Last visit was: 17 May 2026, 05:18 It is currently 17 May 2026, 05:18
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
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 May 2026
Posts: 110,496
Own Kudos:
815,340
 [5]
Given Kudos: 106,273
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: 110,496
Kudos: 815,340
 [5]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 08:00
Kudos
Add Kudos
5
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:

45% (medium)

Question Stats:

75% (01:46) correct 25% (01:59) wrong based on 815 sessions

History

Date
Time
Result
Not Attempted Yet
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

 

ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 May 2026
Posts: 110,496
Own Kudos:
815,340
Given Kudos: 106,273
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: 110,496
Kudos: 815,340
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 08:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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. \(\frac{b + c - a + d}{a-d}\)
Show more

­

GMAT Club Official Explanation:



Total = cybersecurity + cloud computing - both + neither

So:

a = b + c - both + d

Solving for both gives: both = b + c + d - a

Therefore, the required fraction both/total is (b + c + d - a)/a

Answer: C.
General Discussion
User avatar
MaxFabianKirchner
User avatar
Joined: 02 Jun 2025
Last visit: 12 Jul 2025
Posts: 65
Own Kudos:
63
 [1]
Given Kudos: 122
Status:26' Applicant
Location: Denmark
Concentration: Finance, International Business
Schools: ESSEC MiF '26 ESADE HEC Imperial LBS Oxford MFE '26 Sloan (MIT) NYU Stern NUS Bocconi IE'26
GPA: 4.0
WE:Other (Student)
Schools: ESSEC MiF '26 ESADE HEC Imperial LBS Oxford MFE '26 Sloan (MIT) NYU Stern NUS Bocconi IE'26
Posts: 65
Kudos: 63
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 08:05
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The formula for two overlapping sets is:
Total = Group 1 + Group 2 - Both + Neither

Substitute the variables from the problem:
a = b + c - Both + d

Solve for the number of participants who attended both sessions:
Both = b + c + d - a

To find the fraction of participants who attended both, divide this by the total number of participants, 'a':
Fraction = (b + c + d - a) / a

The correct answer is (C).
avatar
ManifestDreamMBA
avatar
Joined: 17 Sep 2024
Last visit: 21 Feb 2026
Posts: 1,387
Own Kudos:
901
 [1]
Given Kudos: 243
Posts: 1,387
Kudos: 901
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 08:06
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Total = CS + CC - both + None
a=b+c-both+d
both = b+c+d-a

Fraction of the participants attended both sessions = b+c+d-a/a

Answer 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
Karanjotsingh
User avatar
Joined: 18 Feb 2024
Last visit: 03 Oct 2025
Posts: 139
Own Kudos:
95
 [1]
Given Kudos: 362
Location: India
Concentration: Finance, Entrepreneurship
Posts: 139
Kudos: 95
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 08:06
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Answer
(C) (b + c + d - a) / a

Explanation

This is a classic overlapping sets problem. The easiest way to solve it is with a formula.

1. The Formula:

The formula for any two overlapping groups is:
Total = Group A + Group B - Both + Neither

2. Plug in the Variables:

Let's use the variables from the problem:

  • a = Total
  • b = Attended Cybersecurity (Group A)
  • c = Attended Cloud Computing (Group B)
  • d = Attended Neither

Plugging these into the formula gives us:
a = b + c - Both + d

3. Solve for "Both":

The question asks for the number of people who attended both sessions. We just need to rearrange the formula to solve for "Both":
Both = b + c + d - a

4. Find the Fraction:

The question asks for the fraction of participants who attended both. To get the fraction, we divide the number who attended "Both" by the "Total" number of participants, which is a.
Fraction = (b + c + d - a) / a
User avatar
BeachStudy
User avatar
Joined: 30 Jun 2025
Last visit: 18 Aug 2025
Posts: 61
Own Kudos:
37
Given Kudos: 4
Posts: 61
Kudos: 37
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 08:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
a = Total participants
d = attend neither

a-d = attended one or both


answer e : (cyber total) + ( cloud total) - (total) + (didnt attend) / (attended)

Im not so sure on this one. Guessing E


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
anuraagnandi9
User avatar
Joined: 25 Mar 2025
Last visit: 21 Jan 2026
Posts: 11
Own Kudos:
12
 [1]
Given Kudos: 3
Location: India
GMAT Focus 1: 705 Q87 V84 DI84
GPA: 3.34
GMAT Focus 1: 705 Q87 V84 DI84
Posts: 11
Kudos: 12
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 08:08
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
We can say that - people who attended at least one session = a − d (Total - neither session)

also - people who attended at least one session = b + c − both (because we are taking union here)

