Last visit was: 12 May 2025, 02:02 It is currently 12 May 2025, 02:02
Home
GMAT
Messages
Tests
Schools
Events
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
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 28 Apr 2025
Posts: 11,317
Own Kudos:
40,543
 [2]
Given Kudos: 333
Status:Math and DI Expert
Products:
My Reviews
Expert
Expert reply
Posts: 11,317
Kudos: 40,543
 [2]
Of a group of 50 households, how many have at least one cat or at 02 Sep 2020, 22:07
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
INSEADIESE
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,


Neither A nor B means NONE of the two should be there.
Not A and Not B also means both should not be there.....Since AND is used we consider cases where BOTH condition exist, that is NO A and NO B.

In these questions there is nothing known as NOT (BOTH A and B), it is simply NOT (A and B), that is Neither A nor B

Quote:
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 can draw a Venn diagram or 2*2 matrix.
........D......n(D)...Total
C......a.......b.....
n(C)..x......y.....
TOTAL.............a+b+x+y=50

We are looking for at least one cat or at least one dog, but not both => b+x

(1) The number of households that have at least one cat and at least one dog is 4....=> a=4
........D......n(D)...Total
C......4.......b.....
n(C)..x......y.....
TOTAL.............a+b+x+y=50=4+b+x+y...We require to know y.
Insuff

(2) The number of households that have no cats and no dogs is 14.....=> y=14
........D......n(D)...Total
C......a.......b.....
n(C)..x......14.....
TOTAL.............a+b+x+y=50=a+b+x+14...We require to know a.
Insuff

Combined..
........D......n(D)...Total
C......4.......b.....
n(C)..x......14.....
TOTAL.............a+b+x+y=50=4+b+x+14...
b+x=50-18=32
Suff

C
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 03 Sep 2020, 12:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
INSEADIESE
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,


Neither A nor B means NONE of the two should be there.
Not A and Not B also means both should not be there.....Since AND is used we consider cases where BOTH condition exist, that is NO A and NO B.

In these questions there is nothing known as NOT (BOTH A and B), it is simply NOT (A and B), that is Neither A nor B

Quote:
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 can draw a Venn diagram or 2*2 matrix.
........D......n(D)...Total
C......a.......b.....
n(C)..x......y.....
TOTAL.............a+b+x+y=50

We are looking for at least one cat or at least one dog, but not both => b+x

(1) The number of households that have at least one cat and at least one dog is 4....=> a=4
........D......n(D)...Total
C......4.......b.....
n(C)..x......y.....
TOTAL.............a+b+x+y=50=4+b+x+y...We require to know y.
Insuff

(2) The number of households that have no cats and no dogs is 14.....=> y=14
........D......n(D)...Total
C......a.......b.....
n(C)..x......14.....
TOTAL.............a+b+x+y=50=a+b+x+14...We require to know a.
Insuff

Combined..
........D......n(D)...Total
C......4.......b.....
n(C)..x......14.....
TOTAL.............a+b+x+y=50=4+b+x+14...
b+x=50-18=32
Suff

C


thank you for the reply

what would be not(both A and B), I mean how do we write it?? would the expression have to have the word "both" ??

regards,
User avatar
dave13
User avatar
Joined: 09 Mar 2016
Last visit: 23 Nov 2024
Posts: 1,114
Own Kudos:
1,077
Given Kudos: 3,851
Posts: 1,114
Kudos: 1,077
Of a group of 50 households, how many have at least one cat or at 04 Sep 2020, 06:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasKarishma
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.

VeritasKarishma could you pls slightly tweak :grin: this DS question into the one where we would need to use Total = A + B - Both + Neither
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 11 May 2025
Posts: 15,959
Own Kudos:
73,053
 [1]
Given Kudos: 467
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 15,959
Kudos: 73,053
 [1]
Of a group of 50 households, how many have at least one cat or at 08 Sep 2020, 05:45
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
dave13
VeritasKarishma
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.

VeritasKarishma could you pls slightly tweak :grin: this DS question into the one where we would need to use Total = A + B - Both + Neither

Normally, the questions ask for number of households having at least one cat or at least one dog.
That is n(C or D)

"Total - Neither" is "at least one cat or at least one dog".

