It is currently 20 Sep 2017, 13:30

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the city of San Durango, 60 people own cats, dogs, or rab

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Intern
Intern
avatar
Joined: 30 Jun 2012
Posts: 12

Kudos [?]: 41 [1], given: 4

In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

Show Tags

New post 02 Dec 2012, 01:45
1
This post received
KUDOS
10
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

68% (00:48) correct 32% (01:10) wrong based on 435 sessions

HideShow timer Statistics

In the city of San Durango, 60 people own cats, dogs, or rabbits. If 30 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?

A 2
B 4
C 8
D 12
E 32
[Reveal] Spoiler: OA

Kudos [?]: 41 [1], given: 4

2 KUDOS received
Director
Director
User avatar
S
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 623

Kudos [?]: 742 [2], given: 59

Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

Show Tags

New post 02 Dec 2012, 02:08
2
This post received
KUDOS
2
This post was
BOOKMARKED
apoorvarora wrote:
In the city of San Durango, 60 people own cats, dogs, or rabbits. If 30 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?

A 2
B 4
C 8
D 12
E 32



Total = C + D + R - (CD + DR + CR) - 2CDR

60 = 30 + 40 + 10 - (12) - 2x

x = 4

So, answer will be B
Hope it helps!
_________________

Ankit

Check my Tutoring Site -> Brush My Quant

GMAT Quant Tutor
How to start GMAT preparations?
How to Improve Quant Score?
Gmatclub Topic Tags
Check out my GMAT debrief

How to Solve :
Statistics || Reflection of a line || Remainder Problems || Inequalities


Last edited by BrushMyQuant on 02 Dec 2012, 02:23, edited 1 time in total.

Kudos [?]: 742 [2], given: 59

Intern
Intern
avatar
Joined: 30 Jun 2012
Posts: 12

Kudos [?]: 41 [0], given: 4

Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

Show Tags

New post 02 Dec 2012, 02:16
No the ans is 4...

You are considering a case when cat dogs and rabbit are not exactly equal to 12 .

The solution shall be 60=30+40+10-12-2x

and hence x shall be 4.

Kudos [?]: 41 [0], given: 4

Moderator
Moderator
User avatar
Joined: 02 Jul 2012
Posts: 1219

Kudos [?]: 1621 [0], given: 116

Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Premium Member
Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

Show Tags

New post 02 Dec 2012, 02:19
1
This post was
BOOKMARKED
Total = C + D + R - Exactly two - 2*All three

60 = 30 + 40 + 10 - 12 - 2x

2x = 8

x = 4
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Kudos [?]: 1621 [0], given: 116

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41640

Kudos [?]: 124181 [0], given: 12075

Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

Show Tags

New post 02 Dec 2012, 04:12
apoorvarora wrote:
In the city of San Durango, 60 people own cats, dogs, or rabbits. If 30 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?

A 2
B 4
C 8
D 12
E 32


3 overlapping sets with theory, diagrams and examples: ADVANCED OVERLAPPING SETS PROBLEMS
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 124181 [0], given: 12075

Manager
Manager
avatar
Joined: 06 Jun 2010
Posts: 159

Kudos [?]: 19 [0], given: 151

Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

Show Tags

New post 09 Dec 2012, 00:19
Can any1 show it by using venn diagrams?
I tried to set up the equation as follows:
People owning all 3 pets = 'X'.

People owning cats and dogs only = a

Owning rabbits and cats only = b

Owning dogs and rabbits only = c

Then i set up eqn as follows to find X

30-(a+b+x) + 40-(a+x+c) +10 - (b+x+c) = 60

and got the equation:

80-2(a+b+c)-3X = 60

also,can we select either a+c =12 or b+c =12 or a + b=12?
Please help.

