Last visit was: 19 Apr 2025, 07:05 It is currently 19 Apr 2025, 07:05
Home
GMAT
Messages
Tests
Schools
Reviews
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
 1   2   3   
555-605 Level|   Overlapping Sets|                     
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Apr 2025
Posts: 100,761
Own Kudos:
717,703
 [160]
Given Kudos: 93,108
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 100,761
Kudos: 717,703
 [160]
Of a group of 50 households, how many have at least one cat or at 26 Jun 2017, 02:27
8
Kudos
Add Kudos
152
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

73% (01:28) correct 27% (01:34) wrong based on 4567 sessions

History

Date
Time
Result
Not Attempted Yet
Of a group of 50 households, how many have at least one cat or at least one dog, but not both?

(1) The number of households that have at least one cat and at least one dog is 4.
(2) The number of households that have no cats and no dogs is 14.
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 18 Apr 2025
Posts: 20,592
Own Kudos:
25,600
 [37]
Given Kudos: 292
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 20,592
Kudos: 25,600
 [37]
Of a group of 50 households, how many have at least one cat or at 15 Nov 2017, 17:26
12
Kudos
Add Kudos
25
Bookmarks
Bookmark this Post
Bunuel
Of a group of 50 households, how many have at least one cat or at least one dog, but not both?

(1) The number of households that have at least one cat and at least one dog is 4.
(2) The number of households that have no cats and no dogs is 14.

We have a group of 50 households and need to determine how many of those households have at least one cat or at least one dog, but not both.

We can use the following formula:

total = # with at least one dog only + # with at least one cat only + # with both + # with neither

50 = # with at least one dog only + # with at least one cat only + # with both + # with neither

So, we need to determine # with at least one dog only + # with at least one cat only

Statement One Alone:

The number of households that have at least one cat and at least one dog is 4.

So, we have:

50 = # with at least one dog only + # with at least one cat only + 4 + # with neither

46 = # with at least one dog only + # with at least one cat only + # with neither

Since we don’t know the # with neither, we can not determine # with at least one dog only + # with at least one cat only. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

The number of households that have no cats and no dogs is 14.

So, we have:

50 = # with at least one dog only + # with at least one cat only + # with both + 14

36 = # with at least one dog only + # with at least one cat only + # with both

Since we don’t know the # with both, we cannot determine # with at least one dog only + # with at least one cat only. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using statements one and two, we have:

50 = # with at least one dog only + # with at least one cat only + 4 + 14

50 = # with at least one dog only + # with at least one cat only + 18

32 = # with at least one dog only + # with at least one cat only

Answer: C
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 18 Apr 2025
Posts: 15,889
Own Kudos:
72,688
 [17]
Given Kudos: 462
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 15,889
Kudos: 72,688
 [17]
Of a group of 50 households, how many have at least one cat or at 07 Apr 2020, 01:37
15
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
sjung92
Why is everybody adding both instead of subtracting? Official GMAT also adds both and I'm confused as to why.

I thought the formula was Total = A + B - Both + Neither

A different formula is being used here:

Total = Only A + Only B + Both + Neither

In the formula given by you, A includes Both and B also includes Both so we subtract out Both once.
In the formula being used in this question, we are considering those who have dogs only and those who have cats only. So we add to them those who have both and those who have neither to give us the total number of people.
General Discussion
User avatar
pushpitkc
User avatar
Joined: 26 Feb 2016
Last visit: 19 Feb 2025
Posts: 2,830
Own Kudos:
5,761
 [15]
Given Kudos: 47
Location: India
GPA: 3.12
Posts: 2,830
Kudos: 5,761
 [15]
Of a group of 50 households, how many have at least one cat or at 26 Jun 2017, 03:00
8
Kudos
Add Kudos
7
Bookmarks
Bookmark this Post
P(Total) = 50
P(at least one Dog) = x
P(at least one Cat) = y
P(Both at least one dog and at least one cat) = z
P(Neither) = Households which have neither a dog nor a cat.

