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605-655 (Medium)|   Overlapping Sets|         
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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 19:56
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e is the number of participants who attended both sessions

total = a = b+c-e+d
e=b+c+d-a

Dividing by a:
(b+c+d-a)/a

Answer C
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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 20:40
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Total Number of participants= a
let no of participants who attended both sessions be x
b-x+c+d=a
x=b+c+d-a
Percentage of Participants = b+c+d-a/a
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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 20:42
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Using set theory we have

a = b+c+d-both
both = b+c+d-a

fraction=both/a=(b+c+d-a)/a

Correct answer is C
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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 20:44
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Apply Set formula (Two Sets) : Total = All Group 1 + All Group 2 - Intersection (Both) + Neither

In this case:
a = b+c+d-x

x = b+c+d-a
Fraction: (b+c+d-a)/a
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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 21:16
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Group 1 + Group 2 – Both + Neither = Total
b+c-Both+d=a

Both = b+c+d-a

The fraction of the participants who attended both sessions is (b+c+d-a)/a

The right answer is C
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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 21:18
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Solve using set properties
Total number of participants= Attendants + Non Attendants
a= bUc + d
a = b + c - (b and c) + d
we want (b and c)
(b and c)= b+c+d- a
fraction of participants who attended both sessions =
\(\frac{b + c + d - a}{a}\) (a is the total number of participants)
Answer is 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. \(\frac{b + c - a + d}{a-d}\)


 


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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 21:19
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Total participants = a
Let x be the number of participants who attended both sessions.

Then:
Only cybersecurity = b - x
Only cloud computing = c - x
Both sessions = x
Neither = d

So total = (b - x) + (c - x) + x + d = a
Simplify: b + c - x + d = a
So: b + c + d - x = a
Solve for x: x = b + c + d - a

We are asked to find the fraction who attended both sessions: x / a
So the answer is (b + c + d - a) / a

Answer is C
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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 21:25
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Answer (C)

Let double overlap be x
a= b+c - x
so d = a - (b + c -x)
d = a - b - c + x
x = d-a+b+c

ques asks for what fraction of the participants

x/a= d-a+b+c/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. \(\frac{b + c - a + d}{a-d}\)


 


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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 21:26
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If we see total no of participants who attended the sessions it would be a+b+c-d, as a would be total no of participants and adding b and c, and subtracting d would give us people who attended atleast one session. Now we need intersection so we would subtract a-d from b+c which would give us b+c-a+d. For fraction divide by total i.e. a. Option 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. \(\frac{b + c - a + d}{a-d}\)


 


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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 21:27
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Quote:
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.
[ltr]a−b−c+daa−b−c+da[/ltr]


B.
[ltr]a−b−c−daa−b−c−da[/ltr]


C.
[ltr]b+c+d−aab+c+d−aa[/ltr]


D.
[ltr]a−b−c+2daa−b−c+2da[/ltr]


E.
[ltr]b+c−a+da−db+c−a+da−d[/ltr]
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This can be solved using a 2 set matrix for overlapping sets as in the attached picture.

The correct answer is (C)
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WhatsApp Image 2025-07-02 at 9.51.17 AM.jpeg [ 256.51 KiB | Viewed 471 times ]

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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 21:45
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a= b+c+d- both. interchanging both and a and then dividing the result by total , you get the answer, which is, 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. \(\frac{b + c - a + d}{a-d}\)


 


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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 22:20
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Total Participants= a
Cybersecurity(A)=b
cloud security(B)= c
Neither=d
Both =?

Now in order to find the answer we use formula of Venn diagrams:
Total-Neither=A+B-Both
(Now we substitute the values
a-d= b+c-both
a-d-b-c=-both
(multiply both sides by Negative sign)
both= b+c+d-a

fraction OF BOTH=b+c+d-a/a
therefore answer is 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. \(\frac{b + c - a + d}{a-d}\)


 


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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 22:29
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Let x be the number of people attending both cybersecurity and cloud computing sessions.

According to basic set theory, it will follow that,

b + c - x + d = a

Rearranging the above, we get x = b+c+d-a

The questions asks for x / a. Therefore the answer is (b+c+d-a) / a

Therefore, Option C
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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 22:31
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The answer is C. It will be solved by SET rules
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. \(\frac{b + c - a + d}{a-d}\)


 


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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 22:35
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The formula is:

total participants = cybersecurity + cloud computing - both + neither

or a = b + c + d - (both)

so the fraction of the total participants that attended both will be \(\frac{b + c + d - a}{a}\)

Option 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. \(\frac{b + c - a + d}{a-d}\)


 


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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 22:36
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Quote:
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.
a−b−c+daa−b−c+da


B.
a−b−c−daa−b−c−da


C.
b+c+d−aab+c+d−aa


D.
a−b−c+2daa−b−c+2da


E.
b+c−a+da−db+c−a+da−d
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This can be solved using a 2 set matrix for overlapping sets as in the attached picture.

The correct answer is (C)
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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 22:46
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Option B is the answer.
The fraction of the participants who attended both sessions = (b - (a-c-d) )/ a
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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 22:47
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Cloud ComputingNo Cloud ComputingTotal
Cyber Securityb+c+d-a b
No Cyber Securitya-b-dda-b
Totalc a

Therefore required fraction = 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. \(\frac{b + c - a + d}{a-d}\)


 


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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 22:51
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It uses a simple forumla of sets that is - total-neither=a+b-both so here it would be a-d=b+c-x solving that we would get the answer a 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. \(\frac{b + c - a + d}{a-d}\)


 


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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 01 Jul 2025, 23:23
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This is an overlapping sets concept.
The total participants, a, is basically = b + c - x + d
x is the number of participants who attended both sessions (and we subtract it once, as we are counting it twice while counting participants attending the first session and participants attending the second session)
It gives x as b + c + d - a
Now fraction of the participants who attended both sessions would be (b + c + d - a) / a
Option 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. \(\frac{b + c - a + d}{a-d}\)


 


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