Thanks,
Shreeraj

Kudos [?]: 19 [0], given: 151

1 KUDOS received
Moderator
Moderator
User avatar
G
Joined: 01 Sep 2010
Posts: 3346

Kudos [?]: 8728 [1], given: 1138

Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

Show Tags

New post 09 Dec 2012, 10:19
1
This post received
KUDOS
1
This post was
BOOKMARKED
\(@apoorvarora\)

when a problem is like you posted here or similar, like this one

Quote:
Each of the 59 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 22 students sign up for the poetry club, 27 students for the history club, and 28 students for the writing club. If 6 students sign up for exactly two clubs, how many students sign up for all three clubs?


is much better to use the formula Total = C + D + R - Exactly two - 2*All three (refers also to the post linked by Bunuel (the second one)

\(IF\) the problem is like this

Quote:
Workers are grouped by their areas of expertise, and are placed on at least one team. 20 are on the marketing team, 30 are on the Sales team, and 40 are on the Vision team. 5 workers are on both the Marketing and Sales teams, 6 workers are on both the Sales and Vision teams, 9 workers are on both the Marketing and Vision teams, and 4 workers are on all three teams. How many workers are there in total?


or this

Quote:
The 38 movies in the video store fall into the following three categories: 10 action, 20 drama, and 18 comedy. However, some movies are classified under more than one category: 5 are both action and drama, 3 are both action and comedy, and 4 are both drama and comedy. How many action-drama-comedy movies are there?
(souce MGMAT)

you can use either \(venn diagram\) or the formula \(Total= A+B+C - (AnB+AnC+BnC) +AnBnC + Neither\) is the same thing: it depends on which you are more comfortable

In the first case, that is the case of the question of the post at stake, is much better use the formula because is faster ans because set up a Venn diagram is more convoluted and prone of errors. Try to stay flexible.

Hope this is useful :)
_________________

COLLECTION OF QUESTIONS AND RESOURCES
Quant: 1. ALL GMATPrep questions Quant/Verbal 2. Bunuel Signature Collection - The Next Generation 3. Bunuel Signature Collection ALL-IN-ONE WITH SOLUTIONS 4. Veritas Prep Blog PDF Version 5. MGMAT Study Hall Thursdays with Ron Quant Videos
Verbal:1. Verbal question bank and directories by Carcass 2. MGMAT Study Hall Thursdays with Ron Verbal Videos 3. Critical Reasoning_Oldy but goldy question banks 4. Sentence Correction_Oldy but goldy question banks 5. Reading-comprehension_Oldy but goldy question banks


Last edited by carcass on 09 Dec 2012, 10:30, edited 1 time in total.

Kudos [?]: 8728 [1], given: 1138

1 KUDOS received
Intern
Intern
avatar
Joined: 30 Jun 2012
Posts: 12

Kudos [?]: 41 [1], given: 4

Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

Show Tags

New post 09 Dec 2012, 10:27
1
This post received
KUDOS
@ shreeraj

Just check u cant take any two values to be 12

i.e a+ c =12 is not possible coz we are given exact value as 12 and not either of the 2 value as 12...a+b+c-x will be 12...

Kudos [?]: 41 [1], given: 4

1 KUDOS received
Moderator
Moderator
User avatar
Joined: 02 Jul 2012
Posts: 1219

Kudos [?]: 1621 [1], given: 116

Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Premium Member
Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

Show Tags

New post 09 Dec 2012, 12:26
1
This post received
KUDOS
shreerajp99 wrote:
Actually i dont want to use the formulas.


I've tried my best to put this into Venn form.... From the below figure, we can see that

Cats + Dogs + Rabbits - Total - Exactly Two = All Three + All Three

Dividing this by 2, we get what "All Three" is.

As you can see, venn diagramming in this case is quite tedious and when the question has "Exactly Two" in it, it is better to use the formula.
Attachments

Untitled.png
Untitled.png [ 40.91 KiB | Viewed 8917 times ]


_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Kudos [?]: 1621 [1], given: 116

Moderator
Moderator
User avatar
Joined: 02 Jul 2012
Posts: 1219

Kudos [?]: 1621 [0], given: 116

Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Premium Member
Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

Show Tags

New post 10 Dec 2012, 00:17
The problem with Venn diagramming in this case is that we do not know in what ratio the "exactly two" is divided into each group.
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Kudos [?]: 1621 [0], given: 116

Expert Post
1 KUDOS received
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1503

Kudos [?]: 765 [1], given: 2

Location: United States (CA)
Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

Show Tags

New post 19 Apr 2017, 16:15
1
This post received
KUDOS
Expert's post
apoorvarora wrote:
In the city of San Durango, 60 people own cats, dogs, or rabbits. If 30 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?

