Last visit was: 19 Nov 2025, 14:27 It is currently 19 Nov 2025, 14:27
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.
Close
Request Expert Reply
Confirm Cancel
User avatar
BarneyStinson
Joined: 21 Jul 2009
Last visit: 24 Sep 2010
Posts: 217
Own Kudos:
500
 [84]
Given Kudos: 22
Concentration: World Domination, Finance, Political Corporatization, Marketing, Strategy
Schools:LBS, INSEAD, IMD, ISB - Anything with just 1 yr program.
Posts: 217
Kudos: 500
 [84]
5
Kudos
Add Kudos
79
Bookmarks
Bookmark this Post
Most Helpful Reply
avatar
PareshGmat
Joined: 27 Dec 2012
Last visit: 10 Jul 2016
Posts: 1,534
Own Kudos:
8,102
 [19]
Given Kudos: 193
Status:The Best Or Nothing
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Posts: 1,534
Kudos: 8,102
 [19]
15
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
Given Kudos: 99,977
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,361
 [19]
6
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
General Discussion
avatar
piyushpachori
Joined: 08 Sep 2011
Last visit: 05 May 2014
Posts: 22
Own Kudos:
19
 [3]
Status:Accepted - SMU, Singapore (Class of 2013)
Location: Singapore
Concentration: Finance, General Management
GMAT 1: 620 Q46 V29
GMAT 2: 710 Q50 V35
WE:Information Technology (Computer Software)
GMAT 2: 710 Q50 V35
Posts: 22
Kudos: 19
 [3]
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Ans. A - 62

I solved this using Venn Diagrams. Attaching the solution for you. This is my first ever attachment in the forum. Not sure if it will display the image of the attachment has to be opened. Please check.
Attachments

sets_answer.jpg
sets_answer.jpg [ 12.5 KiB | Viewed 62634 times ]

User avatar
g106
Joined: 21 Aug 2010
Last visit: 21 Oct 2015
Posts: 128
Own Kudos:
370
 [9]
Given Kudos: 141
Location: United States
GMAT 1: 700 Q49 V35
GMAT 1: 700 Q49 V35
Posts: 128
Kudos: 370
 [9]
7
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Ans C
Attachments

Ans C.jpg
Ans C.jpg [ 46.5 KiB | Viewed 57000 times ]

avatar
alexjoh89
Joined: 17 Sep 2012
Last visit: 06 Aug 2014
Posts: 1
Own Kudos:
7
 [7]
Posts: 1
Kudos: 7
 [7]
7
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I have a question. If the formula is:

Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither

why is it then + 4 instead of -2*4?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,361
 [8]
Given Kudos: 99,977
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,361
 [8]
2
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
alexjoh89
I have a question. If the formula is:

Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither

why is it then + 4 instead of -2*4?

There are two formulas for 3 overlapping sets:
\(Total = A + B + C - (sum \ of \ 2-group \ overlaps) + (all \ three) + Neither\).

\(Total = A + B + C - (sum \ of \ EXACTLY \ 2-group \ overlaps) - 2*(all \ three) + Neither\).

For more check here: ADVANCED OVERLAPPING SETS PROBLEMS
avatar
elc280
Joined: 29 May 2013
Last visit: 29 Oct 2013
Posts: 1
Own Kudos:
2
 [2]
Posts: 1
Kudos: 2
 [2]
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Can you give an example of a problem where you would know to use the 2nd equation? Would the problem say something like "5 workers are in Marketing and Sales but not Vision, 4 are in Sales and Vision but not marketing," etc., so you know that each number does not include members that belong to all three sets?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,361
 [2]
Given Kudos: 99,977
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,361
 [2]
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
elc280
Can you give an example of a problem where you would know to use the 2nd equation? Would the problem say something like "5 workers are in Marketing and Sales but not Vision, 4 are in Sales and Vision but not marketing," etc., so you know that each number does not include members that belong to all three sets?

All examples are here: ADVANCED OVERLAPPING SETS PROBLEMS

DS questions on Overlapping Sets: search.php?search_id=tag&tag_id=45
PS questions on Overlapping Sets: search.php?search_id=tag&tag_id=65

Hope it helps.
avatar
dobrecf
Joined: 27 May 2013
Last visit: 03 Feb 2021
Posts: 1
Posts: 1
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Workers are grouped by their areas of expertise and are placed on at least one

team. There are 20 workers on the Marketing team, 30 on the Sales team, and 40

on the Vision team. 5 workers are on both the Marketing and Sales teams, 6 workers

are on both the Sales and Vision teams, 9 workers are on both the Marketing

and Vision teams, and 4 workers are on all three teams. How many workers are

there in total?

