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GATE 2018 ME (ME2) – Question 6

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 2 marks · Multiple choice

Forty students watched films A, B and C over a week. Each watched either only one film or all three. Thirteen watched A, sixteen B and nineteen C. How many watched all three?

  1. 0
  2. 2
  3. 4
  4. 8

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Show answer and explanation

Correct answer: (C) 4

Explanation

Let x students watch all three. Total film attendance is $13+16+19=48$. The $40-x$ others count once and these x count three times: $48=(40-x)+3x$. Thus $x=4$: **C**.