People who attended both = b + c + d − a

therefore fraction would be (b + c + d − a) / a
User avatar
Duongduong273
User avatar
Joined: 08 Apr 2023
Last visit: 03 Feb 2026
Posts: 32
Own Kudos:
32
 [1]
Given Kudos: 4
Posts: 32
Kudos: 32
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 08:09
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Participants who attended at least one of the two b & c sessions: b+c-x(participants who attended both b & c). And a = b+c-x+d => x=b+c+d-a => Fraction of participants who attended both b & c : (b+c+d-a)/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
APram
User avatar
Joined: 23 Jun 2024
Last visit: 17 Mar 2026
Posts: 708
Own Kudos:
280
 [1]
Given Kudos: 248
Location: India
Schools: ISB '26 HEC INSEAD Jan '26
GMAT Focus 1: 605 Q86 V78 DI76
GPA: 3.608
Schools: ISB '26 HEC INSEAD Jan '26
GMAT Focus 1: 605 Q86 V78 DI76
Posts: 708
Kudos: 280
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 08:09
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
a = total number of participants
b = Attended cybersecurity
c = Attended cloud computing

No of participants not attended cloud computing = a-b
No of participants not attended cybersecurity = a-c

d = Attended neither cloud computing nor cybersecurity

No of participants attended cybersecurity but not cloud computing = a-c-d
No of participants attended both cybersecurity and cloud computing = b-(a-c-d) = b+c+d-a

Hence required fraction is \(\frac{b + c + d - a}{a}\)

Option C is correct
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
AVMachine
User avatar
Joined: 03 May 2024
Last visit: 26 Mar 2026
Posts: 190
Own Kudos:
154
 [1]
Given Kudos: 40
Posts: 190
Kudos: 154
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 08:10
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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. \(\frac{b + c - a + d}{a-d}\)
Show more
Union Formula: a = b + c - both(b&c) + d;

Than b&c = b+c+d-a;

Than Fraction b&c/a = (b+c+d-a)/a; Answer
User avatar
chasing725
User avatar
Joined: 22 Jun 2025
Last visit: 13 Jan 2026
Posts: 176
Own Kudos:
174
 [1]
Given Kudos: 5
Location: United States (OR)
Schools: Stanford
Schools: Stanford
Posts: 176
Kudos: 174
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 08:10
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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


We can plot the information on a 2*2 matrix and get the following table

Cybersecurity Not Cybersecurity
Cloud Computingc
Not Cloud computing
ba

Adding the missing values we get

CybersecurityNot Cybersecurity
Cloud Computingb - (a - c - d) = b - a + c + da - b - dc
Not Cloud computinga - c - dd
ba-ba

Both Cloud Computing and Cybersecurity = b - a + c + d

Ratio= (b - a + c + d) / a

Option C
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 17 May 2026
Posts: 6,004
Own Kudos:
5,877
 [1]
Given Kudos: 163
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 6,004
Kudos: 5,877
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 08:11
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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?

Basic information give in the question: -
Cyber securityNot cyber securityTotal
Cloud computingc
Not cloud computingd
Totalba


After filling up the blank fields: -
Cyber securityNot cyber securityTotal
Cloud computingb + c + d - aa - b - dc
Not cloud computinga - c -d da - c
Totalba - ba

The fraction of the participants attended both sessions = \(\frac{b+c+d-a}{a}\)

IMO C
User avatar
Gargi7777
User avatar
Joined: 21 Dec 2024
Last visit: 22 Mar 2026
Posts: 13
Own Kudos:
6
 [1]
Given Kudos: 65
Posts: 13
Kudos: 6
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 08:11
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Total participants = a
Attended cybersecurity = b
Attended cloud computing = c
Attended neither = d
We’re asked: What fraction of participants attended both sessions?
Let’s call the number of people who attended both sessions = x