P(Total) = P(at least one Dog) + P(at least one Cat) + P(Both at least one dog and at least one cat) + P(Neither)

1) The number of households that have at least one cat and at least one dog is 4 - z = 4
Since we do not have any information about houses with neither, we cannot clearly
tell how many households have at least one cat or at least one dog(but not both). (Insufficient)

2) The number of households that have no cats and no dogs is 14 - P(Neither) = 14
Since we do not have any information about houses with both, we cannot clearly
tell how many households have at least one cat or at least one dog(but not both). (Insufficient)

Combining information from both the statements, 50 = x + y + 4 + 14 | x+y = 32 (Sufficient - Option C)
User avatar
amanvermagmat
User avatar
Retired Moderator
Joined: 22 Aug 2013
Last visit: 28 Mar 2025
Posts: 1,168
Own Kudos:
2,708
 [37]
Given Kudos: 480
Location: India
Posts: 1,168
Kudos: 2,708
 [37]
Of a group of 50 households, how many have at least one cat or at 03 Jul 2017, 01:04
28
Kudos
Add Kudos
9
Bookmarks
Bookmark this Post
As in the attached picture.

Answer should be C.
Attachments

IMG_20170703_133141-2.jpg
IMG_20170703_133141-2.jpg [ 52.07 KiB | Viewed 58586 times ]

User avatar
akshayk
User avatar
Joined: 06 Jul 2016
Last visit: 21 Sep 2020
Posts: 274
Own Kudos:
392
 [2]
Given Kudos: 99
Location: Singapore
Concentration: Strategy, Finance
Posts: 274
Kudos: 392
 [2]
Of a group of 50 households, how many have at least one cat or at 08 Aug 2017, 09:43
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
Of a group of 50 households, how many have at least one cat or at least one dog, but not both?

(1) The number of households that have at least one cat and at least one dog is 4.
(2) The number of households that have no cats and no dogs is 14.

Total = 50
Households with at least 1 cat OR 1 dog = ?

1) Households with at least 1 cat AND 1 dog = 4
Remaining Households = 46
We cannot determine the number of households with at least 1 cat OR 1 dog.
Insufficient.

2) No Cats and No Dogs = 14
Remaining Households = 36
We cannot determine the number of households with at least 1 cat OR 1 dog.
Insufficient.

1+2)
Total = 50
Households with 1 cat AND 1 dog = 4
Households with NO cats and dogs = 14
=> Households with at least 1 cat OR 1 god = 32

Sufficient. C is the answer.
avatar
sadikabid27
avatar
Joined: 10 Sep 2014
Last visit: 23 Jul 2021
Posts: 59
Own Kudos:
32
 [3]
Given Kudos: 417
Location: Bangladesh
GPA: 3.5
WE:Project Management (Manufacturing)
Posts: 59
Kudos: 32
 [3]
Of a group of 50 households, how many have at least one cat or at 27 Aug 2017, 19:47
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
pushpitkc
P(Total) = 50
P(at least one Dog) = x
P(at least one Cat) = y
P(Both at least one dog and at least one cat) = z
P(Neither) = Households which have neither a dog nor a cat.

P(Total) = P(at least one Dog) + P(at least one Cat) + P(Both at least one dog and at least one cat) + P(Neither)

1) The number of households that have at least one cat and at least one dog is 4.
z = 4
Since, we do not have any information about houses with neither,
we cannot clearly tell how many households have at at least one cat or at least one dog(but not both). Insufficient.

2) The number of households that have no cats and no dogs is 14.
P(Neither) = 14.
Since, we do not have any information about houses with both,
we cannot clearly tell how many households have at at least one cat or at least one dog(but not both). Insufficient.

Combining information from both the statements,
50 = x +y +4 +14
x+y = 32(Sufficient) (Option C)

I'm not understanding the fact that, isn't the formula for this set problem is total=(a+b-both+neither)? Why are you adding "both" here? Could you please clarify me.
avatar
pks02
avatar
Joined: 16 Oct 2016
Last visit: 30 Apr 2020
Posts: 4
Own Kudos:
3
 [2]
Given Kudos: 3
Posts: 4
Kudos: 3
 [2]
Of a group of 50 households, how many have at least one cat or at 13 Oct 2018, 23:23
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
How to solve this question with a double set matrix ?
avatar
sakuac
avatar
Joined: 25 Sep 2018
Last visit: 07 May 2021
Posts: 4
Own Kudos:
1
Given Kudos: 115
GMAT 1: 640 Q46 V35
GMAT 1: 640 Q46 V35
Posts: 4
Kudos: 1
Of a group of 50 households, how many have at least one cat or at 26 Oct 2018, 14:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
pks02
How to solve this question with a double set matrix ?

waiting for the same.
User avatar
Salsanousi
User avatar
Joined: 19 Oct 2013
Last visit: 29 Dec 2020
Posts: 399
Own Kudos:
340
 [5]
Given Kudos: 117
Location: Kuwait
GPA: 3.2
WE:Engineering (Real Estate)
Posts: 399
Kudos: 340
 [5]
Of a group of 50 households, how many have at least one cat or at 26 Oct 2018, 15:42
5
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi sakuac and pks02

Please refer to the attached image I hope it helps.