Total = n(C or D) + Neither
n(C or D) = n(C) + n(D) - Both

Look at what this question is asking and that is what makes it special:

Of a group of 50 households, how many have at least one cat or at least one dog, but not both?

It just wants you to remove Both from n(C or D).

n(C or D) - Both = n(C) + n(D) - Both - Both
n(C or D) - Both = n(C) - Both + n(D) - Both
n(C or D) - Both = n(Only C) + n(Only D)

That is how the two are equivalent.

Use your std formula if you wish.

Total = n(C or D) + Neither
50 = n(C or D) + 14
n(C or D) = 36
This includes those households that have both. So remove Both
n(C or D) - Both = 36 - 4 = 32
User avatar
MHIKER
User avatar
Joined: 14 Jul 2010
Last visit: 24 May 2021
Posts: 946
Own Kudos:
5,381
Given Kudos: 690
Status:No dream is too large, no dreamer is too small
Concentration: Accounting
Posts: 946
Kudos: 5,381
Of a group of 50 households, how many have at least one cat or at 17 Sep 2020, 09:06
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.


The general formula of two overlapping sets is ; TOTAL = A + B -BOTH + NEITHER

At least one for two overlapping sets:

TOTAL - BOTH + NEITHER= AT LEAST CATS OR DOGS

1. BOTH IS GIVEN BUT NO INFORMATION ABOUT NEITHER; INSUFF.

2. NEITHER ' 14 IS GIVEN BUT BOTH IS ABSENT; INSUFF.

1 & 2 TOGATHER IS SUFFICIENT. ANS C.
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 11 May 2025
Posts: 20,731
Own Kudos:
25,775
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: 20,731
Kudos: 25,775
Of a group of 50 households, how many have at least one cat or at 18 Sep 2020, 07:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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,

"not A and not B" is not the same thing as "not(A and B)". In order for "not A and not B" to hold, both "not A" and "not B" must hold; in other words, your element should not belong to A and should not belong to B. In a two-set Venn diagram, this would correspond to the area outside the two sets, which is usually denoted as "Neither". So, "not A and not B" is actually the same thing as "Neither A nor B".

On the other hand, "not(A and B)" is true when your element is not in "A and B", meaning your element either isn't in A or isn't in B. As long as the element misses at least one of the sets, your element is not in "A and B" (which is the same thing as saying your element is in "not(A and B)"). In a two-set Venn diagram, this would correspond to the area outside the overlap of the two sets.
User avatar
ManyataM
User avatar
Joined: 27 Apr 2020
Last visit: 12 Jun 2021
Posts: 100
Own Kudos:
24
Given Kudos: 24
Posts: 100
Kudos: 24
Of a group of 50 households, how many have at least one cat or at 18 Dec 2020, 08:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ScottTargetTestPrep
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



Why did we use the formula
total= cat+dog+both+neither

whereas the formula is : Total- neither= cat+dog-both+neither?????

can you please explain?
User avatar
ManyataM
User avatar
Joined: 27 Apr 2020
Last visit: 12 Jun 2021
Posts: 100
Own Kudos:
24
Given Kudos: 24
Posts: 100
Kudos: 24
Of a group of 50 households, how many have at least one cat or at 18 Dec 2020, 09:04
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.


can you please explain why did we use the formula

Total = cat+dog+both+neither

whereas the formula is

total = cat+ dog -both+neither
User avatar
MHIKER
User avatar
Joined: 14 Jul 2010
Last visit: 24 May 2021
Posts: 946
Own Kudos:
5,381
Given Kudos: 690
Status:No dream is too large, no dreamer is too small
Concentration: Accounting
Posts: 946
Kudos: 5,381
Of a group of 50 households, how many have at least one cat or at 18 Dec 2020, 13:51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ManyataM
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.


can you please explain why did we use the formula

Total = cat+dog+both+neither

whereas the formula is

total = cat+ dog -both+neither

ScottTargetTestPrep Please answer.
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 28 Apr 2025
Posts: 11,317
Own Kudos:
40,543
 [1]
Given Kudos: 333
Status:Math and DI Expert
Products:
My Reviews
Expert
Expert reply
Posts: 11,317
Kudos: 40,543
 [1]
Of a group of 50 households, how many have at least one cat or at 18 Dec 2020, 19:53
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ManyataM
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.


can you please explain why did we use the formula

Total = cat+dog+both+neither

whereas the formula is

total = cat+ dog -both+neither


The formula depends on what cat + dog means.
If it is only, then only cat + only dog + both + neither.
And that is exactly what at least one cat or at least one dog but not both means, so we look for only cat + only dog.