How do you solve it using the formula:(Total in Group 1) + (Total in Group 2) + (Total in Group 3) – (Overlap of 1 and 2) – (Overlap of 1 and 3) – (Overlap of 2 and 3) – [2 * (Overlap of 1, 2, and 3)] + (total in none of the groups) = Overall total
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
Given Kudos: 99,977
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,361
Kudos
Add Kudos
Bookmarks
Bookmark this Post
dobrecf
Workers are grouped by their areas of expertise and are placed on at least one

team. There are 20 workers on the Marketing team, 30 on the Sales team, and 40

on the Vision team. 5 workers are on both the Marketing and Sales teams, 6 workers

are on both the Sales and Vision teams, 9 workers are on both the Marketing

and Vision teams, and 4 workers are on all three teams. How many workers are

there in total?

How do you solve it using the formula:(Total in Group 1) + (Total in Group 2) + (Total in Group 3) – (Overlap of 1 and 2) – (Overlap of 1 and 3) – (Overlap of 2 and 3) – [2 * (Overlap of 1, 2, and 3)] + (total in none of the groups) = Overall total

Merging similar topics. Please refer to the solutions above.

Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules, 1, 2, 3, 7, 8, and 10. Thank you.
User avatar
NGGMAT
Joined: 20 Oct 2013
Last visit: 26 May 2014
Posts: 37
Own Kudos:
10
 [2]
Given Kudos: 27
Posts: 37
Kudos: 10
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi

How to identify when the qs is meaning to say exactly 2 overlaps and when the qs means otherwise? This qs seemed like it meant exactly 2.
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 19 Nov 2025
Posts: 16,267
Own Kudos:
77,000
 [3]
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 77,000
 [3]
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nandinigaur
Hi

How to identify when the qs is meaning to say exactly 2 overlaps and when the qs means otherwise? This qs seemed like it meant exactly 2.

The question will have words such as 'only' or 'exactly' when it wants to specify that n number of people are in exactly 2 teams.
10 people belong to A and B implies that there are 10 people who belong to both. Some of them could belong to another set C too but that information is not available. All we know is that 10 belong to both A and B.
User avatar
NGGMAT
Joined: 20 Oct 2013
Last visit: 26 May 2014
Posts: 37
Own Kudos:
Given Kudos: 27
Posts: 37
Kudos: 10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasPrepKarishma
nandinigaur
Hi

How to identify when the qs is meaning to say exactly 2 overlaps and when the qs means otherwise? This qs seemed like it meant exactly 2.

The question will have words such as 'only' or 'exactly' when it wants to specify that n number of people are in exactly 2 teams.
10 people belong to A and B implies that there are 10 people who belong to both. Some of them could belong to another set C too but that information is not available. All we know is that 10 belong to both A and B.

Dear Karishma

I thought i understood but then i saw the following qs:

In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?

in this how to know that we r being asked: people in exactly 2 grps + people in exactly 3 grps... no word is mentioned....
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
Given Kudos: 99,977
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,361
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nandinigaur
VeritasPrepKarishma
nandinigaur
Hi

How to identify when the qs is meaning to say exactly 2 overlaps and when the qs means otherwise? This qs seemed like it meant exactly 2.

The question will have words such as 'only' or 'exactly' when it wants to specify that n number of people are in exactly 2 teams.
10 people belong to A and B implies that there are 10 people who belong to both. Some of them could belong to another set C too but that information is not available. All we know is that 10 belong to both A and B.

Dear Karishma

I thought i understood but then i saw the following qs:

In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?

in this how to know that we r being asked: people in exactly 2 grps + people in exactly 3 grps... no word is mentioned....

This question is discussed here: in-a-consumer-survey-85-of-those-surveyed-liked-at-least-98018.html

Hope it helps.
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 19 Nov 2025
Posts: 16,267
Own Kudos:
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 77,000
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nandinigaur

I thought i understood but then i saw the following qs:

In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?

in this how to know that we r being asked: people in exactly 2 grps + people in exactly 3 grps... no word is mentioned....

