Among 150 faculty members in an institute, 55 are connected with each other…
2016
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
Attempted by 28 students.
Show answer & explanation
Correct answer: A
Key idea: Use the inclusion-exclusion principle to find the intersection and then the number only on Facebook.
Total faculty = 150; those with neither Facebook nor WhatsApp = 30, so number with at least one = 150 - 30 = 120.
Let Facebook = 55 and WhatsApp = 85. Intersection = 55 + 85 - 120 = 20.
Only Facebook = Facebook total - intersection = 55 - 20 = 35.
Therefore, 35 faculty members are connected only through Facebook.
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