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

Last visit was: 11 Sep 2026, 10:29

It is currently 11 Sep 2026, 10:29

Toolkit

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

Sep 13
GMAT 615 to 715 in Just 15 Days! Riya’s 100-pt Improvement Strategy
12:30 AM EDT
-
01:30 AM EDT
Struggling to find the right strategies to score a 99 %ile on GMAT Focus? Riya (GMAT 715) boosted her score by 100-points in just 15 days! Discover how the right mentorship, tailored strategies, and an unwavering mindset can transform your GMAT prep.
Sep 13
From ‘GMAT Is Not for Me’ to a 695— Beating Her Target by 50 Points
01:30 AM EDT
-
02:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Sep 15
Live Online Class with Top GMAT Expert Rich Zwelling
07:00 PM EDT
-
09:00 PM EST
Elite scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thurs Sept. 15, 2026 - Nov. 15, 2027, 7:00pm-9:00pm EST
Sep 21
Live Online Bootcamp Class with Top GMAT Expert Chris Peckover
07:00 PM EDT
-
10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included! Class starts Mon, Tues, Wed, Thur, Fri Sept. 21, 2026 - Oct. 9, 2027, 7:00pm-10:00pm EST

bart08241192

Joined: 03 Dec 2024

Last visit: 28 Dec 2025

Posts: 75

Own Kudos:

[1]

Given Kudos: 13

Posts: 75

Kudos: 64

[1]

01 Jul 2025, 08:52

Kudos

Bookmarks

a total participants
b attended a session on cybersecurity,
c attended a session on cloud computing.
If exactly d participants attended neither session

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

answer is c

Show Spoiler

Attachment:

GMAT-Club-Forum-iwziylkb.png [ 13.52 KiB | Viewed 407 times ]

romanmoonshine

Joined: 26 Apr 2025

Last visit: 04 Sep 2025

Posts: 12

Own Kudos:

[1]

Given Kudos: 1

GMAT Focus 1: 645 Q83 V84 DI84 Verified score

GPA: 3.24

Products:

GMAT Focus 1: 645 Q83 V84 DI84 Verified score

Posts: 12

Kudos: 6

[1]

01 Jul 2025, 08:56

Kudos

Bookmarks

Use table method.

Total-= a
Total who participated in Cyber one= b
those who didnt= a-b

total who participated in cloud one- c
those who didnt- a-c

THose who did in neither = d

Thus those who did in cloud one but not cyber = a-b-d

Those who did in both = C - (a-b-d)
= c-a+b+d

fraction of total participants
= (b+c+d-a)/a

option c

RDM42

Joined: 20 Jan 2025

Last visit: 24 Aug 2026

Posts: 464

Own Kudos:

329

[1]

Given Kudos: 29

Posts: 464

Kudos: 329

[1]

01 Jul 2025, 09:04

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?
Total participants= a
People who attended Cybersecurity Session= b
People who attended session on cloud computing= c
People who attended neither session = d
People who attended Cloud computing session but not Cybersecurity = a-b-d
People who attended both session= c-(a-b-d)= c-a+b+d
Fraction= (c-a+b+d)/a

C

WrickR

Joined: 22 Dec 2024

Last visit: 11 Dec 2025

Posts: 37

Own Kudos:

[1]

Given Kudos: 50

Location: India

GPA: 3.7

Posts: 37

Kudos: 26

[1]

01 Jul 2025, 09:05

Kudos

Bookmarks

Clearly,

a = b + c - Both + Neither
So, Both = b + c + d - a

Both as a fraction of total = \frac{ (b + c +d - a)}{a }

Attachments

Screenshot 2025-07-01 213224.png [ 22.78 KiB | Viewed 410 times ]

crimson_king

Joined: 21 Dec 2023

Last visit: 11 Sep 2026

Posts: 148

Own Kudos:

157

[1]

Given Kudos: 118

GRE 1: Q170 V170 Verified score

Posts: 148

Kudos: 157

[1]

01 Jul 2025, 09:08

Kudos

Bookmarks

If total number of participants are equal to a & we have b & c members attending sessions on cybersecurity & cloud computing respectively & if we assume there are x members attending both & there are d members attending neither, we can break down the problem as:

b-x (Only attend cyber sec)+x (Attend both) + c-x (Only attend cloud computing)+d(Attend neither)=a (Total members)

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

The fraction of the total participants will hence be equal to x/a = (b+c+d-a)/a. Hence the answer to this question is option (C) (b+c+d-a)/a

yadirmendez

Joined: 09 Jun 2025

Last visit: 07 Sep 2025

Posts: 4

Own Kudos:

[1]

Given Kudos: 2

Posts: 4

Kudos: 2

[1]

01 Jul 2025, 09:09

Kudos

Bookmarks

a= Total
b= attended cybersecurity
c= attended cloud computing
d= neither
x= both

(b-x)= Attended Cybersecurity only
(c-x)= Attended cloud computing only

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

(b+c+d-a)/a is the fraction of people that attended both divided by the total.

