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

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01 Jul 2025, 09:28

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ANS C

a= total participants
b= attended a session on cybersecurity
c= attended a session on cloud computing
d= participants attended neither
x= both sessions
a=b+c-x+d
x=b+c+d-a

% of participants that attend both sessions= x/a=(b+c+d-a)/a

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01 Jul 2025, 09:29

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Total Participants = a

Participants attended Cybersecurity session =b

Participants attended Cloud computing = c

Participants attended neither session = d

Using Venn diagram following equation is obtained

a=b+c-b ∩ c+d

let b∩c=x

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

Fraction of participants attended both sessions= (b+c+d-a)/a

Answer is C

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01 Jul 2025, 09:33

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total participants = participants in cybersecurity + participants in cloud computing - participants in both cybersecurity and cloud computing + participants in Neither session
a = b + c - both + d
both = (b + c + d -a)
so fraction = participants in both cybersecurity and cloud computing/ total participants = (b + c + d -a)/a

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01 Jul 2025, 09:35

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Total participants (a) = cybersecurity (b) + cloud (c) - both + neither (d)
both = b+c+d-a
Fraction = $\frac{both}{total} $= $\frac{b+c+d-a}{a}$

Answer: C

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01 Jul 2025, 09:42

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I did something like this,
let x be people who attend both.
then
people who attend only b : b-x
people who attendes only c : c- x
total to be b-x + c-x + x + d = a
Which means x = (B+ c + d -a )
x/a = (B+ c + d -a )/ a

answer C

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01 Jul 2025, 09:43

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

Ans: b+c+d-a/a (C)

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01 Jul 2025, 09:49

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Total = Group1 + Group2 + Group3 - Both + Neither
Therefore,
a = b + c + - "both" + d
We need to find "both"/a
Then,
"both" = (b + c + d - a)/a,
Hence, option C

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01 Jul 2025, 09:50

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Bunuel

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To find the fraction of participants who attended both we need to find: \frac{People who attended both}{Total people}

We already know total number of people is a

Now to find people who attended both sessions we must take the following formula:

=> Total number of participants = People in Cybersecurity + People in Could Computing - People in Both + Attended Neither

Now if we rearrange the equation to find People in Both-

->People in Both = People in Cybersecurity + People in Could Computing - Total number of participants + Attended Neither

Let's substitute values of a, b, c, d in equation:

===> People in Both = b + c - a + d

Final answer: \frac{(People who attended both)}{(Total people)}

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

Answer:
(C)

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01 Jul 2025, 09:50

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Let's say x people attended both sessions.
So:
==>Only cybersecurity = b-x
==>Only cloud computing = c-x
==> Both = x
==> Neither = d
Therefore,
Total = Only cyber + Only cloud + both + Neither
=(b-x) + (c-x) + x + d
= b + c + d - x
But total people also given as a,so:
==> a = b + c + d - x
==> x = b + c + d - a
Now fraction who attended both = x/a
= (b + c + d -a) / a
Correct answer option C

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AorB= A+B-AandB+ Neither
a=b+c-both+d (Substituting the values given in the equation)
both=(b+c+d-a)
both/total=(b+c+d-a)/a

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01 Jul 2025, 09:53

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Bunuel

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Let a be the total number of participants.

Let b be the number of Cyber security.

Let c be the number of Cloud Computing.

Let d be the number of participants who has not attended neither session.

Let x be the number of participants who attended both cyber security and cloud computing.

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

x = (b+c+d)-a

Fraction that attended both session = x/a

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

Option C

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01 Jul 2025, 10:01

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Let x be the number of persons who attended both sessions.

Therefore, Total people who took part in the conference = People who only attended Cybersecurity session + People who only attended Cloud Computing session +People who attended both sessions + People who attended neither sessions,
or, a = (b-x)+(c-x)+x+d => x = (b+c+d-a)/a.

Answer = C

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01 Jul 2025, 10:03

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Let x= attended both sessions.

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

Thus, x/total = b+c+d-a / a => answer is C

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01 Jul 2025, 10:06

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Total Paricipant = a
Cyber Security = b
Cloud Computing = c
Non = d
Let both Cyber Security and Cloud Computing be, e

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

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

The correct answer is C

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01 Jul 2025, 10:14

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Total = A + B + Neither - AUB

a = b + c + d - Both
Both = b + c + d - a

Fraction = Both / a = (b + c + d - a)/a

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01 Jul 2025, 10:18

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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= total participants
b=cybersecurity attendees
c=cloud computing attendees
d=neither

No of participants who attended at least one session= a-d

Again, number of participants who attended at least one session is
= b +c - x

where x is participants who attended both sessions

b + c- x=a-d

x= b + c - a + d

Hence, the fraction of the participants attended both sessions is

(B+C-A+D)/A

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01 Jul 2025, 10:22

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What is Given :
Total Participants = a
Attendees for Cybersecurity = b
Attendees for Cloud computing = c
Participants attended no sessions = d

What is Asked?

'Fraction of participants attended both sessions' => [attendees common for both Cybersecurity and Cloud computing sessions][/Total Attendees]

Solution :

Attendees common for both Cybersecurity and Cloud computing sessions, implies

Total attendance in Cybersecurity and Cloud computing session (a) - Total Participants who attended any session (b) ; as there is an overlap of participants in Cybersecurity and Cloud computing sessions
=> (a) = b+c ;
(b) = Total participants - Participants attended no session = a-d
=> Attendees common for both Cybersecurity and Cloud computing sessions = (b+c) - (a-d) = b+c-a+d

Now, we know total number of attendees = a

Therefore, the Fraction of participants who attended both sessions = [b+c+d-a][/a]
Option C is the answer.

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01 Jul 2025, 10:25

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Bunuel

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01 Jul 2025, 10:26

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Option C

total no of participants :a
No in cybersecurity:b
No. in cloud computing :c
Neither-d
No of no Cloud Computing: (a-c)
No. of no Cloud Computing but yes to Cybersecurity: (a-c-d)
Hence no of both cybersecurity and cloud computing: (c-a+b+d)
Fraction of participants attending both sessions= (c-a+b+d)/a

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01 Jul 2025, 10:27

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So, this is what we are given:

Total # of participats = a
# of attendees for cybersecurity = b
# of attendees for cloud computing = c
# of participants that attended neither cybersecurity or cloud computing = d

We have to find = $\frac{Participants that attended both cybersecurity and cloud computing}{Total # of participants } $

For two sets, we know that

Total = A + B - both + neither

Putting in the values we have from the info given:

a = b + c - both + d

Solving for "both", we get,

both = b+c+d-a

Dividing this by the total # of participants, we get:

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

And that is the correct answer, option C