We use the formula c+d-both+neither, when c includes all households that is only cat + both cat and dog.
As both gets added twice we subtract it once.

Both the formula mean the same depending on what c and d include.
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 11 May 2025
Posts: 20,731
Own Kudos:
25,775
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: 20,731
Kudos: 25,775
Of a group of 50 households, how many have at least one cat or at 22 Dec 2020, 19:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ManyataM
ScottTargetTestPrep
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



Why did we use the formula
total= cat+dog+both+neither

whereas the formula is : Total- neither= cat+dog-both+neither?????

can you please explain?

So, the following formula exists for a two category overlapping sets problem:

Total = Only A + Only B + both + neither
avatar
KANNUPRIYA17
avatar
Joined: 12 May 2020
Last visit: 23 Jan 2022
Posts: 9
Own Kudos:
11
Given Kudos: 28
Location: India
Posts: 9
Kudos: 11
Of a group of 50 households, how many have at least one cat or at 29 Dec 2020, 10:47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Firstly we know, Total member=50.
Formula used= (A or b)= (A)+(B)-(A and B).
OR
Total= None+(A or b)+ (A and B)

(1) The number of households that have at least one cat and at least one dog is 4.
From 1 we get (A and B)=4 But only statement 1 is not sufficient to find (A or b).

(2) The number of households that have no cats and no dogs is 14.
Now we know Total=50 and none= 14. But we still have no clue about (A and B) and (A or B)

COMBINING BOTH
Total= None+(A or b)+ (A and B)
50=14+ (A or b)+4
(A or b)=50-14-4=38

:)
avatar
KANNUPRIYA17
avatar
Joined: 12 May 2020
Last visit: 23 Jan 2022
Posts: 9
Own Kudos:
11
Given Kudos: 28
Location: India
Posts: 9
Kudos: 11
Of a group of 50 households, how many have at least one cat or at 29 Dec 2020, 10:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Firstly we know, Total member=50.
Formula used= (A or b)= (A)+(B)-(A and B).
OR
Total= None+(A or b)+ (A and B)

(1) The number of households that have at least one cat and at least one dog is 4.
From 1 we get (A and B)=4 But only statement 1 is not sufficient to find (A or b).

(2) The number of households that have no cats and no dogs is 14.
Now we know Total=50 and none= 14. But we still have no clue about (A and B) and (A or B)

COMBINING BOTH
Total= None+(A or b)+ (A and B)
50=14+ (A or b)+4
(A or b)=50-14-4=38
User avatar
avigutman
User avatar
Joined: 17 Jul 2019
Last visit: 08 May 2025
Posts: 1,296
Own Kudos:
1,878
 [9]
Given Kudos: 66
Location: Canada
Schools: NYU Stern (WA)
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Expert
Expert reply
Schools: NYU Stern (WA)
GMAT 3: 770 Q50 V45
Posts: 1,296
Kudos: 1,878
 [9]
Of a group of 50 households, how many have at least one cat or at 06 Jan 2021, 08:15
7
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 11 May 2025
Posts: 15,959
Own Kudos:
73,053
 [1]
Given Kudos: 467
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 15,959
Kudos: 73,053
 [1]
Of a group of 50 households, how many have at least one cat or at 18 Feb 2021, 01:23
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasKarishma
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

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

Quote:
hello expert,

do't we need to deduct 4 two times in order to get number of household only in blue and orange?