Posted from my mobile device
Attachments

F862B01F-3F62-4163-A022-A0156EB66CB7.jpeg
F862B01F-3F62-4163-A022-A0156EB66CB7.jpeg [ 51.22 KiB | Viewed 51961 times ]

avatar
lstsch
avatar
Joined: 09 Aug 2018
Last visit: 10 Apr 2020
Posts: 9
Own Kudos:
3
Given Kudos: 134
Posts: 9
Kudos: 3
Of a group of 50 households, how many have at least one cat or at 21 Feb 2019, 10:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Salsanousi: How are you getting 32? Because according to your picture -z + z = 0.
avatar
jwang157
avatar
Joined: 23 Feb 2019
Last visit: 04 Jul 2019
Posts: 1
Own Kudos:
3
 [3]
Given Kudos: 4
Posts: 1
Kudos: 3
 [3]
Of a group of 50 households, how many have at least one cat or at 25 Feb 2019, 08:09
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
It should be P(Total) = P(at least one Dog) + P(at least one Cat)-P(Both at least one dog and at least one cat) + P(Neither)
Not P(Total) = P(at least one Dog) + P(at least one Cat) + P(Both at least one dog and at least one cat) + P(Neither)

But anyway, you don't need to get an accurate number, Im just saying.
User avatar
sakshamchhabra
User avatar
Joined: 09 Mar 2018
Last visit: 09 Nov 2020
Posts: 36
Own Kudos:
82
Given Kudos: 182
Location: India
Schools: CBS Deferred "24
Schools: CBS Deferred "24
Posts: 36
Kudos: 82
Of a group of 50 households, how many have at least one cat or at 29 Mar 2019, 23:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u VeritasKarishma
Salsanousi
Hi sakuac and pks02

Please refer to the attached image I hope it helps.

Posted from my mobile device

This is wrong because X + Z + Y + 14 should always be equal to total sum i.e 50

moreover, Z will cancel out and which variable is 32 then ??

I guess the first statement is incorrect, it should rather say

"The number of households that have at least one cat and at least one dog but not both is 4"

because in that scenario

X+Y+Z+14 = 50

we know, X+Y = 4

which gives Z= 32.


please correct me, experts
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 18 Apr 2025
Posts: 15,889
Own Kudos:
72,688
 [8]
Given Kudos: 462
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 15,889
Kudos: 72,688
 [8]
Of a group of 50 households, how many have at least one cat or at 30 Mar 2019, 23:23
5
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
Bunuel
Of a group of 50 households, how many have at least one cat or at least one dog, but not both?

(1) The number of households that have at least one cat and at least one dog is 4.
(2) The number of households that have no cats and no dogs is 14.

It is fairly simple.

You have 50 households. No of households with no cats and no dogs = 14.
So 50 - 14 = 36 households have at least one cat or at least one dog or both.

So 36 households lie in the two overlapping circles, some in yellow region (only at least 1 cat), some in blue (only at least 1 dog) and 4 in green (both).

Attachment:
Screenshot 2019-03-31 at 11.50.25.png
Screenshot 2019-03-31 at 11.50.25.png [ 44.06 KiB | Viewed 48488 times ]

Question: "how many have at least one cat or at least one dog, but not both?"
There are 4 households in both region. So number of households in yellow + blue only = 36 - 4 = 32
avatar
forrgrav
avatar
Joined: 16 Apr 2019
Last visit: 30 Oct 2019
Posts: 3
Own Kudos:
1
Given Kudos: 7
Posts: 3
Kudos: 1
Of a group of 50 households, how many have at least one cat or at 11 May 2019, 04:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Are we not double counting the middle of the diagram? Is it not included when you calculate x or z since those houses are counted? For example, if z = 20 then wouldnt counting the 4 houses that have cats as well as the 4 that have dogs be double counting since we have already included them in the calculation for z? I am reading the equation as this.

