GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Oct 2019, 19:30

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58340
In a group of people, 3/5 have brown hair and 3/4 of the people with  [#permalink]

### Show Tags

21 Jun 2019, 00:36
2
1
00:00

Difficulty:

25% (medium)

Question Stats:

80% (02:35) correct 20% (02:06) wrong based on 34 sessions

### HideShow timer Statistics

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

_________________
Intern
Joined: 16 Apr 2019
Posts: 10
Location: India
GPA: 4
Re: In a group of people, 3/5 have brown hair and 3/4 of the people with  [#permalink]

### Show Tags

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.

Posted from my mobile device
Director
Joined: 22 Nov 2018
Posts: 557
Location: India
GMAT 1: 640 Q45 V35
GMAT 2: 660 Q48 V33
Re: In a group of people, 3/5 have brown hair and 3/4 of the people with  [#permalink]

### Show Tags

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
_________________
Give +1 kudos if this answer helps..!!
Director
Joined: 20 Jul 2017
Posts: 887
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: In a group of people, 3/5 have brown hair and 3/4 of the people with  [#permalink]

### Show Tags

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

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
Attachments

32.png [ 8.52 KiB | Viewed 593 times ]

ISB School Moderator
Joined: 08 Dec 2013
Posts: 594
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB '21
GMAT 1: 630 Q47 V30
WE: Operations (Non-Profit and Government)
Re: In a group of people, 3/5 have brown hair and 3/4 of the people with  [#permalink]

### Show Tags

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
_________________
Kindly drop a '+1 Kudos' if you find this post helpful.

GMAT Math Book

-I never wanted what I gave up
I never gave up what I wanted-
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4999
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: In a group of people, 3/5 have brown hair and 3/4 of the people with  [#permalink]

### Show Tags

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
Re: In a group of people, 3/5 have brown hair and 3/4 of the people with   [#permalink] 21 Jun 2019, 11:25
Display posts from previous: Sort by