Last visit was: 18 Nov 2025, 21:10

It is currently 18 Nov 2025, 21:10

Toolkit

Practice Tests

Quantitative Questions

Problem Solving (PS)

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

Request Expert Reply

Confirm Cancel

Nov 22
GMAT RC Masterclass
11:00 AM IST
-
01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment
Nov 23
Conquer Algebra on the GMAT Focus Edition
11:00 AM IST
-
01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease.
Nov 25
Try OnDemand GMAT Masterclass
10:00 AM EST
-
11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.

Back to Forum

Create Topic

GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total

1 2 3 4 5 6 7 8 9 10 11

Bunuel

Math Expert

Joined: 02 Sep 2009

Last visit: 18 Nov 2025

Posts: 105,355

Own Kudos:

778,092

[4]

Given Kudos: 99,964

Products:

Expert

Expert reply

Posts: 105,355

Kudos: 778,092

[4]

01 Jul 2025, 08:00

Kudos

Bookmarks

00:00

Start Timer

Pause Timer

Resume Timer

Show Answer

Hide

Show

History

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% (01:45) correct

25% (01:56) wrong

based on 699 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

Show Answer

Official Answer

Most Helpful Reply

Bunuel

Math Expert

Joined: 02 Sep 2009

Last visit: 18 Nov 2025

Posts: 105,355

Own Kudos:

778,092

Given Kudos: 99,964

Products:

Expert

Expert reply

Posts: 105,355

Kudos: 778,092

01 Jul 2025, 08:30

Kudos

Bookmarks

Bunuel

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

MaxFabianKirchner

Joined: 02 Jun 2025

Last visit: 12 Jul 2025

Posts: 65

Own Kudos:

[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: 62

[1]

01 Jul 2025, 08:05

Kudos

Bookmarks

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).

ManifestDreamMBA

Joined: 17 Sep 2024

Last visit: 18 Nov 2025

Posts: 1,282

Own Kudos:

784

[1]

Given Kudos: 236

Products:

Posts: 1,282

Kudos: 784

[1]

01 Jul 2025, 08:06

Kudos

Bookmarks

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

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

Karanjotsingh

Joined: 18 Feb 2024

Last visit: 03 Oct 2025

Posts: 139

Own Kudos:

[1]

Given Kudos: 362

Location: India

Concentration: Finance, Entrepreneurship

Posts: 139

Kudos: 94

[1]

01 Jul 2025, 08:06

Kudos

Bookmarks

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

BeachStudy

Joined: 30 Jun 2025

Last visit: 18 Aug 2025

Posts: 61

Own Kudos:

Given Kudos: 4

Posts: 61

Kudos: 37

01 Jul 2025, 08:07

Kudos

Bookmarks

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

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

anuraagnandi9

Joined: 25 Mar 2025

Last visit: 18 Nov 2025

Posts: 11

Own Kudos:

[1]

Given Kudos: 3

Location: India

GMAT Focus 1: 705 Q87 V84 DI84 Verified score

GPA: 3.34

GMAT Focus 1: 705 Q87 V84 DI84 Verified score

Posts: 11

Kudos: 12

[1]

01 Jul 2025, 08:08

Kudos

Bookmarks

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

Duongduong273

Joined: 08 Apr 2023

Last visit: 02 Sep 2025

Posts: 32

Own Kudos:

[1]

Given Kudos: 4

Posts: 32

Kudos: 32

[1]

01 Jul 2025, 08:09

Kudos

Bookmarks

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

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

APram

Joined: 23 Jun 2024

Last visit: 17 Nov 2025

Posts: 671

Own Kudos:

263

[1]

Given Kudos: 240

Location: India

Schools: ISB '26 HEC INSEAD Jan '26

GMAT Focus 1: 605 Q86 V78 DI76 Verified score

GPA: 3.608

Products:

Schools: ISB '26 HEC INSEAD Jan '26

GMAT Focus 1: 605 Q86 V78 DI76 Verified score

Posts: 671

Kudos: 263

[1]

01 Jul 2025, 08:09

Kudos

Bookmarks

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

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

AVMachine

Joined: 03 May 2024

Last visit: 26 Aug 2025

Posts: 190

Own Kudos:

154

[1]

Given Kudos: 40

Posts: 190

Kudos: 154

[1]

01 Jul 2025, 08:10

Kudos

Bookmarks

Bunuel

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

chasing725

Joined: 22 Jun 2025

Last visit: 17 Aug 2025

Posts: 85

Own Kudos:

[1]

Given Kudos: 5

Location: United States (OR)

Schools: Stanford

Posts: 85

Kudos: 81

[1]

