|
Author |
Message |
|
TAGS:
|
|
|
Manager
Joined: 27 Oct 2011
Posts: 186
Location: United States
Concentration: Finance, Strategy
GPA: 3.7
WE: Account Management (Consumer Products)
|
Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]
Show Tags
 05 Feb 2012, 16:50
7
This post received
KUDOS
9
This post was
BOOKMARKED
D
E
Question Stats:
40% (02:19) correct
60% (01:19) wrong based on 496 sessions
HideShow timer Statistics
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.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
DETERMINED TO BREAK 700!!!
|
|
|
|
|
|
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4132
|
Re: Cats and Dogs [#permalink]
Show Tags
05 Feb 2012, 18:24
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
_________________
Mike McGarry
Magoosh Test Prep
|
|
|
|
|
|
Manager
Joined: 31 Jan 2012
Posts: 74
|
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]
Show Tags
05 Feb 2012, 21:24
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
Joined: 28 Dec 2011
Posts: 4132
|
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]
Show Tags
05 Feb 2012, 23:13
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 Please let me know if you have any questions. Mike
_________________
Mike McGarry
Magoosh Test Prep
|
|
|
|
|
|
Manager
Joined: 31 Jan 2012
Posts: 74
|
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]
Show Tags
06 Feb 2012, 02:02
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
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)
|
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]
Show Tags
06 Feb 2012, 02:39
I thought it was C as well... Can someone explain further?
|
|
|
|
|
|
Math Expert
Joined: 02 Sep 2009
Posts: 39756
|
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]
Show Tags
06 Feb 2012, 03:08
2
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
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 [ 2.53 KiB | Viewed 6694 times ]
(1) 28 of the families in this neighborhood have a cat but not a dog. Attachment: 
Statement 1.PNG [ 2.68 KiB | Viewed 6689 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 [ 2.94 KiB | Viewed 6696 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 the Math Forum?
Please read this: 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
|
|
|
|
|
|
Manager
Joined: 31 Jan 2012
Posts: 74
|
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]
Show Tags
06 Feb 2012, 03:28
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 [ 22.91 KiB | Viewed 6665 times ]
|
|
|
|
|
|
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4132
|
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]
Show Tags
06 Feb 2012, 09:46
My apologies to kys123The 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
Last edited by mikemcgarry on 06 Oct 2013, 13:57, edited 1 time in total.
|
|
|
|
|
|
Director
Status: Final Countdown
Joined: 17 Mar 2010
Posts: 537
Location: India
GPA: 3.82
WE: Account Management (Retail Banking)
|
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]
Show Tags
03 Sep 2012, 03:56
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
_________________
" Make more efforts "
Press Kudos if you liked my post
|
|
|
|
|
|
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7452
Location: Pune, India
|
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]
Show Tags
03 Sep 2012, 06:35
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 [ 6.73 KiB | Viewed 6127 times ]
Attachment: 
Ques4.jpg [ 6.91 KiB | Viewed 6125 times ]
Attachment: 
Ques5.jpg [ 7.11 KiB | Viewed 6124 times ]
_________________
Karishma
Veritas Prep | GMAT Instructor
My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews
|
|
|
|
|
|
Senior Manager
Joined: 23 Oct 2010
Posts: 383
Location: Azerbaijan
Concentration: Finance
|
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]
Show Tags
23 Jan 2013, 10:32
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
I am still on all gmat forums. msg me if you want to ask me smth
|
|
|
|
|
|
Manager
Joined: 26 Apr 2013
Posts: 50
Location: United States
Concentration: Marketing, Nonprofit
GPA: 3.5
WE: Marketing (Telecommunications)
|
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]
Show Tags
04 Oct 2013, 21:09
mikemcgarry wrote: My apologies to kys123The 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
|
|
|
|
|
|
Manager
Joined: 14 Sep 2014
Posts: 94
WE: Engineering (Consulting)
|
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]
Show Tags
25 Sep 2014, 08:41
1
This post received
KUDOS
Bunuel wrote: 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 (1) 28 of the families in this neighborhood have a cat but not a dog. Attachment: Statement 1.PNG 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 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. If we use Venn Diagram it's a lot faster and space saver. Even though, because of timer, I misread question and thought 'the examiner asked about families with just a dog' and marked wrong answer 
|
|
|
|
|
|
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16031
|
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]
Show Tags
08 Oct 2015, 08:04
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources
|
|
|
|
|
|
Current Student
Joined: 12 Aug 2015
Posts: 306
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37 GMAT 2: 650 Q43 V36 GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
|
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]
Show Tags
12 Nov 2015, 11:20
indeed Venn + formula solve Statement 2 in 15 secs - very straightforward. on the overlapping sets very often matrix is the best approach however this question is the case when Venn is the shortest solution
_________________
KUDO me plenty
|
|
|
|
|
|
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 3480
GPA: 3.82
|
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]
Show Tags
15 Nov 2015, 10:59
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. 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. We get a '2by2' table as below: Attachment: 
GCDS calreg11 Of the 60 families in a certain neighborhood (20151113).jpg [ 29.17 KiB | Viewed 1787 times ]
The question asks a+c=? There are 4 variables (a,b,c,d) and 2 equations (a+b=38, a+b+c+d=60). 2 more equations are given by the 2 conditions, so there is high chance (C) will be our answer. Condition 1) a=28 Condition 2) a=d. question is asking for the same thing as whether a+c=d+c? so we get a+b+c+d=60, 38+c+d=60, c+d=22 from the original condition, and the answer becomes (B). For cases where we need 2 more equation, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________
 MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo
|
|
|
|
|
|
Director
Joined: 10 Mar 2013
Posts: 597
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)
|
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]
Show Tags
02 Jan 2016, 09:09
I've also solved this one easily using double-matrix. When you have 2 terms use always double-matrix, if you have >2 use formulas.
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660
|
|
|
|
|
|
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 3480
GPA: 3.82
|
Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]
Show Tags
02 Jan 2016, 23:22
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution 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. This is a “2-by-2” question, one of the most common types of questions in GMAT math. From modifying the original condition and the question, we can obtain a table below. From the table, we can see that the question is a+b=? There are 4 variables (a,b,c, and d) and 2 equations (a+b+c+d=60 and a+c=38). In order to match the number of variables and the number of equations, we need 2 more equations. Since the condition 1) and 2) each has 1 equation, there is high chance that C is the answer. Using both the condition 1) and 2), we get c=28. Also, since a=d, we get a+c=d+c=a+28=d+28=38. Then, a=d=10. So, if we substitute in a+b+c+d=60, we get 10+b+28+10=60. Then, b=12. So, a+b=10+12=22. So, the answer is unique and the condition is sufficient. So we can see how C could be the answer. However, a question involving hidden integer is one of key questions (integer, statistics, inequality, probability, absolute value) and we have to consider Mistake Type 4(A). In the case of the condition 2), since a=d, we get a+c=d+c=38. Then, if we substitute it into a+b+c+d=60, we get a+b+38=60. So, a+b=22. The answer is unique and the condition is sufficient. If both C and B are the answers to the question, the final correct answer choice is B. For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
Attachments
GCDS calreg11 Of the 60 families in a certain (20160103).jpg [ 23.73 KiB | Viewed 1531 times ]
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo
|
|
|
|
|
|
|
Re: Of the 60 families in a certain neighborhood, 38 have a cat.
[#permalink]
02 Jan 2016, 23:22
|
|
|
|
|
|
|
|
|
|
|
|
|
1
