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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 Updated on: 11 Sep 2014, 05:40
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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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Originally posted by aadikamagic on 11 Sep 2014, 05:25.
Last edited by Bunuel on 11 Sep 2014, 05:40, edited 1 time in total.
RENAMED THE TOPIC.
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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 12 Sep 2014, 01:11
3
aadikamagic 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


Attachment:
mat.png
mat.png [ 6.1 KiB | Viewed 2799 times ]


1. Let total number of people = 1

2. Total Brown Hair \(= \frac{3}{5}\)

3. \(\frac{3}{4}\) th of Total Brown Hair have Brown Eyes \(= \frac{3}{4} * \frac{3}{5} = \frac{9}{20}\)

4. Total People with No Brown Hair \(= 1 - \frac{3}{5} = \frac{2}{5}\)

5. \(\frac{1}{4}\) th of (Total No Brown Hair) have Brown Eyes \(=\frac{1}{4} * \frac{2}{5} = \frac{1}{10}\)

6. So, people with (No Brown Hair) and (NO Brown Eyes) \(= \frac{2}{5} - \frac{1}{10} = \frac{3}{10}\)

Ratio \(= \frac{\frac{9}{20}}{\frac{3}{10}} = \frac{9}{20}* \frac{10}{3} = \frac{3}{2}\)

Answer = 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 12 Sep 2014, 02:41
PareshGmat wrote:
aadikamagic 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


Attachment:
mat.png


1. Let total number of people = 1

2. Total Brown Hair \(= \frac{3}{5}\)

3. \(\frac{3}{4}\) th of Total Brown Hair have Brown Eyes \(= \frac{3}{4} * \frac{3}{5} = \frac{9}{20}\)

4. Total People with No Brown Hair \(= 1 - \frac{3}{5} = \frac{2}{5}\)

5. \(\frac{1}{4}\) th of (Total No Brown Hair) have Brown Eyes \(=\frac{1}{4} * \frac{2}{5} = \frac{1}{10}\)

6. So, people with (No Brown Hair) and (NO Brown Eyes) \(= \frac{2}{5} - \frac{1}{10} = \frac{3}{10}\)

Ratio \(= \frac{\frac{9}{20}}{\frac{3}{10}} = \frac{9}{20}* \frac{10}{3} = \frac{3}{2}\)

Answer = C



Thank you so much for reply. I am trying it with circled venn diagrams but not getting the answer. I am really confused.
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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 12 Sep 2014, 08:53
I used smart numbers in this case, so that to not get confused with fractions.
Total number of people = 100
brown hair 3/5 or 60
not brown hair hence 40
3/4 of people with brown hair have brown eyes, thus 3/4*60 = 45
1/4 of people who do not have brown hair have brown eyes = 1/4*40 = 10
people with neither = 30

ratio 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 12 Sep 2014, 22:02
Hi victor ,

From where we got people with neither = 30
I have done the same way ,
Brown hair = 60
Not Brown hair = 40
No brown hair + Brown eyes = 10
Brown hair + Brown eyes = 45
What about No brown eyes + But only brown hair ?
Neither?

:?
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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 13 Sep 2014, 03:57
kanusha wrote:
Hi victor ,

From where we got people with neither = 30
I have done the same way ,
Brown hair = 60
Not Brown hair = 40
No brown hair + Brown eyes = 10
Brown hair + Brown eyes = 45
What about No brown eyes + But only brown hair ?
Neither?

:?


Hi Kanusha,

here is the chart that I have used
hope that helps
Attachments

chart.jpg
chart.jpg [ 14.75 KiB | Viewed 2688 times ]

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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 13 Sep 2014, 07:12
aadikamagic wrote:
PareshGmat wrote:
aadikamagic 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


Attachment:
mat.png


1. Let total number of people = 1

2. Total Brown Hair \(= \frac{3}{5}\)

3. \(\frac{3}{4}\) th of Total Brown Hair have Brown Eyes \(= \frac{3}{4} * \frac{3}{5} = \frac{9}{20}\)

4. Total People with No Brown Hair \(= 1 - \frac{3}{5} = \frac{2}{5}\)

5. \(\frac{1}{4}\) th of (Total No Brown Hair) have Brown Eyes \(=\frac{1}{4} * \frac{2}{5} = \frac{1}{10}\)

6. So, people with (No Brown Hair) and (NO Brown Eyes) \(= \frac{2}{5} - \frac{1}{10} = \frac{3}{10}\)

Ratio \(= \frac{\frac{9}{20}}{\frac{3}{10}} = \frac{9}{20}* \frac{10}{3} = \frac{3}{2}\)

Answer = C



Thank you so much for reply. I am trying it with circled venn diagrams but not getting the answer. I am really confused.


I solved using double matrix method..... I'm not sure if this can be solved by Venn Diagram? But this method was indeed comfortable for me
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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 13 Sep 2014, 08:20
PareshGmat wrote:

I solved using double matrix method..... I'm not sure if this can be solved by Venn Diagram? But this method was indeed comfortable for me



MGMAT recommends using Charts instead of Venn Diagram, since it is more convenient to visualize which is which. Before, I was using as well this method, but now I use it only when there are 3 sets only.
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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 24 Dec 2014, 21:36
Number of people is 20

3/5*20=12 (brown hair)

3/4*12=9 (brown hair+brown eyes)

1/4*8 (not brown hair)=2 (not brown hair but brown eyes)

we need ratio both brown hair and eyes, i.e 9 to neither, which is 8-2=6

9/6=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 25 Dec 2014, 02:20
Total =60 assumption
B.H= Brown hair N.B.H= No brown hair. Same representation for eyes.

B.H N.BH
B.E 27=36*3/4 6=(1/4)*24

N.BE 9= 36-27 18=24-6

Total 36=60*3/5 24=60-36

Thus answer = 27/18 =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 05 Jan 2015, 05:15
Just to let everyone know, the Manhattan guide has a very good chapter on this --> word translations guide, overlapping sets chapter. You can donwload the manhattan guides easily.
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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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