Find all School-related info fast with the new School-Specific MBA Forum

It is currently 18 Apr 2014, 03:10

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Of the 60 families in a certain neighborhood, 38 have a cat.

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
4 KUDOS received
Manager
Manager
User avatar
Joined: 27 Oct 2011
Posts: 192
Location: United States
Concentration: Finance, Strategy
GMAT 1: Q V
GPA: 3.7
WE: Account Management (Consumer Products)
Followers: 2

Kudos [?]: 32 [4] , given: 4

Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink] New post 05 Feb 2012, 15:50
4
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

  55% (medium)

Question Stats:

32% (02:31) correct 67% (01:15) wrong based on 176 sessions
Of the 60 families in a certain neighborhood, 38 have a cat. How many of the families in this neighborhood have a dog?

(1) 28 of the families in this neighborhood have a cat but not a dog
(2) The number of families in the neighborhood who have a dog and a cat is the same as the number of families who have neither a cat nor a dog.
[Reveal] Spoiler: OA

_________________

DETERMINED TO BREAK 700!!!

1 KUDOS received
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 1691
Followers: 388

Kudos [?]: 1530 [1] , given: 25

GMAT Tests User
Re: Cats and Dogs [#permalink] New post 05 Feb 2012, 17:24
1
This post received
KUDOS
Expert's post
Hi, there. I'm happy to help. :)

I solved this with a double-matrix method --- because that can get sloppy in the plaintext of these posting windows, I created a pdf attachment.

The double matrix method is a tremendously powerful method for solving these overlapping set problems. At Magoosh, we have a whole series of video lessons going over everything you need to know for GMAT math, including one that explains exactly how to set up the double matrix method of solution.

Please let me know if you should have any questions.

Mike :)
Attachments

cats & dogs DS question.pdf [49.04 KiB]
Downloaded 233 times

To download please login or register as a user


_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Manager
Manager
Joined: 31 Jan 2012
Posts: 75
Followers: 1

Kudos [?]: 17 [0], given: 2

Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink] New post 05 Feb 2012, 20:24
Finally get why it's B.
Total residence = 60.
Those with no pets = X
Those with cats = 38. Those with cats only = 38 -x
With cats n dogs = x.
Dogs = D. Dogs only = D - x

Total residence with pet = Dogs + Cats only.
60 - x = Cats only (38 - x) + D. The reason for doing this is because total amount of pet owners is people with cats + people with dogs plus people with both. If you add total # of dog owners plus total # of cat owners together your adding owners of both pets twice.

Therefore 60 - X + X -38 = D.
D = 22.

B only is significant
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 1691
Followers: 388

Kudos [?]: 1530 [0], given: 25

GMAT Tests User
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink] New post 05 Feb 2012, 22:13
Expert's post
kys123 wrote:
Finally get why it's B.
Total residence = 60.
Those with no pets = X
Those with cats = 38. Those with cats only = 38 -x
With cats n dogs = x.
Dogs = D. Dogs only = D - x

Total residence with pet = Dogs + Cats only.
60 - x = Cats only (38 - x) + D. The reason for doing this is because total amount of pet owners is people with cats + people with dogs plus people with both. If you add total # of dog owners plus total # of cat owners together your adding owners of both pets twice.

Therefore 60 - X + X -38 = D.
D = 22.

B only is significant


It's true that

(# with 1+ pets) = (# with cats only) + (# with dogs only) + (number with both)

Using the notation you adopted,

60 - x = (38 - x) + D + x ---> you forgot that last term.

60 - x + x - 38 - x = D

22 - x = D

And, thus, we cannot establish the value of D with knowing the value of x, so Statement #2, by itself, is insufficient.

As I show in the pdf posted above, the answer is

[Reveal] Spoiler:
C


Please let me know if you have any questions.

