Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 30 Jun 2012
Posts: 11

In the city of San Durango, 60 people own cats, dogs, or rab
[#permalink]
Show Tags
02 Dec 2012, 01:45
Question Stats:
71% (00:49) correct 29% (01:00) wrong based on 603 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
Official Answer and Stats are available only to registered users. Register/ Login.




Director
Status: Tutor  BrushMyQuant
Joined: 05 Apr 2011
Posts: 610
Location: India
Concentration: Finance, Marketing
GPA: 3
WE: Information Technology (Computer Software)

Re: In the city of San Durango, 60 people own cats, dogs, or rab
[#permalink]
Show Tags
Updated on: 02 Dec 2012, 02:23
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
Originally posted by BrushMyQuant on 02 Dec 2012, 02:08.
Last edited by BrushMyQuant on 02 Dec 2012, 02:23, edited 1 time in total.




Intern
Joined: 30 Jun 2012
Posts: 11

Re: In the city of San Durango, 60 people own cats, dogs, or rab
[#permalink]
Show Tags
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+10122x
and hence x shall be 4.



VP
Joined: 02 Jul 2012
Posts: 1184
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: In the city of San Durango, 60 people own cats, dogs, or rab
[#permalink]
Show Tags
02 Dec 2012, 02:19
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



Math Expert
Joined: 02 Sep 2009
Posts: 50002

Re: In the city of San Durango, 60 people own cats, dogs, or rab
[#permalink]
Show Tags
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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 06 Jun 2010
Posts: 154

Re: In the city of San Durango, 60 people own cats, dogs, or rab
[#permalink]
Show Tags
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:
802(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



Board of Directors
Joined: 01 Sep 2010
Posts: 3304

Re: In the city of San Durango, 60 people own cats, dogs, or rab
[#permalink]
Show Tags
Updated on: 09 Dec 2012, 10:30
\( @apoorvarora\) 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 actiondramacomedy 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 ALLINONE 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. Readingcomprehension_Oldy but goldy question banks
Originally posted by carcass on 09 Dec 2012, 10:19.
Last edited by carcass on 09 Dec 2012, 10:30, edited 1 time in total.



Intern
Joined: 30 Jun 2012
Posts: 11

Re: In the city of San Durango, 60 people own cats, dogs, or rab
[#permalink]
Show Tags
09 Dec 2012, 10:27
@ 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+cx will be 12...



VP
Joined: 02 Jul 2012
Posts: 1184
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: In the city of San Durango, 60 people own cats, dogs, or rab
[#permalink]
Show Tags
09 Dec 2012, 12:26
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 [ 40.91 KiB  Viewed 12733 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



VP
Joined: 02 Jul 2012
Posts: 1184
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

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



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3888
Location: United States (CA)

Re: In the city of San Durango, 60 people own cats, dogs, or rab
[#permalink]
Show Tags
19 Apr 2017, 16:15
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 WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 17 Jul 2017
Posts: 15

Re: In the city of San Durango, 60 people own cats, dogs, or rab
[#permalink]
Show Tags
31 Jul 2017, 11:18
Here is a good way to think about it:
Attachments
full solutions.png [ 186.48 KiB  Viewed 4235 times ]



Intern
Joined: 15 Jul 2017
Posts: 2

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



Math Expert
Joined: 02 Sep 2009
Posts: 50002

Re: In the city of San Durango, 60 people own cats, dogs, or rab
[#permalink]
Show Tags
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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 06 Sep 2018
Posts: 105
Location: Pakistan
Concentration: Finance, Operations
GPA: 2.87
WE: Engineering (Other)

Re: In the city of San Durango, 60 people own cats, dogs, or rab
[#permalink]
Show Tags
07 Oct 2018, 08:25
\(cats+dogs+rabit(exactly 2)2(exatctly 3)=Total\) \(30+40+10122(T)=60\) \(682T=60\) \(2T=8\) \(T=4\)
_________________
Eric Thomas, "When you want to succeed as bad as you want to breathe, then you'll be successful."




Re: In the city of San Durango, 60 people own cats, dogs, or rab &nbs
[#permalink]
07 Oct 2018, 08:25






