Last visit was: 19 May 2026, 11:18 It is currently 19 May 2026, 11:18
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
   1   2   3   4   5   6   7   8   9   10   11   
605-655 (Medium)|   Overlapping Sets|         
User avatar
Lemniscate
User avatar
Joined: 28 Jun 2025
Last visit: 09 Nov 2025
Posts: 80
Own Kudos:
72
 [1]
Posts: 80
Kudos: 72
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 19:56
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
e is the number of participants who attended both sessions

total = a = b+c-e+d
e=b+c+d-a

Dividing by a:
(b+c+d-a)/a

Answer C
User avatar
Praveena_10
User avatar
Joined: 01 Jan 2024
Last visit: 15 May 2026
Posts: 46
Own Kudos:
47
 [1]
Given Kudos: 24
Location: India
Schools: INSEAD Jan '27 ISB '27 HEC Sept '26
GPA: 7.3
WE:Engineering (Energy)
Schools: INSEAD Jan '27 ISB '27 HEC Sept '26
Posts: 46
Kudos: 47
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 20:40
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Total Number of participants= a
let no of participants who attended both sessions be x
b-x+c+d=a
x=b+c+d-a
Percentage of Participants = b+c+d-a/a
User avatar
RedYellow
User avatar
Joined: 28 Jun 2025
Last visit: 09 Nov 2025
Posts: 80
Own Kudos:
74
 [1]
Posts: 80
Kudos: 74
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 20:42
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Using set theory we have

a = b+c+d-both
both = b+c+d-a

fraction=both/a=(b+c+d-a)/a

Correct answer is C
User avatar
patronumbeagle
User avatar
Joined: 20 Nov 2022
Last visit: 11 May 2026
Posts: 34
Own Kudos:
13
 [1]
Given Kudos: 178
Location: Peru
GMAT Focus 1: 645 Q83 V82 DI80
WE:Analyst (Finance: Diversified Financial Services)
GMAT Focus 1: 645 Q83 V82 DI80
Posts: 34
Kudos: 13
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 20:44
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Apply Set formula (Two Sets) : Total = All Group 1 + All Group 2 - Intersection (Both) + Neither

In this case:
a = b+c+d-x

x = b+c+d-a
Fraction: (b+c+d-a)/a
User avatar
LastHero
User avatar
Joined: 15 Dec 2024
Last visit: 12 Dec 2025
Posts: 134
Own Kudos:
147
 [1]
Given Kudos: 1
Posts: 134
Kudos: 147
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 21:16
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Group 1 + Group 2 – Both + Neither = Total
b+c-Both+d=a

Both = b+c+d-a

The fraction of the participants who attended both sessions is (b+c+d-a)/a

The right answer is C
User avatar
Gg153
User avatar
Joined: 25 Oct 2024
Last visit: 02 Feb 2026
Posts: 99
Own Kudos:
52
 [1]
Given Kudos: 102
Location: India
Products:
My Reviews
Posts: 99
Kudos: 52
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 21:18
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Solve using set properties
Total number of participants= Attendants + Non Attendants
a= bUc + d
a = b + c - (b and c) + d
we want (b and c)
(b and c)= b+c+d- a
fraction of participants who attended both sessions =
\(\frac{b + c + d - a}{a}\) (a is the total number of participants)
Answer is C.

Bunuel
At a tech seminar with a total participants, b attended a session on cybersecurity, and c attended a session on cloud computing. If exactly d participants attended neither session, then in terms of a, b, c, and d, what fraction of the participants attended both sessions?

A. \(\frac{a - b - c + d}{a}\)

B. \(\frac{a - b - c - d}{a}\)

C. \(\frac{b + c + d - a}{a}\)

D. \(\frac{a - b - c + 2d}{a}\)

E. \(\frac{b + c - a + d}{a-d}\)


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more
avatar
Nipunh
avatar
Joined: 15 Jun 2024
Last visit: 19 May 2026
Posts: 165
Own Kudos:
143
 [1]
Given Kudos: 537
Location: India
Concentration: Strategy, Finance
Schools: HBS '26 ISB '26 IIMB
GMAT Focus 1: 635 Q85 V84 DI75
GPA: 3.556
WE:Research (Consulting)
Schools: HBS '26 ISB '26 IIMB
GMAT Focus 1: 635 Q85 V84 DI75
Posts: 165
Kudos: 143
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 21:19
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Total participants = a
Let x be the number of participants who attended both sessions.

