Related Articles

GATE | GATE-CS-2016 (Set 2) | Question 6

• Last Updated : 28 Jun, 2021

Among 150 faculty members in an institute, 55 are connected with each other through Facebook ® and 85 are connected through WhatsApp ® . 30 faculty members do not have Facebook ® or WhatsApp ® accounts. The number of faculty members connected only through Facebook ® accounts is ______________.

(A) 35

(B) 45
(C) 65
(D) 90

Explanation: Suppose

n(F) : number of faculty connected through facebook
n(W) : number of faculty connected through whatsapp

n(F ∪ W) : number of faculty connected through either facebook and whatsapp
n(F ∩ W) : number of faculty connected through both facebook and whatsapp

n(F ∪ W) = (total faculty – faculty not connected to anything) = (150-30) = 120

From number theory:
n(F ∪ W) = n(F) + n(W) – n(F ∩ W)
n(F) – n(F ∩ W) = n(F ∪ W) – n(W)
n(F) – N(F ∩ W) = (120-85) = 35

n(F)- n(F ∩ W) is the faculty that has only facebook account, Hence answer is 35.

This explanation has been contributed by Dharmesh Singh.

Quiz of this Question

Attention reader! Don’t stop learning now.  Practice GATE exam well before the actual exam with the subject-wise and overall quizzes available in GATE Test Series Course.

Learn all GATE CS concepts with Free Live Classes on our youtube channel.

My Personal Notes arrow_drop_up