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Difficulty:
45%
(medium)
Question Stats:
75% (01:46) correct
25%
(01:59)
wrong
based on 866
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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. \(\frac{b + c - a + d}{a-d}\)
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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. \(\frac{b + c - a + d}{a-d}\)
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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.
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General Discussion
MaxFabianKirchner
Joined: 02 Jun 2025
Last visit: 12 Jul 2025
Posts: 65
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
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).
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).
Posts: 1,382
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
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
Karanjotsingh
Joined: 18 Feb 2024
Last visit: 03 Oct 2025
Posts: 139
Location: India
Concentration: Finance, Entrepreneurship
Posts: 139
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:
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
(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
Posts: 61
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
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
anuraagnandi9
Joined: 25 Mar 2025
Last visit: 21 Jan 2026
Posts: 11
Location: India
GMAT Focus 1: 705 Q87 V84 DI84 
GPA: 3.34
GMAT Focus 1: 705 Q87 V84 DI84
Posts: 11
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
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
Posts: 32
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
APram
Joined: 23 Jun 2024
Last visit: 08 Sep 2026
Posts: 704
Location: India
Schools: ISB '26 HEC INSEAD Jan '26
GMAT Focus 1: 605 Q86 V78 DI76 
GPA: 3.608
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
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
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
Bunuel
We can plot the information on a 2*2 matrix and get the following table
| Cybersecurity | Not 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: 11 Sep 2026
Posts: 6,127
Location: India
Schools: HBS '28 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
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: -
After filling up the blank fields: -
The fraction of the participants attended both sessions = \(\frac{b+c+d-a}{a}\)
IMO C
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
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
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
krutarth21
Joined: 28 May 2025
Last visit: 23 Feb 2026
Posts: 21
Location: India
Schools: ISB '26 (A$)
GMAT Focus 1: 675 Q88 V82 DI81
GPA: 3.82
Correct answer is C, below attached is the solution for the question
Attachments
IMG_1887.JPG [ 1.72 MiB | Viewed 4562 times ]
Posts: 23
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
d-a+(b+c)/a
Posts: 18
Bunuel
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
Posts: 136
a= b+c -(Both)+d
(Both)=b+c+d-a
Both/a = (b+c+d-a)/a
Hence Ans C
(Both)=b+c+d-a
Both/a = (b+c+d-a)/a
Hence Ans C
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
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
Posts: 14
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
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: 13 Jul 2026
Posts: 495
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:
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
- 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
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