Mike :)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

1 KUDOS received
Manager
Manager
Joined: 31 Jan 2012
Posts: 75
Followers: 1

Kudos [?]: 17 [1] , given: 2

Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink] New post 06 Feb 2012, 01:02
1
This post received
KUDOS
Okay, but answer still true. D who only only dogs. Individuals who only own dogs plus individual who only own cats = Total individual who own dogs. That's what we're trying to find, so therefore B is correct.
22 = Number in the neighbourhood with a dog (D [# of people who own only dogs] +X [# of people who own dogs and cats].

Same equation you stated
Intern
Intern
Joined: 29 Jan 2012
Posts: 21
Location: United Kingdom
Concentration: Finance, General Management
GMAT 1: 660 Q45 V35
GMAT 2: 720 Q47 V42
GPA: 3.53
WE: Business Development (Investment Banking)
Followers: 0

Kudos [?]: 6 [0], given: 4

Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink] New post 06 Feb 2012, 01:39
I thought it was C as well... Can someone explain further?
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17306
Followers: 2873

Kudos [?]: 18371 [1] , given: 2348

GMAT Tests User CAT Tests
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink] New post 06 Feb 2012, 02:08
1
This post received
KUDOS
Expert's post
Good question. +1 to calreg11.

Mike is right that a double-matrix method is probably the easiest way to solve this problem and kys123 is right that the answer to the question is B (+1).

Of the 60 families in a certain neighborhood, 38 have a cat. How many of the families in this neighborhood have a dog?

Consider matrix below. Numbers in black are given and numbers in red are calculated.
Attachment:
Stem.PNG
Stem.PNG [ 2.53 KiB | Viewed 2828 times ]

(1) 28 of the families in this neighborhood have a cat but not a dog.
Attachment:
Statement 1.PNG
Statement 1.PNG [ 2.68 KiB | Viewed 2828 times ]
So you can see that we can no way get # of the families in this neighborhood who has a dog (? in the matrix). Not sufficient.

(2) The number of families in the neighborhood who have a dog and a cat is the same as the number of families who have neither a cat nor a dog.
Attachment:
Statement 2.PNG
Statement 2.PNG [ 2.94 KiB | Viewed 2829 times ]
You can see that if # of families who have a dog and a cat and # of families who have neither a cat nor a dog is x, then # of families who has cat but not dog is 38-x. Next, total # of families who has no dog is (38-x)+x=38 and # of families who has a dog is 60-38=22. Sufficient.

Answer: B.

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Manager
Manager
Joined: 31 Jan 2012
Posts: 75
Followers: 1

Kudos [?]: 17 [0], given: 2

Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink] New post 06 Feb 2012, 02:28
This is what I did. The way that Bunuel solve this problem was a lot more elegant, but for me my way is more intuitive. I know everything inside the matrix should add to 60. Hence my solution.
Attachments

Picture 16.png
Picture 16.png [ 22.91 KiB | Viewed 2809 times ]

Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 1691
Followers: 388

Kudos [?]: 1530 [0], given: 25

GMAT Tests User
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink] New post 06 Feb 2012, 08:46
Expert's post
My apologies to kys123

The solution given by Bunuel & kys123 is perfectly correct.

I realize I was misreading/misinterpreting the question, thinking it was asking for the number of people who owned only a dog, i.e. a dog and no cat, not simply the number of dog owners. A good reminder how crucial careful reading is.

If the question were asking for the people who owned only a dog, the answer would be C.

As it stands, though, with the question asking for the number of people who own only a dog, the answer is clearly B, as Bunuel and kys123 have shown.

Again, my apologies for any confusion.

Mike :)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image


Last edited by mikemcgarry on 06 Oct 2013, 12:57, edited 1 time in total.
Director
Director
User avatar
Status: Final Countdown
Joined: 17 Mar 2010
Posts: 565
Location: India
GPA: 3.82
WE: Account Management (Retail Banking)
Followers: 11

Kudos [?]: 109 [0], given: 75

Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink] New post 03 Sep 2012, 02:56
very very tricky,
Bunuel's response is fantastic(as usual :) )

well, (i) is insufficient
(ii) is sufficient , here is the catch;
as we all know that A+B=C
so, A=C-B
& B=C-A
Now check out the file attached :)
Attachments

cats and dogs.docx [10.37 KiB]
Downloaded 45 times

To download please login or register as a user


_________________

" Make more efforts "
Press Kudos if you liked my post

Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4176
Location: Pune, India
Followers: 894

Kudos [?]: 3787 [0], given: 148

Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink] New post 03 Sep 2012, 05:35
Expert's post
calreg11 wrote:
Of the 60 families in a certain neighborhood, 38 have a cat. How many of the families in this neighborhood have a dog?

