NIMCET 2018
Forty 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?
Answer (Detailed Solution Below)View answer ▾Hide ▴
Answer: Option C — 4
Detailed Solution
Let x students watch all three films; then 40 - x watched exactly one.
Counting viewings: (40 - x) x 1 + 3x = 13 + 16 + 19 = 48.
40 + 2x = 48, so x = 4.
✓ Check
Only A = 9, only B = 12, only C = 15; 9 + 12 + 15 + 4 = 40 students and 9 + 12 + 15 + 3 x 4 = 48 viewings.⚠ Common trap
(D) 8 (the source key) is 48 - 40, the extra viewings; each all-three student adds 2 extra, so divide by 2.Quick tip
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Venn Diagram — Preparation
This question tests your understanding of Venn Diagram, a key topic in the Logical Reasoning section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
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