A 2
B 4
C 8
D 12
E 32


We can use the following formula:

total pet owners = # who own dogs + # who own cats + # who own rabbits - # who own exactly two types - 2 x # who own three types + # who own none

Thus:

60 = 40 + 30 + 10 - 12 - 2T + 0

60 = 68 - 2T

2T = 8

T = 4

Answer: B
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 765 [1], given: 2

Intern
Intern
avatar
Joined: 17 Jul 2017
Posts: 17

Kudos [?]: 1 [0], given: 4

Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

Show Tags

New post 31 Jul 2017, 11:18
Here is a good way to think about it:
Attachments

full solutions.png
full solutions.png [ 186.48 KiB | Viewed 398 times ]

Kudos [?]: 1 [0], given: 4

Intern
Intern
avatar
B
Joined: 15 Jul 2017
Posts: 2

Kudos [?]: 0 [0], given: 5

Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

Show Tags

New post 03 Sep 2017, 21:05
Hi Bunuel,
This is my first post after learning and watching solutions by all experts.
I solved this and got the right answer, however I approached it in a different way but was quicker for me to understand. Please advise if this is also an alternate way?
Total 60.
Exactly 2 pets : CD,CR,DR = 12.
As we are asked to find common among total 3 group : I just divided 12/3 : 4.

I know the method was ridiculous. However please advise the correct way or if this can be used?

Best regards

Kudos [?]: 0 [0], given: 5

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41640

Kudos [?]: 124181 [0], given: 12075

Re: In the city of San Durango, 60 people own cats, dogs, or rab [#permalink]

Show Tags

New post 03 Sep 2017, 23:18
rbane7 wrote:
Hi Bunuel,
This is my first post after learning and watching solutions by all experts.
I solved this and got the right answer, however I approached it in a different way but was quicker for me to understand. Please advise if this is also an alternate way?
Total 60.
Exactly 2 pets : CD,CR,DR = 12.
As we are asked to find common among total 3 group : I just divided 12/3 : 4.

I know the method was ridiculous. However please advise the correct way or if this can be used?

Best regards


No, this is not correct. The number of people who owned exactly two of the three types of pet is not always thrice the number of people who owned all three.

Foe example, if the number of people who owned exactly two of the three types of pet were 18 instead of 12, the answer would be 1, not 18/3 = 6 (from Total = C + D + R - Exactly two - 2*All three + Neither).

There are several correct approaches above and here is a link which explains the theory behind the formula used: 3 overlapping sets with theory, diagrams and examples: ADVANCED OVERLAPPING SETS PROBLEMS.

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 124181 [0], given: 12075

Re: In the city of San Durango, 60 people own cats, dogs, or rab   [#permalink] 03 Sep 2017, 23:18
    Similar topics Author Replies Last post
Similar
Topics:
3 EXPERTS_POSTS_IN_THIS_TOPIC There are twice as many dog owners as cat owners Cez005 3 22 Mar 2017, 09:38
2 In a city, 40% of the people are illiterate and 60% are poor. Among aveek86 6 18 Aug 2017, 10:31
8 EXPERTS_POSTS_IN_THIS_TOPIC The ratio of dogs to cats at a certain shelter in City X is 2:3 and Bunuel 4 06 May 2017, 17:13
1 If 45% of study participants liked dogs, 60% liked cats, and 25% liked shasadou 1 12 Sep 2015, 21:57
6 EXPERTS_POSTS_IN_THIS_TOPIC There are 49 people that own pets. 15 people own only dogs, 10 people emranhstu 6 27 Feb 2016, 04:20
Display posts from previous: Sort by

In the city of San Durango, 60 people own cats, dogs, or rab

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.