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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 02 Jul 2025, 05:56
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Option C. People who participated n(bUc) = a - d. People who attended session i.e n(b intersection c) = n(b) + n(c) - n(bUc). Since we require fraction of people participating, we divide by total participants. Therefore answer would be [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 02 Jul 2025, 06:19
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Let x be the number of participants who attended both CS and CC.
Total number of participants = (b+c-x) + d [ Subtract x because it will be counted twice in b+c]
Given Total number of participants = a, therefore

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

Fraction of the number of participants who attended both CS and CC = x/a = b+c+d-a/a

So, correct answer is, 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 02 Jul 2025, 07:44
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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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Total = Present in cyber sec or Present in cloud comp. + Present in neither

a = b + c - both + d

both = b+c+d -a
Fraction attended both = C. \(\frac{b + c + d - a}{a}\)
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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 26 Jul 2025, 18:52
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Here in the question it is not told that b people only attended a session on Cybersecurity. So b will be outside of the circle inthe venndiagram. Same with C as well. If we take X as the both b & c . Total given as a .

a = b-x+x+c-x+d. Now x = a-b-c-d fraction is required so a-b-c-d/a is the solution right? where am i missing bunuel
Bunuel
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. \(\frac{b + c - a + d}{a-d}\)

­

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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GMAT Club Olympics 2025 (Day 2): At a tech seminar with a total 26 Jul 2025, 20:01
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Check signs.
a = b-x+x+c-x+d = b+c-x+d
x = b+c+d-a

pavanhra
Here in the question it is not told that b people only attended a session on Cybersecurity. So b will be outside of the circle inthe venndiagram. Same with C as well. If we take X as the both b & c . Total given as a .

a = b-x+x+c-x+d. Now x = a-b-c-d fraction is required so a-b-c-d/a is the solution right? where am i missing bunuel
Bunuel
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. \(\frac{b + c - a + d}{a-d}\)

­

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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