Last visit was: 27 Apr 2026, 18:44 It is currently 27 Apr 2026, 18:44
Home
Messages
Tests
Schools
Events
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 27 Apr 2026
Posts: 109,929
Own Kudos:
811,621
 [3]
Given Kudos: 105,914
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: 109,929
Kudos: 811,621
 [3]
A and B are the sets shown above. Another set C also has a total of 4 21 Jul 2022, 01:30
Kudos
Add Kudos
3
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:

85% (hard)

Question Stats:

51% (02:34) correct 49% (02:48) wrong based on 150 sessions

History

Date
Time
Result
Not Attempted Yet
\(A = {2, 4, 7, 8}\)
\(B = {3, 6, 7, 8}\)

A and B are the sets shown above. Another set C also has a total of 4 elements. Exactly two elements are shared by sets A and C. Exactly two elements are shared by sets B and C, and these could be the elements shared by A and C. If none of the elements in the sets appears more than once in the same set, how many elements do the three sets share?

(1) 6 is not in set C.

(2) 3 is in set C.


Are You Up For the Challenge: 700 Level Questions

Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here
ShowHide Answer
Official Answer
C
avatar
Jezza
avatar
Joined: 11 Jan 2022
Last visit: 01 Sep 2022
Posts: 27
Own Kudos:
3
Given Kudos: 17
Posts: 27
Kudos: 3
A and B are the sets shown above. Another set C also has a total of 4 23 Jul 2022, 02:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
\(A = {2, 4, 7, 8}\)
\(B = {3, 6, 7, 8}\)

A and B are the sets shown above. Another set C also has a total of 4 elements. Exactly two elements are shared by sets A and C. Exactly two elements are shared by sets B and C, and these could be the elements shared by A and C. If none of the elements in the sets appears more than once in the same set, how many elements do the three sets share?

(1) 6 is not in set C.

(2) 3 is in set C.


Are You Up For the Challenge: 700 Level Questions

Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here
Show more


Imagine C includes (7,2,3,x), in which x is a number not in either A or B. The 3 sets share 1 element: 7
now if C includes (7,8,3,x). The 3 sets now share 2 elements: 7 and 8.
Both suffices (1)and (2).
So the answer is E imo.
User avatar
Rahul257
User avatar
Joined: 06 Sep 2021
Last visit: 01 Mar 2024
Posts: 44
Own Kudos:
19
 [1]
Given Kudos: 53
Location: India
Concentration: Strategy, Operations
Schools: NUS '25 (A)
GMAT 1: 660 Q49 V32
GMAT 2: 750 Q50 V42
GPA: 3.48
Schools: NUS '25 (A)
GMAT 2: 750 Q50 V42
Posts: 44
Kudos: 19
 [1]
A and B are the sets shown above. Another set C also has a total of 4 23 Jul 2022, 21:34
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
IMO Answer is C


A=2,4,7,8A=2,4,7,8
B=3,6,7,8B=3,6,7,8

A and B are the sets shown above. Another set C also has a total of 4 elements. Exactly two elements are shared by sets A and C. Exactly two elements are shared by sets B and C, and these could be the elements shared by A and C. If none of the elements in the sets appears more than once in the same set, how many elements do the three sets share?
So basically asking is it 7&8 or just 7or8 or nothing

(1) 6 is not in set C.
Not sufficient
Set C can have 7,8 are common and also have only 7or 8 as elements

(2) 3 is in set C.
Not Sufficient
if 3 is an element if C, then as only 2 elements can be shared between B and C, the other element can only be 7or 8 or 6
if it is 7 or 8 it shares 1 element and if it is 6 then no elements

combining B&C

it can share only either 7 or 8, as statement 1 gives 6 not an element of C

So Sufficient

Hence C is the answer
avatar
Jezza
avatar
Joined: 11 Jan 2022
Last visit: 01 Sep 2022
Posts: 27
Own Kudos:
3
Given Kudos: 17
Posts: 27
Kudos: 3
A and B are the sets shown above. Another set C also has a total of 4 24 Jul 2022, 00:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Rahul257
IMO Answer is C


A=2,4,7,8A=2,4,7,8
B=3,6,7,8B=3,6,7,8

A and B are the sets shown above. Another set C also has a total of 4 elements. Exactly two elements are shared by sets A and C. Exactly two elements are shared by sets B and C, and these could be the elements shared by A and C. If none of the elements in the sets appears more than once in the same set, how many elements do the three sets share?
So basically asking is it 7&8 or just 7or8 or nothing

(1) 6 is not in set C.
Not sufficient
Set C can have 7,8 are common and also have only 7or 8 as elements