Total number of participants who attended at least one session = b + c – x
We're subtracting x because participants who attended both got counted twice (once in b and once in c).
So:
Attended at least one session = b + c – x
We also know:
Attended neither session = d
So total participants = (Attended at least one) + (Attended neither)
a=(b+c–x)+da = (b + c – x) + da=(b+c–x)+d
Rearranging:
a=b+c–x+d⇒x=b+c+d–aa = b + c – x + d \Rightarrow x = b + c + d – aa=b+c–x+d⇒x=b+c+d–a
That’s the number of people who attended both.
We’re asked for the fraction of participants who attended both = x / a
From above:
x = b + c + d – a
So:
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
avatar
krutarth21
avatar
Joined: 28 May 2025
Last visit: 23 Feb 2026
Posts: 21
Own Kudos:
13
 [1]
Given Kudos: 50
Location: India
Schools: ISB '26 (A$)
GMAT Focus 1: 675 Q88 V82 DI81
GPA: 3.82
Schools: ISB '26 (A$)
GMAT Focus 1: 675 Q88 V82 DI81
Posts: 21
Kudos: 13
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 08:11
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Correct answer is C, below attached is the solution for the question
Attachments

IMG_1887.JPG
IMG_1887.JPG [ 1.72 MiB | Viewed 4285 times ]

User avatar
dthaman1201
User avatar
Joined: 08 Dec 2024
Last visit: 11 Mar 2026
Posts: 23
Own Kudos:
18
 [1]
Given Kudos: 165
Posts: 23
Kudos: 18
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 08:11
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
total are A and b,c are part of individual pool if x is the no present in both then neither would be = a - (b+C+x)=d
d-a+(b+c)/a
User avatar
Benedictng
User avatar
Joined: 21 Jan 2025
Last visit: 10 Jul 2025
Posts: 18
Own Kudos:
12
 [1]
Given Kudos: 1
Posts: 18
Kudos: 12
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 08:11
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
Let x = people who attended both sessions
Number who attended at least one = b+c-x
Number who attended neither = d
a = (b+c-x) + d
x = b+c+d-a
x/a = (b+c+d-a)/a
User avatar
iamchinu97
User avatar
Joined: 14 Dec 2020
Last visit: 09 May 2026
Posts: 136
Own Kudos:
146
 [1]
Given Kudos: 35
Products:
My Reviews
Posts: 136
Kudos: 146
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 08:13
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
a= b+c -(Both)+d
(Both)=b+c+d-a
Both/a = (b+c+d-a)/a
Hence Ans C
User avatar
imAman
User avatar
Joined: 23 Mar 2025
Last visit: 23 Jul 2025
Posts: 5
Own Kudos:
3
 [1]
Given Kudos: 1
Posts: 5
Kudos: 3
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 08:13
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
let both cs and cc be x.
so, total = only cs + only cc + (cs and cc) + neither( cs and cc)

a = (b-x) + (c-x) + x + d

x = b+c+d-a
so fraction = x/a = (b+c+d-a)/a

ans is C
User avatar
Kanika2409
User avatar
Joined: 19 Feb 2025
Last visit: 17 Sep 2025
Posts: 14
Own Kudos:
11
 [1]
Given Kudos: 1
Posts: 14
Kudos: 11
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 08:13
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Total participant = a
Participant attended cybersecurity = b
Participant attended cloud computing = c
Participant attended neither = d
Participant attended both = x

a-d = b+c-x
Hence C
x = b+c+d-a
Fraction = b+c+d-a/a
User avatar
Heix
User avatar
Joined: 21 Feb 2024
Last visit: 05 May 2026
Posts: 474
Own Kudos:
170
 [1]
Given Kudos: 63
Location: India
Concentration: Finance, Entrepreneurship
Schools: Ross MM "26 NUS Columbia '27
GMAT Focus 1: 485 Q76 V74 DI77
GPA: 3.4
WE:Accounting (Finance)
Products:
My Reviews
Schools: Ross MM "26 NUS Columbia '27
GMAT Focus 1: 485 Q76 V74 DI77
Posts: 474
Kudos: 170
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 08:14
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given information:
- Total number of participants = a
- Number who attended cybersecurity session = b
- Number who attended cloud computing session = c
- Number who attended neither session = d
Let's define x as the number who attended both sessions (the overlap region).
Using the formula for the total number of elements:
Total = (Cybersecurity only) + (Cloud only) + (Both) + (Neither)
We can express this as:
a = (b -x) + (c -x) +x+ d
a = b+c-x+d
Solving for x (the number who attended both sessions): b+c-x+d= a
-x= a - b-c-d
x=b+c+d-a
The question asks for the fraction of participants who attended both sessions:
Fraction = x/a = (b+ c+ d - a)/a
this matches with choice C (b+c+d-a)/a
 1   2   3   4   5   6   7   8   9   10   11   
Moderators:
Bunuel
Math Expert
110496 posts
Krunaal
Tuck School Moderator
852 posts