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# 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 Â® and 85 are connected through WhatsApp Â® . 30 faculty members do not have Facebook Â® or WhatsApp Â® accounts. The number of faculty members connected only through Facebook Â® 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.

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