50 - 14 = 36 gives you n(C or D)

Note that n(C or D) = n(C) + n(D) - Both = 36

So already 1 Both has been subtracted out and we got 36. Now to remove Both, all we need to do is subtract it out once more only.
You get 36 - 4 = 32
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 12 May 2025
Posts: 6,290
Own Kudos:
15,307
 [2]
Given Kudos: 127
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,290
Kudos: 15,307
 [2]
Of a group of 50 households, how many have at least one cat or at 06 May 2021, 23:11
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.
Answer: Option C

Video solution by GMATinsight

User avatar
AntonioGalindo
User avatar
Joined: 22 Jul 2017
Last visit: 09 Oct 2024
Posts: 31
Own Kudos:
22
Given Kudos: 222
Posts: 31
Kudos: 22
Of a group of 50 households, how many have at least one cat or at 18 Feb 2022, 09:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
avigutman
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1


avigutman, could you please explain me why Statement I means that 4 is the value for both cats and dogs?

When I first attempted the question, I placed it as the sum of (Both Cat and Dog) + (Cat, but not Dog) +( Dog, but not Cat).

Will appreciate your input!
User avatar
avigutman
User avatar
Joined: 17 Jul 2019
Last visit: 08 May 2025
Posts: 1,296
Own Kudos:
1,878
 [1]
Given Kudos: 66
Location: Canada
Schools: NYU Stern (WA)
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Expert
Expert reply
Schools: NYU Stern (WA)
GMAT 3: 770 Q50 V45
Posts: 1,296
Kudos: 1,878
 [1]
Of a group of 50 households, how many have at least one cat or at 18 Feb 2022, 12:00
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AntonioGalindo
could you please explain me why Statement I means that 4 is the value for both cats and dogs?

When I first attempted the question, I placed it as the sum of (Both Cat and Dog) + (Cat, but not Dog) +( Dog, but not Cat).


AntonioGalindo consider these two statements:
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 at least one cat or at least one dog is 4.

For the first statement (the original statement from the problem), in order to be counted, you have to have:
at least one cat and at least one dog
For the second statement, in order to be counted, you have to have:
at least one cat or at least one dog is 4

Please let me know if you need further explanation.
User avatar
AntonioGalindo
User avatar
Joined: 22 Jul 2017
Last visit: 09 Oct 2024
Posts: 31
Own Kudos:
22
Given Kudos: 222
Posts: 31
Kudos: 22
Of a group of 50 households, how many have at least one cat or at 25 Feb 2022, 08:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
avigutman
AntonioGalindo
could you please explain me why Statement I means that 4 is the value for both cats and dogs?

When I first attempted the question, I placed it as the sum of (Both Cat and Dog) + (Cat, but not Dog) +( Dog, but not Cat).


AntonioGalindo consider these two statements:
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 at least one cat or at least one dog is 4.

For the first statement (the original statement from the problem), in order to be counted, you have to have:
at least one cat and at least one dog
For the second statement, in order to be counted, you have to have:
at least one cat or at least one dog is 4

Please let me know if you need further explanation.

Thank you Avi! Makes sense! Appreciate your valuable help.
User avatar
Mananjain
User avatar
Joined: 13 Jul 2020
Last visit: 21 Mar 2024
Posts: 8
Own Kudos:
1
Given Kudos: 15
Location: India
Schools: ISB '24
GMAT 1: 670 Q50 V30
GMAT 2: 690 Q50 V31
GPA: 4
Schools: ISB '24
GMAT 2: 690 Q50 V31
Posts: 8
Kudos: 1
Of a group of 50 households, how many have at least one cat or at 28 Jan 2024, 09:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Statement 1 says "atleast 1 cat and atleast 1 dog" . It means both Cat and dog,
Thus-
Dog Dog(not Total
Cat 4 b
Cat(not) a ?
Total 50
​We need to find a+b. ​Not sufficient.

Statement 2 says - "No cats and dogs"
Dog Dog(not Total
Cat ? b
Cat(not) a 14
Total 50
​We need to find a+b. ​Not sufficient.

​Combining these two,

Dog Dog(not Total
Cat 4 b 4+b
Cat(not) a 14 14+a
Total 4+a 14+b 50

​Now, 4+a + 14 + b = 50
a+b = 32
Sufficient.

Answer: C
   1   2   3   
Moderator:
Bunuel
Math Expert
101320 posts