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

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Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]

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05 Feb 2012, 16:50
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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

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05 Feb 2012, 18:24
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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]

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Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]

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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
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Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]

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05 Feb 2012, 23:13
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)

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
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Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]

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06 Feb 2012, 02:02
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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
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Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]

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06 Feb 2012, 02:39
I thought it was C as well... Can someone explain further?
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Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]

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06 Feb 2012, 03:08
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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 5642 times ]

(1) 28 of the families in this neighborhood have a cat but not a dog.
Attachment:

Statement 1.PNG [ 2.68 KiB | Viewed 5641 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 5647 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.

Hope it helps.
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Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]

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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.
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Picture 16.png [ 22.91 KiB | Viewed 5616 times ]

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Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]

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06 Feb 2012, 09:46
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
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Last edited by mikemcgarry on 06 Oct 2013, 13:57, edited 1 time in total.
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Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]

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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
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cats and dogs.docx [10.37 KiB]

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Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink]

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03 Sep 2012, 06:35
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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 5080 times ]

Attachment:

Ques4.jpg [ 6.91 KiB | Viewed 5078 times ]

Attachment:

Ques5.jpg [ 7.11 KiB | Viewed 5075 times ]

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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Current Student Joined: 23 Oct 2010 Posts: 386 Location: Azerbaijan Concentration: Finance Schools: HEC '15 (A) GMAT 1: 690 Q47 V38 Followers: 21 Kudos [?]: 264 [0], given: 73 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) Followers: 0 Kudos [?]: 67 [0], given: 2 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 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 Manager Joined: 14 Sep 2014 Posts: 94 WE: Engineering (Consulting) Followers: 1 Kudos [?]: 25 [1] , given: 51 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: 9647 Followers: 465 Kudos [?]: 120 [0], given: 0 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. _________________ Senior Manager Joined: 12 Aug 2015 Posts: 309 Concentration: General Management, Operations GMAT 1: 640 Q40 V37 GMAT 2: 650 Q43 V36 GPA: 3.3 WE: Management Consulting (Consulting) Followers: 4 Kudos [?]: 110 [0], given: 1472 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: 1205 GPA: 3.82 Followers: 72 Kudos [?]: 560 [0], given: 0 Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink] ### Show Tags 15 Nov 2015, 10:59 Expert's post 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 736 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. Unlimited Access to over 120 free video lessons - try it yourself See our Youtube demo Director Joined: 10 Mar 2013 Posts: 605 Location: Germany Concentration: Finance, Entrepreneurship GMAT 1: 580 Q46 V24 GPA: 3.88 WE: Information Technology (Consulting) Followers: 8 Kudos [?]: 143 [0], given: 200 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: 1205 GPA: 3.82 Followers: 72 Kudos [?]: 560 [0], given: 0 Re: Of the 60 families in a certain neighborhood, 38 have a cat. [#permalink] ### Show Tags 02 Jan 2016, 23:22 Expert's post 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 479 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. 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 Similar topics Replies Last post Similar Topics: 1 What percentage of families in the state have annual incomes over$50 3 09 Jul 2015, 03:56
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