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

Last visit was: 20 Apr 2026, 16:04

It is currently 20 Apr 2026, 16:04

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

Apr 16
Sneak Peek: $200 Off GMAT Prep
12:00 PM EDT
-
11:59 PM EDT
You’re first to know: Save $200 on GMAT prep starting tomorrow, 4/13. Get 6 official practice tests and study with real questions. Be ready to save!
Apr 22
From ‘GMAT Is Not for Me’ to a 695— Beating Her Target by 50 Points
12:30 AM EDT
-
01:30 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.
Apr 23
A Non-Native’s Journey to GMAT 695 with V88 (99th percentile)
01:30 AM EDT
-
02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 23
Free full-length test!
08:00 PM PDT
-
09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 26
Score High on the GMAT with Target Test Prep
10:00 AM EDT
-
11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 27
Try OnDemand GMAT Masterclass
11:00 AM EDT
-
12:00 PM EDT
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
Apr 28
Join - GMAT Day!
08:00 AM PDT
-
11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.

Edwin555

Joined: 10 Aug 2023

Last visit: 16 Apr 2026

Posts: 88

Own Kudos:

[1]

Given Kudos: 17

Location: India

Posts: 88

Kudos: 54

[1]

02 Jul 2025, 00:17

Kudos

Bookmarks

This is a problem on sets.

Total Participants = a
Cybersecurity = b
Cloud Computing = c
Neither sessions = d
Both sessions = x

cybersecurity alone = (b - x)
Cloud Computing alone = (c - x)

Now a = (b - x) + (c - x) + d + x
∴ a = b + c + d - x
∴ fraction of the participants attended both sessions = x/a = (b + c + d - a)/a

Correct option is Option C

Rahilgaur

Joined: 24 Jun 2024

Last visit: 26 Jan 2026

Posts: 162

Own Kudos:

125

[1]

Given Kudos: 47

GMAT Focus 1: 575 Q81 V82 DI72 Verified score

Products:

GMAT Focus 1: 575 Q81 V82 DI72 Verified score

Posts: 162

Kudos: 125

[1]

02 Jul 2025, 01:01

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

Total Participants = Cyber security + Cloud Computing – Both + None
a = b + c – Both + d
Both = b+c+d-a

Answer = Both/Total Participants
= (b+c+d-a)/a (C)

SaanjK26

Joined: 08 Oct 2022

Last visit: 19 Apr 2026

Posts: 77

Own Kudos:

[1]

Given Kudos: 74

Location: India

Posts: 77

Kudos: 63

[1]

02 Jul 2025, 01:15

Kudos

Bookmarks

Let total participants = a
Let x = number who attended both sessions

a = b + c - x + d

x = b + c + d - a

So, the fraction who attended both=
x/ a = b + c + d - a/ a

Answer: C. (b + c + d - a)/a

Shub1994

Joined: 05 Feb 2023

Last visit: 18 Apr 2026

Posts: 17

Own Kudos:

Given Kudos: 53

Posts: 17

Kudos: 10

02 Jul 2025, 01:20

Kudos

Bookmarks

The total = attended + not attended
a = (b+c-(Attended Both))+d
Attend both = a-b-c-d
Fraction = (a-b-c-d)/a

Abhishek_Relan

Joined: 30 Nov 2023

Last visit: 24 Jan 2026

Posts: 19

Own Kudos:

[1]

Given Kudos: 77

GMAT Focus 1: 565 Q75 V81 DI78 Verified score

Posts: 19

Kudos: 13

[1]

02 Jul 2025, 01:22

Kudos

Bookmarks

Total no. of people attending or not attending the sessions = a ----- (1)
Total no. of people not attending either of the sessions = d ----- (2)

Let no. of people who attended both sessions = z ----- (3)
No. of people attended cybersecurity session exclusively = b - z ----- (4)
No. of people attended cloud computing session exclusively = c - z ----- (5)

No. of people attended cybersecurity session exclusively + No. of people attended cloud computing session exclusively + no. of people who attended both sessions + no. of people not attending either of the sessions = Total no. of people attending or not attending the sessions --------- (6)

Putting respective values of (1), (2), (3), (4), (5) in (6)

b - z + c - z + z + d = a
b + c + d - z = a
b + c + d - a = z

Fraction of the participants attended both sessions = z/ a
= (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

cyang8

Joined: 04 Jun 2022

Last visit: 04 Apr 2026

Posts: 12

Own Kudos:

[1]

Given Kudos: 111

Posts: 12

Kudos: 3

[1]

02 Jul 2025, 01:50

Kudos

Bookmarks

C.

The number of participants who attended at least 1 session is A-D. The number of participants who attended either sessions B or C, or both, is B+C-X. We will set A-D=B+C-X and solve for X to get the number of participants who attended both sessions, which is B+C+D-A. Since the question is looking for a fraction, the denominator will be the total number of participants, which is A.

ManifestMBAbay25

Joined: 05 Oct 2022

Last visit: 10 Mar 2026

Posts: 32

Own Kudos:

[1]

Given Kudos: 50

Products:

Posts: 32

Kudos: 28

[1]

02 Jul 2025, 01:56

Kudos

Bookmarks

Cyber security - b
Cloud Computing - c
neither - d
Total - a
Both - x ( need to find this to find the fraction)

Only cyber security - b-x
Only cloud computing - c- x

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

fraction - (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

lepoopa

Joined: 08 Jun 2024

Last visit: 31 Mar 2026

Posts: 4

Own Kudos:

[1]

Given Kudos: 6

Location: Mongolia

Schools: Kelley '27

GMAT Focus 1: 745 Q87 V90 DI84 Verified score

Schools: Kelley '27

GMAT Focus 1: 745 Q87 V90 DI84 Verified score

Posts: 4

Kudos: 3

[1]

02 Jul 2025, 01:58

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

For overlapping sets like these, the formula I use is "Total = A + B - Both + Neither", where "Both" is subtracted because it has been counted twice in both A and B.
It is easier to see it on a Venn diagram.

For this question, if we input the given information, we get "a = b + c - Both + d".
We can put "Both" on one side of the equation by:
1. subtracting b + c + d from both sides => "a - b - c - d = (- Both)"
2. multiplying both sides by (-1) => "(- a) + b + c + d = Both" or "b + c + d - a = Both"

The question is asking for the fraction of participants that attended both sections, which means we need to find "$\frac{Both}{a}$".
By substituting our result for "Both" from step 2, we can get "$\frac{Both}{a}=\frac{b+c+d-a}{a}$", which matches answer choice C.

Pavan1224

Joined: 20 Jun 2018

Last visit: 22 Aug 2025

Posts: 10

Own Kudos:

[1]

Location: India

Schools: Stanford '26 HBS '26 Booth '26 CBS '26 Ross '26 Wharton '26 Sloan '26

GPA: 2.6

Schools: Stanford '26 HBS '26 Booth '26 CBS '26 Ross '26 Wharton '26 Sloan '26

Posts: 10

Kudos: 5

[1]

02 Jul 2025, 02:02

Kudos

Bookmarks

C. Total = Group1 + Group2 - Both + Neither

Total: a (total participants)
Group1: b (attended cybersecurity session)
Group2: c (attended cloud computing session)
Neither: d (attended neither session)
Both: 'x'.

Substitute these into the formula:
a = b + c - x + d

Solving for 'x'
x = b + c + d - a

Finding the Fraction

This is the number of people who attended both (x) divided by the total number of participants (a):
Fraction = x / a = (b + c +d - a) / a

Answer
(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

ArmandParis

Joined: 03 May 2025

Last visit: 18 Apr 2026

Posts: 13

Own Kudos:

[1]

Given Kudos: 26

Location: France

Posts: 13

Kudos: 9

[1]

02 Jul 2025, 02:37

Kudos

Bookmarks

Total = a
Cyber = b
Cloud = c
Neither = d

Question: "what fraction of the participants attended both sessions?" -> Both/Total?

Cyber + Cloud - Both + Neither = Total
-> b + c - Both + d = a
-> Both : b + c + d - a
-> Both/Total = Both/a = (b + c + d - a) / a

Answer choice C.

Phoenix2107

Joined: 02 Oct 2024

Last visit: 20 Apr 2026

Posts: 46

Own Kudos:

Given Kudos: 825

Location: India

Schools: IIM

GMAT Focus 1: 605 Q84 V79 DI77 Verified score

GPA: 9.23

Products:

Schools: IIM

GMAT Focus 1: 605 Q84 V79 DI77 Verified score

Posts: 46

Kudos: 13

02 Jul 2025, 02:58

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

The right answer is c we can also solve it by taking numbers

MinhChau789

Joined: 18 Aug 2023

Last visit: 12 Apr 2026

Posts: 132

Own Kudos:

140

[1]

Given Kudos: 2

Posts: 132

Kudos: 140

[1]

02 Jul 2025, 03:22

Kudos

Bookmarks

Can solve the sets using the table:

	Cyber	n/Cyber
Cloud		a-b-d	c
n/Cloud		d	a-c
	b	a-b	a

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

jkkamau

Joined: 25 May 2020

Last visit: 20 Apr 2026

Posts: 226

Own Kudos:

190

[1]

Given Kudos: 142

Location: Kenya

Schools: Haas '25

GMAT 1: 730 Q50 V46 Verified score

GPA: 3.5

Products:

Schools: Haas '25

GMAT 1: 730 Q50 V46 Verified score

Posts: 226

Kudos: 190

[1]

02 Jul 2025, 03:26

Kudos

Bookmarks

Using a Venn Diagram the total participants is b+c-x+d = a where x is the number of those that attended both
Rearrange the equation and x becomes b+c+d-a
To get the fraction you divide x by the total a which gives us choice 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

GMATNextStep

Joined: 01 Aug 2023

Last visit: 20 Apr 2026

Posts: 34

Own Kudos:

[1]

Given Kudos: 1

GMAT Focus 1: 715 Q85 V88 DI84 (Online) Verified score

Products:

GMAT Focus 1: 715 Q85 V88 DI84 (Online) Verified score

Posts: 34

Kudos: 36

[1]

02 Jul 2025, 03:36

Kudos

Bookmarks

I drew a table to calculate the fraction of those attending both events:

	Cybersecurity	No cybersecurity	Total
Cloud Computing	x		c
not Cloud Computing		d
Total	b		a

b + c - x + d = a
or A + B - both + neither = Total

=> x = b + c + d - a
Fraction = (b + c + d - a)/a, where a is the total

Choose C

jnxci

Joined: 29 Nov 2018

Last visit: 28 Mar 2026

Posts: 39

Own Kudos:

[1]

Given Kudos: 338

Posts: 39

Kudos: 18

[1]

02 Jul 2025, 03:53

Kudos

Bookmarks

Total (a) = At least (b) + At least (c) - Both + None (d)
--> Both = b + c + d - a
--> Fraction = Both/Total = (b + c + d - a)/a

Gladiator59

Joined: 16 Sep 2016

Last visit: 18 Mar 2026

Posts: 841

Own Kudos:

2,714

[1]

Given Kudos: 271

Status:It always seems impossible until it's done.

GMAT 1: 740 Q50 V40 Verified score

GMAT 2: 770 Q51 V42 Verified score

Products:

GMAT 2: 770 Q51 V42 Verified score

Posts: 841

Kudos: 2,714

[1]

02 Jul 2025, 04:23

Kudos

Bookmarks

so we have

a = total people
b = cyberscurity session
c = cloud computing session
d = people who went to neither

i used that inclusion-exclusion thing. basically, people who went to atleast one session = total - people who went to neither = a - d
but also, people who went to atleast one = cybersecurity + cloud - both sessions
so: a - d = b + c - both

solving for both
both = b + c - (a - d)
both = b + c - a + d
so the frction is (b + c - a + d)/a
rearranging: (b + c + d - a)/a

thats option C.

Iamriya

Joined: 04 Nov 2023

Last visit: 08 Jan 2026

Posts: 4

Own Kudos:

[1]

Given Kudos: 12

Posts: 4

Kudos: 2

[1]

02 Jul 2025, 04:25

Kudos

Bookmarks

Answer - C

Total participants = a
Participants who attended Cybersecurity = b
Participants who attended cloud computing = c
Attended Neither = d

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

Attended both = b+c+d-a
Attended both ratio = (b+c+d-a)/a

vp20

Joined: 05 May 2024

Last visit: 02 Apr 2026

Posts: 13

Own Kudos:

[1]

Given Kudos: 94

Location: India

Schools: Yale '26 UNC '26 (I)

GMAT Focus 1: 655 Q85 V86 DI76 Verified score

GPA: 6.57

Schools: Yale '26 UNC '26 (I)

GMAT Focus 1: 655 Q85 V86 DI76 Verified score

Posts: 13

Kudos: 8

[1]

02 Jul 2025, 04:41

Kudos

Bookmarks

To determine the fraction of participants who attended both the sessions, fill up the table as shown below (follow the numbers to determine the expression step wise)

Note that in either case , the numerator of the required fraction will simplify to the same expression i.e.
c - [(a-b) - d] or
b - [(a-c) - d]

And the denominator will be total participants -> a
Thus, we can quickly eliminate Option (E)

We can now observe in options (A), (B) and (D), the numerator expressions all have '+a' terms.
But from the expressions that we came up with, all the terms simplify to '-a' terms.

So we can eliminate options (A), (B) and (D) and select
Option (C) as the correct choice.

(Just to confirm, the expressions simplify to)
c - [(a-b) - d] or
b - [(a-c) - d]
----------------
= b - [ a-c - d]
= b - a + c + d
= b + c + d - a (same as option C numerator)

Show Spoiler

Attachment:

GMAT-Club-Forum-9j5m33d6.png [ 72.57 KiB | Viewed 315 times ]

LucasH20

Joined: 13 Apr 2023

Last visit: 31 Aug 2025

Posts: 52

Own Kudos:

[1]

Given Kudos: 384

Posts: 52

Kudos: 35

[1]

02 Jul 2025, 05:49

Kudos

Bookmarks

To answer this question we can create a set matrix

a-ca-b

	Cyber	Not Cyber	Total
Cloud	b-a+c+d	a-b-d	c
Not Cloud	a-c-d	d
Total	b	a

The marked areas (yellow) are the areas we can determine based on the information provided which are the cells with no colour.
Now we can use the set matrix to determine the fraction of the participants attending both sessions to be [b-a+c+d][/a]. Thus, answer C.

Regards,
Lucas

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

ektalakra

Joined: 29 Jul 2024

Last visit: 26 Mar 2026

Posts: 38

Own Kudos:

[1]

Given Kudos: 84

Posts: 38

Kudos: 16

[1]

02 Jul 2025, 05:53

Kudos

Bookmarks

in a venn diagram,
total participant =a
participant for cybersecurity=b
participant cloud computing =c
neither=d
let who attended both be x
a=b-x+c-x+x+d
so,
x=b+c+d-a
x/a=b+c+d-a/a ---- ans (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