01 Jul 2025, 08:10

Kudos

Bookmarks

Bunuel

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

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

	Cybersecurity
Cloud Computing		c
Not Cloud computing
	b	a

Adding the missing values we get

	Cybersecurity	Not Cybersecurity
Cloud Computing	b - (a - c - d) = b - a + c + d	a - b - d	c
Not Cloud computing	a - c - d	d
	b	a-b	a

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

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

Option C

Kinshook

Major Poster

Joined: 03 Jun 2019

Last visit: 18 Nov 2025

Posts: 5,793

Own Kudos:

5,509

[1]

Given Kudos: 161

Location: India

Schools: HBS '26 CBS '26 Wharton '26

GMAT 1: 690 Q50 V34 Verified score

WE:Engineering (Transportation)

Products:

Schools: HBS '26 CBS '26 Wharton '26

GMAT 1: 690 Q50 V34 Verified score

Posts: 5,793

Kudos: 5,509

[1]

01 Jul 2025, 08:11

Kudos

Bookmarks

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 security	Not cyber security	Total
Cloud computing			c
Not cloud computing		d
Total	b		a

After filling up the blank fields: -

	Cyber security	Not cyber security	Total
Cloud computing	b + c + d - a	a - b - d	c
Not cloud computing	a - c -d	d	a - c
Total	b	a - b	a

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

IMO C

Gargi7777

Joined: 21 Dec 2024

Last visit: 13 Nov 2025

Posts: 13

Own Kudos:

[1]

Given Kudos: 64

Posts: 13

Kudos: 6

[1]

01 Jul 2025, 08:11

Kudos

Bookmarks

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

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

krutarth21

Joined: 28 May 2025

Last visit: 18 Nov 2025

Posts: 21

Own Kudos:

[1]

Given Kudos: 50

Location: India

GPA: 3.82

Products:

Posts: 21

Kudos: 13

[1]

01 Jul 2025, 08:11

Kudos

Bookmarks

Correct answer is C, below attached is the solution for the question

Attachments

IMG_1887.JPG [ 1.72 MiB | Viewed 3421 times ]

dthaman1201

Joined: 08 Dec 2024

Last visit: 18 Nov 2025

Posts: 21

Own Kudos:

[1]

Given Kudos: 151

Posts: 21

Kudos: 17

[1]

01 Jul 2025, 08:11

Kudos

Bookmarks

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

Benedictng

Joined: 21 Jan 2025

Last visit: 10 Jul 2025

Posts: 18

Own Kudos:

[1]

Given Kudos: 1

Posts: 18

Kudos: 12

[1]

01 Jul 2025, 08:11

Kudos

Bookmarks

Bunuel

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

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

iamchinu97

Joined: 14 Dec 2020

Last visit: 18 Nov 2025

Posts: 132

Own Kudos:

139

[1]

Given Kudos: 34

Products:

Posts: 132

Kudos: 139

[1]

01 Jul 2025, 08:13

Kudos

Bookmarks

a= b+c -(Both)+d
(Both)=b+c+d-a
Both/a = (b+c+d-a)/a
Hence Ans C

imAman

Joined: 23 Mar 2025

Last visit: 23 Jul 2025

Posts: 5

Own Kudos:

[1]

Given Kudos: 1

Posts: 5

Kudos: 3

[1]

01 Jul 2025, 08:13

Kudos

Bookmarks

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

Kanika2409

Joined: 19 Feb 2025

Last visit: 17 Sep 2025

Posts: 14

Own Kudos:

[1]

Given Kudos: 1

Posts: 14

Kudos: 11

[1]

01 Jul 2025, 08:13

Kudos

Bookmarks

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

Heix

Joined: 21 Feb 2024

Last visit: 18 Nov 2025

Posts: 361

Own Kudos:

153

[1]

Given Kudos: 63

Location: India

Concentration: Finance, Entrepreneurship

Schools: Ross MM "26 NUS Columbia '27

GMAT Focus 1: 485 Q76 V74 DI77 Verified score

GPA: 3.4

WE:Accounting (Finance)

Products:

Schools: Ross MM "26 NUS Columbia '27

GMAT Focus 1: 485 Q76 V74 DI77 Verified score

Posts: 361

Kudos: 153

[1]

01 Jul 2025, 08:14

Kudos

Bookmarks

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

105355 posts

Krunaal

Tuck School Moderator

805 posts

Prep Toolkit

Announcements

Master in Management, Finance, Business Analytics and more Master’s Programs!

Solving 705+ Level MSR Questions with Data Synthesis Skils

Tuesday, Nov 18, 2025
10:30am NY / 3:30pm London / 9pm Mumbai

Live Profile Evaluation Chat Session with ARINGO

Wednesday, November 19, 2025
09:00 am PDT | 10:30 pm IST
Location: GMAT Club Chat

Top GMAT Focus Debriefs

GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards