hair and 3/4 of the people with  [#permalink]

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New post 21 Jun 2019, 01:13
If we were to make a table, it'd look something like the one below:

BH NoBH Total
BE 45 10 55

NoBE 15 30 45

Total 60 40 100

I don't know if the orientation is understandable but if we were to assume there were 100 people in the group, 3/5 having brown hair equals 60 people with brown hair and 3/4 of those 60 people have brown eyes, that means there are 45 people having both brown hair and brown eyes.
That'd mean 40 people with no brown hair and following the question, a quarter of those 40 people have brown eyes, i.e., 10 people with brown eyes.
With this data if we were to make a table, we can easily fill up the remaining spaces and find out the required ratio, which would be 45/30=3/2.

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Re: In a group of people, 3/5 have brown hair and 3/4 of the people with  [#permalink]

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New post 21 Jun 2019, 01:18
Bunuel 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


Both BH and BE=3/5*3/4=9/20
Neither BH and BE = (1-3/5) No BH*(1-1/4) of No BH No BE=2/5*3/4=6/20
So 9/6=3/2 IMO C
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Re: In a group of people, 3/5 have brown hair and 3/4 of the people with  [#permalink]

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New post 21 Jun 2019, 01:25
Bunuel 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


Image

both brown hair and brown eyes = 27
neither = 18

Fraction = 27/18 = 3/2

IMO Option C

Pls Hit Kudos if you like the solution
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Re: In a group of people, 3/5 have brown hair and 3/4 of the people with  [#permalink]

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New post 21 Jun 2019, 02:10
Bunuel 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

Total=x
BH= 3x/5
BH+BE=9x/20

Not BH= 2x/5
But BE= 2x/20
Not BH and Not BE= 6x/20

Required-> (9x/20) / (6x/20) = 3/2 C
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Re: In a group of people, 3/5 have brown hair and 3/4 of the people with  [#permalink]

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New post 21 Jun 2019, 11:25
Bunuel 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



2x2 matrix

----BH -----NBH---Total
BE--9-------2-----11
NBE-3-------6-----9
total-12------8----20
ratio 9/6 ; 3/2
IMO C
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Re: In a group of people, 3/5 have brown hair and 3/4 of the people with   [#permalink] 21 Jun 2019, 11:25
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