Then:
Only cybersecurity = b - x
Only cloud computing = c - x
Both sessions = x
Neither = d

So total = (b - x) + (c - x) + x + d = a
Simplify: b + c - x + d = a
So: b + c + d - x = a
Solve for x: x = b + c + d - a

We are asked to find the fraction who attended both sessions: x / a
So the answer is (b + c + d - a) / a

Answer is C
User avatar
AA155
User avatar
Joined: 18 Apr 2025
Last visit: 19 May 2026
Posts: 26
Own Kudos:
15
 [1]
Given Kudos: 3
Location: India
Schools: HEC INSEAD Jan '27 Rotterdam'26 LBS '27 FT MBA '27
GPA: 6
Products:
GMAT Club Tests Forum Quiz
Schools: HEC INSEAD Jan '27 Rotterdam'26 LBS '27 FT MBA '27
Posts: 26
Kudos: 15
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 21:25
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Answer (C)

Let double overlap be x
a= b+c - x
so d = a - (b + c -x)
d = a - b - c + x
x = d-a+b+c

ques asks for what fraction of the participants

x/a= d-a+b+c/a


Bunuel
At a tech seminar with a total participants, b attended a session on cybersecurity, and c attended a session on cloud computing. If exactly d participants attended neither session, then in terms of a, b, c, and d, what fraction of the participants attended both sessions?

A. \(\frac{a - b - c + d}{a}\)

B. \(\frac{a - b - c - d}{a}\)

C. \(\frac{b + c + d - a}{a}\)

D. \(\frac{a - b - c + 2d}{a}\)

E. \(\frac{b + c - a + d}{a-d}\)


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more
User avatar
Prathu1221
User avatar
Joined: 19 Jun 2025
Last visit: 20 Jul 2025
Posts: 62
Own Kudos:
40
 [1]
Given Kudos: 1
Posts: 62
Kudos: 40
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 21:26
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If we see total no of participants who attended the sessions it would be a+b+c-d, as a would be total no of participants and adding b and c, and subtracting d would give us people who attended atleast one session. Now we need intersection so we would subtract a-d from b+c which would give us b+c-a+d. For fraction divide by total i.e. a. Option C
Bunuel
At a tech seminar with a total participants, b attended a session on cybersecurity, and c attended a session on cloud computing. If exactly d participants attended neither session, then in terms of a, b, c, and d, what fraction of the participants attended both sessions?

A. \(\frac{a - b - c + d}{a}\)

B. \(\frac{a - b - c - d}{a}\)

C. \(\frac{b + c + d - a}{a}\)

D. \(\frac{a - b - c + 2d}{a}\)

E. \(\frac{b + c - a + d}{a-d}\)


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more
User avatar
bomberjack
User avatar
Schools: Tepper '26 (A$$) Tuck '26 (WL) McCombs '26 (WL) Duke '26 (D) Ross '26 (D) Darden '26 (A$) Booth '26 (D) CBS '26 (D) Johnson '26 (WL) Kelley '26 (A$$$) Kellogg '26 (D) UNC '26 (A$$$$) Owen '26 (A$$$$) Stern '26 (A) Yale '26 (D) McDonough  '26 (A$) Goizueta '26 (A$$$) Jones '26 (A$)
GMAT Focus 1: 715 Q88 V86 DI83
Posts: 71
Kudos: 74
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 21:27
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Quote:
At a tech seminar with a total participants, b attended a session on cybersecurity, and c attended a session on cloud computing. If exactly d participants attended neither session, then in terms of a, b, c, and d, what fraction of the participants attended both sessions?

A.
[ltr]a−b−c+daa−b−c+da[/ltr]


B.
[ltr]a−b−c−daa−b−c−da[/ltr]


C.
[ltr]b+c+d−aab+c+d−aa[/ltr]


D.
[ltr]a−b−c+2daa−b−c+2da[/ltr]


E.
[ltr]b+c−a+da−db+c−a+da−d[/ltr]
Show more
This can be solved using a 2 set matrix for overlapping sets as in the attached picture.

The correct answer is (C)
Attachments

WhatsApp Image 2025-07-02 at 9.51.17 AM.jpeg
WhatsApp Image 2025-07-02 at 9.51.17 AM.jpeg [ 256.51 KiB | Viewed 372 times ]

User avatar
GMAT1034
User avatar
Joined: 21 Feb 2023
Last visit: 13 May 2026
Posts: 269
Own Kudos:
65
 [1]
Given Kudos: 154
Products:
My Reviews GMAT Club Tests
Posts: 269
Kudos: 65
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 21:45
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
a= b+c+d- both. interchanging both and a and then dividing the result by total , you get the answer, which is, c
Bunuel
At a tech seminar with a total participants, b attended a session on cybersecurity, and c attended a session on cloud computing. If exactly d participants attended neither session, then in terms of a, b, c, and d, what fraction of the participants attended both sessions?

