Project ForgeForty students watched films A, B and C over a week. Each student watched either only one film or all three. Thirteen students watched film A, sixteen students watched film B and nineteen students watched film C. How many students watched all three films?
- A0
- B2
- 4
- D8
Explanation
Let a, b, c be the counts of students watching ONLY A, only B, only C, and x be the count watching all three. Total: a+b+c+x=40. Each film's total count includes its 'only' watchers plus the all-three watchers: a+x=13, b+x=16, c+x=19. Summing these three: (a+b+c)+3x=48. Substituting a+b+c=40-x: (40-x)+3x=48, so 2x=8, x=4.
Source: GATE ME 2018 Session 2 (Set 2) (2018)
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