If the question wants to tell you the number of people who like 2 products but not all 3, it will say "30% people liked exactly two products."
Or "52% people liked only one of these products" when it wants to tell you that 52% people liked just a single product and did not like other two products and so on...

In this particular question, you are asked to find the number of people who liked more than one of the three products. This means you want the number of people who liked either 2 of the 3 products or all three products.
So you are looking for "people in exactly 2 grps + people in exactly 3 grps".

Note that you can calculate this in two ways:

Method 1:
people in exactly 2 grps + people in exactly 3 grps

Method 2:
people in 2 grps (including those in all three groups too) - 2* people in 3 grps (because they have been counted 3 times while counting people in 2 groups)
User avatar
GGMAT760
Joined: 22 Feb 2014
Last visit: 13 Jan 2015
Posts: 22
Own Kudos:
Given Kudos: 14
Posts: 22
Kudos: 131
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
alexjoh89
I have a question. If the formula is:

Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither

why is it then + 4 instead of -2*4?

There are two formulas for 3 overlapping sets:
\(Total = A + B + C - (sum \ of \ 2-group \ overlaps) + (all \ three) + Neither\).

\(Total = A + B + C - (sum \ of \ EXACTLY \ 2-group \ overlaps) - 2*(all \ three) + Neither\).

For more check here: ADVANCED OVERLAPPING SETS PROBLEMS


If I use second formula answer comes different.. Am i making any mistake?? Please correct

20+30+40- (20)- 2(4)+0
90-28 = 62

pLEASE aDVICE...are these two formulas suppose to give same answer right???
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
Given Kudos: 99,977
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,361
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GGMAT730
Bunuel
alexjoh89
I have a question. If the formula is:

Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither

why is it then + 4 instead of -2*4?

There are two formulas for 3 overlapping sets:
\(Total = A + B + C - (sum \ of \ 2-group \ overlaps) + (all \ three) + Neither\).

\(Total = A + B + C - (sum \ of \ EXACTLY \ 2-group \ overlaps) - 2*(all \ three) + Neither\).

For more check here: ADVANCED OVERLAPPING SETS PROBLEMS


If I use second formula answer comes different.. Am i making any mistake?? Please correct

20+30+40- (20)- 2(4)+0
90-28 = 62

pLEASE aDVICE...are these two formulas suppose to give same answer right???

They DO give the same answer when applied properly.

As I wrote in my post above: we are applying first formula as we have intersections of two groups and not the number of only (exactly) 2 group members.

You should understand those formulas, know when to apply which and not simply memorize them.
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 19 Nov 2025
Posts: 16,267
Own Kudos:
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 77,000
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GGMAT760



If I use second formula answer comes different.. Am i making any mistake?? Please correct

20+30+40- (20)- 2(4)+0
90-28 = 62

pLEASE aDVICE...are these two formulas suppose to give same answer right???

You should understand the concept of the two formulas. They will obviously give the same answer but the inputs they require are different.

Bunuel has given two formulas:

\(Total = A + B + C- (sum \ of \ 2-group \ overlaps) + (all \ three) + Neither\).

\(Total = A + B + C- (sum \ of \ EXACTLY \ 2-group \ overlaps) - 2*(all \ three) + Neither\).

Note that inputs are different.

In formula 1, you subtract sum of 2 group overlaps, it contains all three thrice and hence all three gets completely removed. So you put it back in.

In formula 2, you subtract sum of exactly two groups and hence it contains no elements of all three. All three has been counted three times in A, B and C and hence you subtract it twice.

You can usually solve these questions with venn diagrams if formulas confuse you.

Check out this post for more on three overlapping sets: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/09 ... ping-sets/
User avatar
devbond
Joined: 26 May 2014
Last visit: 25 May 2017
Posts: 29
Own Kudos:
Given Kudos: 17
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Kudos
Add Kudos
Bookmarks
Bookmark this Post
"20 are on the marketing team, 30 are on the Sales team, and 40 are on the Vision team"

How do we know 20 , 30 and 40 are not intersection values . For eg. if 20 were placed in marketing, 4 out of them could be in Sales also, so how did we assume M=20 ?Likewise for values of S and V
 1   2   
Moderators:
Math Expert
105390 posts
Tuck School Moderator
805 posts