A. \(\frac{a - b - c + d}{a}\)

B. \(\frac{a - b - c - d}{a}\)

C. \(\frac{b + c + d - a}{a}\)

D. \(\frac{a - b - c + 2d}{a}\)

E. \(\frac{b + c - a + d}{a-d}\)


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more
User avatar
VyomBhatnagar21
User avatar
Joined: 20 Oct 2020
Last visit: 31 Mar 2026
Posts: 38
Own Kudos:
11
 [1]
Given Kudos: 1
Posts: 38
Kudos: 11
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 22:20
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Total Participants= a
Cybersecurity(A)=b
cloud security(B)= c
Neither=d
Both =?

Now in order to find the answer we use formula of Venn diagrams:
Total-Neither=A+B-Both
(Now we substitute the values
a-d= b+c-both
a-d-b-c=-both
(multiply both sides by Negative sign)
both= b+c+d-a

fraction OF BOTH=b+c+d-a/a
therefore answer is C
Bunuel
At a tech seminar with a total participants, b attended a session on cybersecurity, and c attended a session on cloud computing. If exactly d participants attended neither session, then in terms of a, b, c, and d, what fraction of the participants attended both sessions?

A. \(\frac{a - b - c + d}{a}\)

B. \(\frac{a - b - c - d}{a}\)

C. \(\frac{b + c + d - a}{a}\)

D. \(\frac{a - b - c + 2d}{a}\)

E. \(\frac{b + c - a + d}{a-d}\)


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more
User avatar
harishg
User avatar
Joined: 18 Dec 2018
Last visit: 09 Apr 2026
Posts: 176
Own Kudos:
174
 [1]
Given Kudos: 31
GMAT Focus 1: 695 Q88 V84 DI81
Products:
My Reviews
GMAT Focus 1: 695 Q88 V84 DI81
Posts: 176
Kudos: 174
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 22:29
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let x be the number of people attending both cybersecurity and cloud computing sessions.

According to basic set theory, it will follow that,

b + c - x + d = a

Rearranging the above, we get x = b+c+d-a

The questions asks for x / a. Therefore the answer is (b+c+d-a) / a

Therefore, Option C
User avatar
Punt
User avatar
Joined: 09 Jul 2024
Last visit: 12 Apr 2026
Posts: 36
Own Kudos:
29
Given Kudos: 16
Location: India
Posts: 36
Kudos: 29
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 22:31
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The answer is C. It will be solved by SET rules
Bunuel
At a tech seminar with a total participants, b attended a session on cybersecurity, and c attended a session on cloud computing. If exactly d participants attended neither session, then in terms of a, b, c, and d, what fraction of the participants attended both sessions?

A. \(\frac{a - b - c + d}{a}\)

B. \(\frac{a - b - c - d}{a}\)

C. \(\frac{b + c + d - a}{a}\)

D. \(\frac{a - b - c + 2d}{a}\)

E. \(\frac{b + c - a + d}{a-d}\)


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more
User avatar
samriddhi1234
User avatar
Joined: 19 Aug 2022
Last visit: 09 Jan 2026
Posts: 45
Own Kudos:
25
 [1]
Given Kudos: 302
Location: India
Schools: Rotterdam'26
GMAT Focus 1: 625 Q80 V85 DI78
GPA: 9.17
Schools: Rotterdam'26
GMAT Focus 1: 625 Q80 V85 DI78
Posts: 45
Kudos: 25
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 22:35
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The formula is:

total participants = cybersecurity + cloud computing - both + neither

or a = b + c + d - (both)

so the fraction of the total participants that attended both will be \(\frac{b + c + d - a}{a}\)

Option C.

Bunuel
At a tech seminar with a total participants, b attended a session on cybersecurity, and c attended a session on cloud computing. If exactly d participants attended neither session, then in terms of a, b, c, and d, what fraction of the participants attended both sessions?

A. \(\frac{a - b - c + d}{a}\)

B. \(\frac{a - b - c - d}{a}\)

C. \(\frac{b + c + d - a}{a}\)

D. \(\frac{a - b - c + 2d}{a}\)

E. \(\frac{b + c - a + d}{a-d}\)


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more
User avatar
AlwaysSuccessful
User avatar
Joined: 24 Aug 2024
Last visit: 10 Apr 2026
Posts: 21
Own Kudos:
6
 [1]
Given Kudos: 140
Location: India
Schools: Darden '26 (A$$) Tuck '26 (D) Kelley '26 (A$$) Owen '26 (A$$) Goizueta '26 (WL) Tepper '26 (A$$) UNC '26 (A$$) Ross '26 (D) Stern '26 (I) Jones '26 (A$$)
GPA: 8.55
Products:
GMAT Club Tests Forum Quiz
Schools: Darden '26 (A$$) Tuck '26 (D) Kelley '26 (A$$) Owen '26 (A$$) Goizueta '26 (WL) Tepper '26 (A$$) UNC '26 (A$$) Ross '26 (D) Stern '26 (I) Jones '26 (A$$)
Posts: 21
Kudos: 6
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 22:36
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Quote:
At a tech seminar with a total participants, b attended a session on cybersecurity, and c attended a session on cloud computing. If exactly d participants attended neither session, then in terms of a, b, c, and d, what fraction of the participants attended both sessions?