Dipan0506

Joined: 24 May 2021

Last visit: 10 Sep 2026

Posts: 88

Own Kudos:

[1]

Given Kudos: 7

Posts: 88

Kudos: 14

[1]

01 Jul 2025, 09:09

Kudos

Bookmarks

Point C states the summation of other candidates attending and non attending from the total on both sessions The remaining students attended both the sessions. Hence, Point C is the answer.

cabii

Joined: 30 Jul 2024

Last visit: 21 Sep 2025

Posts: 29

Own Kudos:

[1]

Given Kudos: 2

Posts: 29

Kudos: 18

[1]

01 Jul 2025, 09:10

Kudos

Bookmarks

Total=a
Cybersecurity= b
Cloud computing= c
neither= d
Both= b+c+d-a

now fraction of who attended both= b+c+d-a/a

KINGofBATTLES

Joined: 29 Jun 2025

Last visit: 11 Oct 2025

Posts: 15

Own Kudos:

[1]

Given Kudos: 1

Posts: 15

Kudos: 11

[1]

01 Jul 2025, 09:10

Kudos

Bookmarks

We are given:
- Total participants: a
- Attended cybersecurity: b
- Attended cloud computing: c
- Attended neither: d
We need to find the fraction that attended both sessions.
Let x be the number who attended both.
Using the principle of inclusion-exclusion:
Total who attended at least one session = b + c - x
But the total who attended at least one session is also a - d.
So:
b + c - x = a - d
Solving for x:
x = b + c - (a - d)
x = b + c - a + d
The fraction is x / a = (b + c - a + d) / a
Hence answer is (b + c - a + d) / a

chattyyee

Joined: 14 Jan 2025

Last visit: 16 Mar 2026

Posts: 29

Own Kudos:

Given Kudos: 88

Location: India

Concentration: Technology, International Business

Schools: ISB '26

GPA: 3.7

WE:Information Technology (Consulting)

Products:

Schools: ISB '26

Posts: 29

Kudos: 11

01 Jul 2025, 09:12

Kudos

Bookmarks

I ultimately had to resolve to option solving as I could not find a clear pathway through basic algebra. Realizing that in the end, the intersection U should be the only component left, the numerator (b+c+d−a) can be broken down as:
[b'+U+c'+U+d-(b'+U+c'+U+d)] where:
b' is only b, and c' is only c. The fraction is then simply to be divided by participants attended both sessions? so denominator becomes a-d.

Ryga

Joined: 12 Aug 2023

Last visit: 19 Aug 2025

Posts: 68

Own Kudos:

[1]

Given Kudos: 4

Location: India

Concentration: General Management, Leadership

Schools: INSEAD Jan '26 NUS '27 Stern '26

GMAT Focus 1: 695 Q90 V80 DI83 Verified score

Schools: INSEAD Jan '26 NUS '27 Stern '26

GMAT Focus 1: 695 Q90 V80 DI83 Verified score

Posts: 68

Kudos: 51

[1]

01 Jul 2025, 09:13

Kudos

Bookmarks

We are given:
Total participants: a
Attended cybersecurity: b
Attended cloud computing: c
Attended neither session: d

Those who attended at least one session = total participants − those who attended neither = a-d

By set theory,
∣B∪C∣=∣B∣+∣C∣−∣B∩C∣ wherein we need to find ∣B∩C∣ = x

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

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

Answer C

Shin0099

Joined: 26 Aug 2024

Last visit: 10 May 2026

Posts: 59

Own Kudos:

Given Kudos: 442

Posts: 59

Kudos: 35

01 Jul 2025, 09:14

Kudos

Bookmarks

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

As a total we have a.
This total equals b+c+d+ All people, that do both.
Therefore, we are looking for a-b-c-d.

As we are looking for the fraction, we have to divide by the total number, that is a.

The result is therefore: (a-b-c-d)/a

Answer: B

missionmba2025

Joined: 07 May 2023

Last visit: 07 Sep 2025

Posts: 341

Own Kudos:

435

[1]

Given Kudos: 50

Location: India

Posts: 341

Kudos: 435

[1]

01 Jul 2025, 09:17

Kudos

Bookmarks

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

Plotting the information over a grid as shown below -

Overlap = c - a + b + d

Ratio = $\frac{b + c + d - a}{a}$

IMO Option C

Show Spoiler

Attachment:

GMAT-Club-Forum-cgukk2wd.jpeg [ 79.37 KiB | Viewed 351 times ]

A_Nishith

Joined: 29 Aug 2023

Last visit: 31 Jul 2026

Posts: 449

Own Kudos:

210

[1]

Given Kudos: 16

Posts: 449

Kudos: 210

[1]

01 Jul 2025, 09:18

Kudos

Bookmarks

We are told:

Total participants = a

b attended cybersecurity

c attended cloud computing

d attended neither session

We are to find the fraction of participants who attended both sessions.

