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 ______________.

  1. A.

    35

  2. B.

    45

  3. C.

    65

  4. 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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