A.
a−b−c+daa−b−c+da


B.
a−b−c−daa−b−c−da


C.
b+c+d−aab+c+d−aa


D.
a−b−c+2daa−b−c+2da


E.
b+c−a+da−db+c−a+da−d
Show more

This can be solved using a 2 set matrix for overlapping sets as in the attached picture.

The correct answer is (C)
Attachments

Question.jpeg
Question.jpeg [ 256.51 KiB | Viewed 351 times ]

User avatar
sayan640
User avatar
Joined: 29 Oct 2015
Last visit: 19 May 2026
Posts: 1,110
Own Kudos:
873
 [1]
Given Kudos: 790
GMAT 1: 570 Q42 V28
Products:
My Reviews
GMAT 1: 570 Q42 V28
Posts: 1,110
Kudos: 873
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 22:46
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Option B is the answer.
The fraction of the participants who attended both sessions = (b - (a-c-d) )/ a
User avatar
MURALIKA
User avatar
Joined: 21 Apr 2024
Last visit: 11 May 2026
Posts: 54
Own Kudos:
20
 [1]
Given Kudos: 218
Location: India
GPA: 77.37
Posts: 54
Kudos: 20
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 22:47
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Cloud ComputingNo Cloud ComputingTotal
Cyber Securityb+c+d-a b
No Cyber Securitya-b-dda-b
Totalc a

Therefore required fraction = b+c+d-a/a

Bunuel
At a tech seminar with a total participants, b attended a session on cybersecurity, and c attended a session on cloud computing. If exactly d participants attended neither session, then in terms of a, b, c, and d, what fraction of the participants attended both sessions?

A. \(\frac{a - b - c + d}{a}\)

B. \(\frac{a - b - c - d}{a}\)

C. \(\frac{b + c + d - a}{a}\)

D. \(\frac{a - b - c + 2d}{a}\)

E. \(\frac{b + c - a + d}{a-d}\)


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more
User avatar
PrameshLuitel123
User avatar
Joined: 18 Sep 2024
Last visit: 14 May 2026
Posts: 12
Own Kudos:
4
 [1]
Given Kudos: 12
Location: Nepal
Schools: Rotman '27 Tepper '27 Booth '27
GMAT Focus 1: 575 Q77 V83 DI76
GPA: 7.7/10
Schools: Rotman '27 Tepper '27 Booth '27
GMAT Focus 1: 575 Q77 V83 DI76
Posts: 12
Kudos: 4
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 22:51
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
It uses a simple forumla of sets that is - total-neither=a+b-both so here it would be a-d=b+c-x solving that we would get the answer a C
Bunuel
At a tech seminar with a total participants, b attended a session on cybersecurity, and c attended a session on cloud computing. If exactly d participants attended neither session, then in terms of a, b, c, and d, what fraction of the participants attended both sessions?

A. \(\frac{a - b - c + d}{a}\)

B. \(\frac{a - b - c - d}{a}\)

C. \(\frac{b + c + d - a}{a}\)

D. \(\frac{a - b - c + 2d}{a}\)

E. \(\frac{b + c - a + d}{a-d}\)


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more
User avatar
gchandana
User avatar
Joined: 16 May 2024
Last visit: 19 May 2026
Posts: 203
Own Kudos:
147
 [1]
Given Kudos: 172
Location: India
Products:
GMAT Club Tests Forum Quiz
Posts: 203
Kudos: 147
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 23:23
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
This is an overlapping sets concept.
The total participants, a, is basically = b + c - x + d
x is the number of participants who attended both sessions (and we subtract it once, as we are counting it twice while counting participants attending the first session and participants attending the second session)
It gives x as b + c + d - a
Now fraction of the participants who attended both sessions would be (b + c + d - a) / a
Option C
Bunuel
At a tech seminar with a total participants, b attended a session on cybersecurity, and c attended a session on cloud computing. If exactly d participants attended neither session, then in terms of a, b, c, and d, what fraction of the participants attended both sessions?

A. \(\frac{a - b - c + d}{a}\)

B. \(\frac{a - b - c - d}{a}\)

C. \(\frac{b + c + d - a}{a}\)

D. \(\frac{a - b - c + 2d}{a}\)

E. \(\frac{b + c - a + d}{a-d}\)


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

Show more
   1   2   3   4   5   6   7   8   9   10   11   
Moderators:
Bunuel
Math Expert
110698 posts
Krunaal
Tuck School Moderator
852 posts