NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 20:43 It is currently 24 Apr 2024, 20:43
Decision Tracker
My Rewards
New posts
New comers' posts

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

Of a group of 50 households, how many have at least one cat or at

SORT BY:
Date
Kudos
   1   2 
Tags:
Difficulty: 555-605 Levelx   Overlapping Setsx                     
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11170
Own Kudos [?]: 31894 [2]
Given Kudos: 290
Send PM
Reviews Badge
Re: Of a group of 50 households, how many have at least one cat or at [#permalink] New post   02 Sep 2020, 22:07
1
Kudos
1
Bookmarks
Expert Reply
INSEADIESE wrote:
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
G
goaltop30mba
Manager
Manager
Joined: 04 Dec 2015
Posts: 186
Own Kudos [?]: 64 [0]
Given Kudos: 407
Send PM
Of a group of 50 households, how many have at least one cat or at [#permalink] New post   03 Sep 2020, 12:05
chetan2u wrote:
INSEADIESE wrote:
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
L
dave13
VP
VP
Joined: 09 Mar 2016
Posts: 1160
Own Kudos [?]: 1017 [0]
Given Kudos: 3851
Send PM
Re: Of a group of 50 households, how many have at least one cat or at [#permalink] New post   04 Sep 2020, 06:59
VeritasKarishma wrote:
sjung92 wrote:
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
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14817
Own Kudos [?]: 64904 [1]
Given Kudos: 426
Location: Pune, India
Send PM
Re: Of a group of 50 households, how many have at least one cat or at [#permalink] New post   08 Sep 2020, 05:45
1
Kudos
Expert Reply
dave13 wrote:
VeritasKarishma wrote:
sjung92 wrote:
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
P
MHIKER
Director
Director
Joined: 14 Jul 2010
Status:No dream is too large, no dreamer is too small
Posts: 972
Own Kudos [?]: 4927 [0]
Given Kudos: 690
Concentration: Accounting
Send PM
Re: Of a group of 50 households, how many have at least one cat or at [#permalink] New post   17 Sep 2020, 09:06
Top Contributor
Bunuel wrote:
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
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18756
Own Kudos [?]: 22049 [0]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: Of a group of 50 households, how many have at least one cat or at [#permalink] New post   18 Sep 2020, 07:23
Expert Reply
INSEADIESE wrote:
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
B
ManyataM
Manager
Manager
Joined: 27 Apr 2020
Posts: 103
Own Kudos [?]: 20 [0]
Given Kudos: 25
Send PM
Re: Of a group of 50 households, how many have at least one cat or at [#permalink] New post   18 Dec 2020, 08:59
ScottTargetTestPrep wrote:
Bunuel wrote:
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
B
ManyataM
Manager
Manager
Joined: 27 Apr 2020
Posts: 103
Own Kudos [?]: 20 [0]
Given Kudos: 25
Send PM
Re: Of a group of 50 households, how many have at least one cat or at [#permalink] New post   18 Dec 2020, 09:04
Bunuel wrote:
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
P
MHIKER
Director
Director
Joined: 14 Jul 2010
Status:No dream is too large, no dreamer is too small
Posts: 972
Own Kudos [?]: 4927 [0]
Given Kudos: 690
Concentration: Accounting
Send PM
Re: Of a group of 50 households, how many have at least one cat or at [#permalink] New post   18 Dec 2020, 13:51
Top Contributor
ManyataM wrote:
Bunuel wrote:
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
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11170
Own Kudos [?]: 31894 [0]
Given Kudos: 290
Send PM
Reviews Badge
Re: Of a group of 50 households, how many have at least one cat or at [#permalink] New post   18 Dec 2020, 19:53
Expert Reply
ManyataM wrote:
Bunuel wrote:
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
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18756
Own Kudos [?]: 22049 [0]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: Of a group of 50 households, how many have at least one cat or at [#permalink] New post   22 Dec 2020, 19:50
Expert Reply
ManyataM wrote:
ScottTargetTestPrep wrote:
Bunuel wrote:
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
B
KANNUPRIYA17
Intern
Intern
Joined: 12 May 2020
Posts: 9
Own Kudos [?]: 8 [0]
Given Kudos: 28
Location: India
Send PM
Re: Of a group of 50 households, how many have at least one cat or at [#permalink] New post   29 Dec 2020, 10:47
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
B
KANNUPRIYA17
Intern
Intern
Joined: 12 May 2020
Posts: 9
Own Kudos [?]: 8 [0]
Given Kudos: 28
Location: India
Send PM
Re: Of a group of 50 households, how many have at least one cat or at [#permalink] New post   29 Dec 2020, 10:49
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
D
avigutman
Tutor
Joined: 17 Jul 2019
Posts: 1304
Own Kudos [?]: 2285 [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
Send PM
Re: Of a group of 50 households, how many have at least one cat or at [#permalink] New post   06 Jan 2021, 08:15
7
Kudos
2
Bookmarks
Expert Reply
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14817
Own Kudos [?]: 64904 [1]
Given Kudos: 426
Location: Pune, India
Send PM
Re: Of a group of 50 households, how many have at least one cat or at [#permalink] New post   18 Feb 2021, 01:23
1
Kudos
Expert Reply
VeritasKarishma wrote:
Bunuel wrote:
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
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5957
Own Kudos [?]: 13387 [2]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: Of a group of 50 households, how many have at least one cat or at [#permalink] New post   06 May 2021, 23:11
1
Kudos
1
Bookmarks
Expert Reply
Bunuel wrote:
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.


Wanna make solving the Official Questions interesting???


Click here and solve 1000+ Official Questions with Video solutions as Timed Sectional Tests
and Dedicated Data Sufficiency (DS) Course


Answer: Option C

Video solution by GMATinsight



Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub :)
User avatar
B
AntonioGalindo
Intern
Intern
Joined: 22 Jul 2017
Posts: 32
Own Kudos [?]: 22 [0]
Given Kudos: 222
Send PM
GMAT ToolKit User
Re: Of a group of 50 households, how many have at least one cat or at [#permalink] New post   18 Feb 2022, 09:41
avigutman wrote:
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
D
avigutman
Tutor
Joined: 17 Jul 2019
Posts: 1304
Own Kudos [?]: 2285 [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
Send PM
Re: Of a group of 50 households, how many have at least one cat or at [#permalink] New post   18 Feb 2022, 12:00
1
Kudos
Expert Reply
AntonioGalindo wrote:
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
B
AntonioGalindo
Intern
Intern
Joined: 22 Jul 2017
Posts: 32
Own Kudos [?]: 22 [0]
Given Kudos: 222
Send PM
GMAT ToolKit User
Re: Of a group of 50 households, how many have at least one cat or at [#permalink] New post   25 Feb 2022, 08:50
avigutman wrote:
AntonioGalindo wrote:
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
B
Mananjain
Intern
Intern
Joined: 13 Jul 2020
Posts: 8
Own Kudos [?]: 1 [0]
Given Kudos: 15
Location: India
Schools: ISB '24
GMAT 1: 670 Q50 V30
GMAT 2: 690 Q50 V31
GPA: 4
Send PM
Re: Of a group of 50 households, how many have at least one cat or at [#permalink] New post   28 Jan 2024, 09:08
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
GMAT Club Bot
gmatclubot
Re: Of a group of 50 households, how many have at least one cat or at [#permalink]
28 Jan 2024, 09:08
   1   2 
Moderator:
Bunuel
Math Expert
92900 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions