Last visit was: 26 Sep 2026, 12:45 It is currently 26 Sep 2026, 12:45
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
Edwin555
User avatar
Joined: 10 Aug 2023
Last visit: 17 Sep 2026
Posts: 88
Own Kudos:
56
 [1]
Given Kudos: 17
Location: India
Posts: 88
Kudos: 56
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 00:17
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
Rahilgaur
User avatar
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
Products:
My Reviews
GMAT Focus 1: 575 Q81 V82 DI72
Posts: 162
Kudos: 125
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 01:01
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

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)
User avatar
SaanjK26
User avatar
Joined: 08 Oct 2022
Last visit: 26 Aug 2026
Posts: 77
Own Kudos:
63
 [1]
Given Kudos: 93
Location: India
Posts: 77
Kudos: 63
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 01:15
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
Shub1994
User avatar
Joined: 05 Feb 2023
Last visit: 18 Jun 2026
Posts: 17
Own Kudos:
10
Given Kudos: 53
Posts: 17
Kudos: 10
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 01:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The total = attended + not attended
a = (b+c-(Attended Both))+d
Attend both = a-b-c-d
Fraction = (a-b-c-d)/a
User avatar
Abhishek_Relan
User avatar
Joined: 30 Nov 2023
Last visit: 24 Jan 2026
Posts: 19
Own Kudos:
13
 [1]
Given Kudos: 77
GMAT Focus 1: 565 Q75 V81 DI78
GMAT Focus 1: 565 Q75 V81 DI78
Posts: 19
Kudos: 13
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 01:22
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
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
cyang8
User avatar
Joined: 04 Jun 2022
Last visit: 04 Apr 2026
Posts: 12
Own Kudos:
3
 [1]
Given Kudos: 111
Posts: 12
Kudos: 3
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 01:50
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
ManifestMBAbay25
User avatar
Joined: 05 Oct 2022
Last visit: 24 May 2026
Posts: 31
Own Kudos:
30
 [1]
Given Kudos: 50
Products:
My Reviews
Posts: 31
Kudos: 30
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 01:56
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
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
lepoopa
User avatar
Joined: 08 Jun 2024
Last visit: 31 Mar 2026
Posts: 4
Own Kudos:
3
 [1]
Given Kudos: 6
Location: Mongolia
Schools: Kelley '27
GMAT Focus 1: 745 Q87 V90 DI84
Schools: Kelley '27
GMAT Focus 1: 745 Q87 V90 DI84
Posts: 4
Kudos: 3
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 01:58
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
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.
User avatar
Pavan1224
User avatar
Joined: 20 Jun 2018
Last visit: 22 Aug 2025
Posts: 10
Own Kudos:
5
 [1]
Location: India
Schools: Stanford '26 HBS '28 Booth '26 CBS '26 Ross '26 Wharton '26 Sloan '26
GPA: 2.6
Schools: Stanford '26 HBS '28 Booth '26 CBS '26 Ross '26 Wharton '26 Sloan '26
Posts: 10
Kudos: 5
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 02:02
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
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
ArmandParis
User avatar
Joined: 03 May 2025
Last visit: 07 May 2026
Posts: 13
Own Kudos:
9
 [1]
Given Kudos: 26
Location: France
Posts: 13
Kudos: 9
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 02:37
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
avatar
ToddlerandGMAT
avatar
Joined: 02 Oct 2024
Last visit: 26 Sep 2026
Posts: 48
Own Kudos:
14
Given Kudos: 831
Location: India
Schools: IIM
GMAT Focus 1: 605 Q84 V79 DI77
GPA: 9.23
Products:
My Reviews
Schools: IIM
GMAT Focus 1: 605 Q84 V79 DI77
Posts: 48
Kudos: 14
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 02:58
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


The right answer is c we can also solve it by taking numbers
User avatar
MinhChau789
User avatar
Joined: 18 Aug 2023
Last visit: 12 Apr 2026
Posts: 131
Own Kudos:
140
 [1]
Given Kudos: 2
Posts: 131
Kudos: 140
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 03:22
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can solve the sets using the table:

Cybern/Cyber
Clouda-b-dc
n/Cloudda-c
ba-ba

Answer = (c -(a-b-d))/a = (b + c + d - a)/a
User avatar
jkkamau
User avatar
Joined: 25 May 2020
Last visit: 26 Sep 2026
Posts: 285
Own Kudos:
244
 [1]
Given Kudos: 148
Location: Kenya
Schools: Jones '26 (A$$)
GMAT 1: 730 Q50 V46
GPA: 3.5
Products:
GMAT Club Tests Forum Quiz
Schools: Jones '26 (A$$)
GMAT 1: 730 Q50 V46
Posts: 285
Kudos: 244
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 03:26
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
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
GMATNextStep
User avatar
Joined: 01 Aug 2023
Last visit: 26 Sep 2026
Posts: 40
Own Kudos:
41
 [1]
Given Kudos: 1
GMAT Focus 1: 715 Q85 V88 DI84 (Online)
GMAT Focus 1: 715 Q85 V88 DI84 (Online)
Posts: 40
Kudos: 41
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 03:36
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I drew a table to calculate the fraction of those attending both events:
CybersecurityNo cybersecurityTotal
Cloud Computingxc
not Cloud Computingd
Totalba

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
User avatar
jnxci
User avatar
Joined: 29 Nov 2018
Last visit: 06 May 2026
Posts: 38
Own Kudos:
18
 [1]
Given Kudos: 336
Posts: 38
Kudos: 18
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 03:53
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Total (a) = At least (b) + At least (c) - Both + None (d)
--> Both = b + c + d - a
--> Fraction = Both/Total = (b + c + d - a)/a
User avatar
Gladiator59
User avatar
Joined: 16 Sep 2016
Last visit: 18 Mar 2026
Posts: 829
Own Kudos:
2,788
 [1]
Given Kudos: 269
Status:It always seems impossible until it's done.
GMAT 1: 740 Q50 V40
GMAT 2: 770 Q51 V42
Products:
My Reviews
GMAT 2: 770 Q51 V42
Posts: 829
Kudos: 2,788
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 04:23
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
Iamriya
User avatar
Joined: 04 Nov 2023
Last visit: 08 Jan 2026
Posts: 4
Own Kudos:
2
 [1]
Given Kudos: 12
Posts: 4
Kudos: 2
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 04:25
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
vp20
User avatar
Joined: 05 May 2024
Last visit: 02 Apr 2026
Posts: 13
Own Kudos:
8
 [1]
Given Kudos: 93
Location: India
Schools: Yale '26 UNC '26 (I)
GMAT Focus 1: 655 Q85 V86 DI76
GPA: 6.57
Schools: Yale '26 UNC '26 (I)
GMAT Focus 1: 655 Q85 V86 DI76
Posts: 13
Kudos: 8
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 04:41
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
GMAT-Club-Forum-9j5m33d6.png [ 72.57 KiB | Viewed 424 times ]
User avatar
LucasH20
User avatar
Joined: 13 Apr 2023
Last visit: 31 Aug 2025
Posts: 49
Own Kudos:
35
 [1]
Given Kudos: 383
Posts: 49
Kudos: 35
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 05:49
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
To answer this question we can create a set matrix

a-ca-b
CyberNot CyberTotal
Cloudb-a+c+da-b-dc
Not Clouda-c-dd
Totalba
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
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
ektalakra
User avatar
Joined: 29 Jul 2024
Last visit: 26 Mar 2026
Posts: 37
Own Kudos:
16
 [1]
Given Kudos: 84
Posts: 37
Kudos: 16
 [1]
GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 05:53
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
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   
Moderator:
Bunuel
Math Expert
113941 posts