GATE | GATE CS Mock 2018 | Set 2 | Question 1

For the workshops organized in college, students can participate more than one workshop saying that all are organized in different timings. 150 students are enrolled in total for one or more than one workshop. Registration details are as follows :

99 students are enrolled for Cyber Security. 56 students are enrolled for Solar Energy, 89 students are enrolled for Artificial Intelligence. 25 students for both Cyber Security and Solar Energy. 65 students for both Cyber Security and Artificial Intelligence and 18 students for both Solar Energy and Artificial Intelligence. How many students are participating in all three workshops ?
(A) 12
(B) 16
(C) 10
(D) 14


Answer: (D)

Explanation: n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – [n(A ∩ B) + n(A ∩ C) + n(B ∩ C)] + n(A ∩ B ∩ C)
150 = 99+56+89 – [25+65+18] + x
150 = 244 – 108 + x

So, x = 14



Answer : Option D

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