GATE ME 2018 Set 2 — Question 6
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General Aptitude → Analytical Aptitude → Numerical Relations & Reasoning
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Question
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?
Correct answer
(C) 4
Solution
Let be the number of students who watched all three films.
Let be the number of students who watched only film A, only film B, and only film C respectively.Since each student watched either only one film or all three, the total number of students is:
--- (1)The total number of students who watched each film is given by:
Substitute into equation (1):
.Thus, 4 students watched all three films.
Let be the number of students who watched only film A, only film B, and only film C respectively.Since each student watched either only one film or all three, the total number of students is:
--- (1)The total number of students who watched each film is given by:
Substitute into equation (1):
.Thus, 4 students watched all three films.
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