P(total) = z+x-y+neither
avatar
shabuzen102
avatar
Joined: 11 Aug 2019
Last visit: 24 Jul 2020
Posts: 68
Own Kudos:
25
 [4]
Given Kudos: 112
Posts: 68
Kudos: 25
 [4]
Of a group of 50 households, how many have at least one cat or at 05 Oct 2019, 07:28
2
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Salsanousi
Hi sakuac and pks02

Please refer to the attached image I hope it helps.

Posted from my mobile device

Salsanousi sakuac pks02
This is wrong. The correct one is in the image attached.

The first statement said: The number of households that have at least one cat AND at least one dog is 4.
That means the box where there's both Dog and Cat is 4. Take 50 minus Neither, minus Both, then we have Cats (not dogs) + Dogs (not cats), which is what the question is asking.
Attachments

GMATclub.png
GMATclub.png [ 5.81 KiB | Viewed 44072 times ]

avatar
pulak1988
avatar
Joined: 15 Jan 2019
Last visit: 09 Sep 2020
Posts: 49
Own Kudos:
6
Given Kudos: 249
Location: India
Schools: ISB '20 IIMA Rotman '22 GMBA '21 (S)
GMAT 1: 650 Q42 V38
GPA: 4
Schools: ISB '20 IIMA Rotman '22 GMBA '21 (S)
GMAT 1: 650 Q42 V38
Posts: 49
Kudos: 6
Of a group of 50 households, how many have at least one cat or at 05 Oct 2019, 09:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Of a group of 50 households, how many have at least one cat or at least one dog, but not both?

(1) The number of households that have at least one cat and at least one dog is 4.
(2) The number of households that have no cats and no dogs is 14.


This is a easy q.

we need number of houses that have only one animal .
stmnt 1 : says about all houses with both animals. so these are substracted from 50. but it doesnt mention about houses with no animals. so, NS
stmnt 2: mentions houses with no animals. so these are substracted from 50. but doesnt mention about houses with animals.. so, NS

both stmnts, mentions houses with 2 animals, and no animals. so left ones are houses with one animal.

hence, answer is 'C'
avatar
sjung92
avatar
Joined: 24 Oct 2016
Last visit: 14 Jul 2020
Posts: 3
Own Kudos:
2
 [2]
Given Kudos: 3
Posts: 3
Kudos: 2
 [2]
Of a group of 50 households, how many have at least one cat or at 06 Apr 2020, 14:06
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Why is everybody adding both instead of subtracting? Official GMAT also adds both and I'm confused as to why.

I thought the formula was Total = A + B - Both + Neither
User avatar
goaltop30mba
User avatar
Joined: 04 Dec 2015
Last visit: 19 Apr 2025
Posts: 186
Own Kudos:
66
Given Kudos: 407
Posts: 186
Kudos: 66
Of a group of 50 households, how many have at least one cat or at 02 Sep 2020, 14:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasKarishma Bunuel chetan2u GMATBusters nick1816

ScottTargetTestPrep

Hi Experts!

Hope you all are doing well

Although i am able to understand that we need both "neither" and "both" so as to find what has been asked in this question, I have a doubt..

For point (2) of the question, Isn't "not A and not B" equal to "not(A and B)", which basically means "not(Both A and B)", which definitely isn't the same as "Neither A nor B" ????

Looking forward to hearing from you

Best Regards,
User avatar
GMATBusters
User avatar
GMAT Tutor
Joined: 27 Oct 2017
Last visit: 18 Apr 2025
Posts: 1,926
Own Kudos:
6,250
 [1]
Given Kudos: 241
WE:General Management (Education)
Expert
Expert reply
Posts: 1,926
Kudos: 6,250
 [1]
Of a group of 50 households, how many have at least one cat or at 02 Sep 2020, 20:05
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
"not A and not B" means there should not be any A

so only A is also not acceptable

similarly, only B is not acceptable.

Hence "not A and not B" = "not(A or B)"


(when you used "not A and not B" = "not(A and B)", you are accepting only A or only B which is NOT right.

INSEADIESE
VeritasKarishma Bunuel chetan2u GMATBusters nick1816

ScottTargetTestPrep

Hi Experts!

Hope you all are doing well

Although i am able to understand that we need both "neither" and "both" so as to find what has been asked in this question, I have a doubt..

For point (2) of the question, Isn't "not A and not B" equal to "not(A and B)", which basically means "not(Both A and B)", which definitely isn't the same as "Neither A nor B" ????

Looking forward to hearing from you

Best Regards,
 1   2   3   
Moderator:
Bunuel
Math Expert
100761 posts