(1) 28 of the families in this neighborhood have a cat but not a dog
(2) The number of families in the neighborhood who have a dog and a cat is the same as the number of families who have neither a cat nor a dog.


Yes, the question is really good. I like to show a series of diagrams to my students to explain what the statement 'number of families with both = number of families with none' implies. It means the sum of number of families with cat and number of families with dog is constant and is equal to 60. For every one family that has both, there is a family that has none (to keep their numbers equal)

Look at the diagrams below. If the number of families that have neither a dog nor a cat is 0, the number of families with a dog is 60 - 38 = 22.
Now what happens when you overlap one family? There is one family which has neither a cat nor a dog. The number of families with a cat or a dog or both reduces by 1 and the number of families with neither increases by 1. The sum is kept constant at 60. The following diagrams should make it clear.

Attachment:
Ques3.jpg
Ques3.jpg [ 6.73 KiB | Viewed 2269 times ]


Attachment:
Ques4.jpg
Ques4.jpg [ 6.91 KiB | Viewed 2268 times ]


Attachment:
Ques5.jpg
Ques5.jpg [ 7.11 KiB | Viewed 2269 times ]

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Senior Manager
Senior Manager
User avatar
Joined: 23 Oct 2010
Posts: 380
Location: Azerbaijan
Concentration: Finance
GMAT 1: 690 Q47 V38
Followers: 11

Kudos [?]: 111 [0], given: 72

GMAT ToolKit User
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink] New post 23 Jan 2013, 09:32
38+x+Neither-Both=60
Neither=Both

38+x=60
x=22
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

Intern
Intern
Joined: 26 Apr 2013
Posts: 49
Location: United States
Concentration: Marketing, Nonprofit
GPA: 3.5
WE: Marketing (Telecommunications)
Followers: 0

Kudos [?]: 19 [0], given: 2

GMAT ToolKit User
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink] New post 04 Oct 2013, 20:09
mikemcgarry wrote:
My apologies to kys123

The solution given by Bunuel[/b ]& [b]kys123 is perfectly correct.

I realize I was misreading/misinterpreting the question, thinking it was asking for the number of people who owned only a dog, i.e. a dog and no cat, not simply the number of dog owners. A good reminder how crucial careful reading is.

If the question were asking for the people who owned only a dog, the answer would be C.

As it stands, though, with the question asking for the number of people who own only a dog, the answer is clearly B, as Bunuel and kys123 have shown.

Again, my apologies for any confusion.

Mike :)


Its strange that a tutor got it wrong and lot of students have got it right :)
Re: Of the 60 families in a certain neighborhood, 38 have a cat.   [#permalink] 04 Oct 2013, 20:09
    Similar topics Author Replies Last post
Similar
Topics:
New posts Of the families in a certain community, 75% have an oven, apollo168 4 20 Aug 2006, 00:45
New posts Experts publish their posts in the topic In a neighborhood having 90 households, 11 did not have navigator123 7 23 May 2012, 11:24
New posts 1 Experts publish their posts in the topic Profile Evaluation : 710(48,38)-Project Manager + Family Biz ritzoo 7 17 Sep 2012, 10:29
New posts Profile Evaluation : 710(48,38)-Project Manager + Family Biz ritzoo 0 17 Sep 2012, 10:30
Popular new posts 2 Experts publish their posts in the topic In a certain neighborhood there are half as many beige house megafan 13 09 Feb 2013, 13:03
Display posts from previous: Sort by

Of the 60 families in a certain neighborhood, 38 have a cat.

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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

Powered by phpBB © phpBB Group and phpBB SEO

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®.