(2) 3 is in set C.
Not Sufficient
if 3 is an element if C, then as only 2 elements can be shared between B and C, the other element can only be 7or 8 or 6
if it is 7 or 8 it shares 1 element and if it is 6 then no elements

combining B&C

it can share only either 7 or 8, as statement 1 gives 6 not an element of C

So Sufficient

Hence C is the answer
Show more

What about (7,2,3,100) and (7,8,3,100)?
each set suffices both conditions, but the first yields only 1 common element: 7, the second yields 2: 7,8
User avatar
av1901
User avatar
Joined: 28 May 2022
Last visit: 12 Apr 2026
Posts: 426
Own Kudos:
478
 [1]
Given Kudos: 82
Status:Dreaming and Working
Affiliations: None
WE:Brand Management (Manufacturing)
Products:
My Reviews
Posts: 426
Kudos: 478
 [1]
A and B are the sets shown above. Another set C also has a total of 4 Updated on: 27 Jul 2022, 05:37
Originally posted by av1901 on 24 Jul 2022, 15:32.
Last edited by av1901 on 27 Jul 2022, 05:37, edited 1 time in total.
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
A={2,4,7,8} B={3,6,7,8}
C shares exactly 2 elements with A as well as with B, and they could be the same too.

1. 6 is not in set C

C={7,8,10,11} or C={2,4,3,8}
In first case: 2 elements shared
In second case: 1 element shared
Not sufficient

2. 3 is in set C

C={3,6,2,4} or C={3,10,8,4}
First case: None shared
Second case: 1 element shared
Not sufficient

Together 1 and 2 combined

A={2,4,7,8} B={3,6,7,8}
6 is NOT in set C and 3 IS IN Set C

Set C contains 3 but cannot have 6, so it has to have either 7 or 8 so as to meet the condition that 2 elements have to be common between B and C
So considering it now:

If 2nd element in C is 7/8: C = {3,7,n1,n2}, now for it to also match with 2 elements common with Set A condition, it needs to have either 2 or 4 in it because it already has 8 in common with Set A and it cannot have 7 because then Set C will have 3 in common with Set B which cannot happen.

So C = {3,7,2,100}/{3,7,4,100}/{3,8,2,100}/{3,8,4,100} and in all these cases there is only 1 element common between all 3 sets

SUFFICIENT

Answer - C
User avatar
Rahul257
User avatar
Joined: 06 Sep 2021
Last visit: 01 Mar 2024
Posts: 44
Own Kudos:
19
Given Kudos: 53
Location: India
Concentration: Strategy, Operations
Schools: NUS '25 (A)
GMAT 1: 660 Q49 V32
GMAT 2: 750 Q50 V42
GPA: 3.48
Schools: NUS '25 (A)
GMAT 2: 750 Q50 V42
Posts: 44
Kudos: 19
A and B are the sets shown above. Another set C also has a total of 4 27 Jul 2022, 04:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Jezza
Rahul257
IMO Answer is C


A=2,4,7,8A=2,4,7,8
B=3,6,7,8B=3,6,7,8

A and B are the sets shown above. Another set C also has a total of 4 elements. Exactly two elements are shared by sets A and C. Exactly two elements are shared by sets B and C, and these could be the elements shared by A and C. If none of the elements in the sets appears more than once in the same set, how many elements do the three sets share?
So basically asking is it 7&8 or just 7or8 or nothing

(1) 6 is not in set C.
Not sufficient
Set C can have 7,8 are common and also have only 7or 8 as elements

(2) 3 is in set C.
Not Sufficient
if 3 is an element if C, then as only 2 elements can be shared between B and C, the other element can only be 7or 8 or 6
if it is 7 or 8 it shares 1 element and if it is 6 then no elements

combining B&C

it can share only either 7 or 8, as statement 1 gives 6 not an element of C

So Sufficient

Hence C is the answer

What about (7,2,3,100) and (7,8,3,100)?
each set suffices both conditions, but the first yields only 1 common element: 7, the second yields 2: 7,8
Show more

(7,2,3,100) in this the answer is what i said earlier, the 3 sets share only 1 element, which is 7.
(7,8,3,100)... This is not possible because the question condition says B and C shares only 2 elements. As 7,8 and 3 are all elements of B, thats 3 elements which is not possible.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,985
Own Kudos:
1,119
Posts: 38,985
Kudos: 1,119
A and B are the sets shown above. Another set C also has a total of 4 03 Jul 2024, 15:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109929 posts
kingbucky
498 posts
Gmat860sanskar
212 posts