Discussion
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 ______________.
Answer: A
35 faculty members are connected only through Facebook.
Of the 150, 30 use neither, so 120 use at least one. By inclusion-exclusion, those on both are
\[ \begin{aligned} |F \cap W| &= 55 + 85 - 120 = 20 \\ \text{only } F &= 55 - 20 = 35 \end{aligned} \]
65 is the number connected only through WhatsApp (85 - 20). 45 and 90 do not fit the counts: with 45 on Facebook only, the 55 Facebook users would include just 10 on both, and the union would be 130, not 120.
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