Step 1: Let’s use the principle of set inclusion:
Let:
Total number of people = a
Number who attended cybersecurity = b
Number who attended cloud computing = c
Number who attended neither = d

Let x be the number who attended both sessions

Then:

People who attended at least one session =
= Cyber only + Cloud only + Both
= b+c−x (since both are double-counted in b and c)

So:
People who attended at least one session=a−d

So set up the equation:
b+c−x=a−d

Solve for x:
x=b+c−(a−d)=b+c+d−a
So the number who attended both = x=b+c+d−a

We’re asked for the fraction of total participants who attended both:

x/a = (b+c+d−a)/a

Final Answer:C.
(b+c+d−a)/a

plpurva

Joined: 12 Nov 2024

Last visit: 15 Feb 2026

Posts: 19

Own Kudos:

[1]

Given Kudos: 31

Location: India

Schools: ISB Carlson '26 CBS '26

GPA: 6.2

WE:Analyst (Consulting)

Schools: ISB Carlson '26 CBS '26

Posts: 19

Kudos: 9

[1]

01 Jul 2025, 09:19

Kudos

Bookmarks

my 2 cents-
The solution is really straightforward when solved using the matrix method

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

Attachments

WhatsApp Image 2025-07-01 at 21.44.29.jpeg [ 213.5 KiB | Viewed 352 times ]

suryabanda

Joined: 20 Apr 2015

Last visit: 12 Dec 2025

Posts: 4

Own Kudos:

[1]

Given Kudos: 2

Location: India

GPA: 4

Posts: 4

Kudos: 17

[1]

01 Jul 2025, 09:22

Kudos

Bookmarks

x be the number of participants who attended both sessions.

Total who attended at least one session = a-d

Number who attended at least one session = b+c-x

Equating both: a-d = b+c-x

x= b+c+d-a

Fraction of total audience = x/a = b+c+d-a/a

lvillalon

Joined: 29 Jun 2025

Last visit: 25 Aug 2025

Posts: 88

Own Kudos:

[1]

Given Kudos: 14

Location: Chile

Concentration: Operations, Entrepreneurship

Schools: HEC Sept '26 INSEAD Aug '26 IMD'26 Rotterdam'26 Booth '26 Sloan '26 Kellogg '26 Anderson '26

GPA: 3,3

WE:Consulting (Consulting)

Schools: HEC Sept '26 INSEAD Aug '26 IMD'26 Rotterdam'26 Booth '26 Sloan '26 Kellogg '26 Anderson '26

Posts: 88

Kudos: 73

[1]

01 Jul 2025, 09:24

Kudos

Bookmarks

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

If x is the intersection of b and c, you can write:

a = b + c - x + d

The reason for this, is that b + c would count x two times.

Solve for x:

x = b + c + d - a

Divide by a to get the fraction:

x/a = (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

Mohit11111

Joined: 26 Mar 2018

Last visit: 11 Sep 2026

Posts: 11

Own Kudos:

[1]

Given Kudos: 8

Location: India

Schools: ISB '27

Posts: 11

Kudos: 5

[1]

01 Jul 2025, 09:26

Kudos

Bookmarks

Total participants = a
Adding the participants in both seminars = b+c
Non participating =d
Now in (b+c), the participants who participated in b and c have overlapped
Hence, participants who participated in both = b+c+d-a
Fraction = (b+c+d-a)/a

Rakshit25

Joined: 16 Jun 2020

Last visit: 23 Mar 2026

Posts: 120

Own Kudos:

[1]

Given Kudos: 25

Location: India

Schools: INSEAD Aug '26 (A) LBS '26 (D) IESE '26 (A)

GPA: 8.4

Schools: INSEAD Aug '26 (A) LBS '26 (D) IESE '26 (A)

Posts: 120

Kudos: 40

[1]

01 Jul 2025, 09:27

Kudos

Bookmarks

IMO should be C

I just took a to be 20, b and c each to be 6 and d to be 10. Only C satisfies the solution for the intersection between b and 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

sameeb

Joined: 22 Jul 2017

Last visit: 15 Jun 2026

Posts: 22

Own Kudos:

[1]

Given Kudos: 123

Posts: 22

Kudos: 5

[1]

01 Jul 2025, 09:28

Kudos

Bookmarks

Answer: C

Total = a
Not participating = d
Participating = a-d

Cyber Security = b
Cloud Computing = c
Both = x (Let's say)

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

Fraction : (b+c+d-a) / a