Forty students watched films A, B and C over a week. Each student watched either only one film or all three. Thirteen st...

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?

A. 0
B. 2
C. 4
D. 8

Accepted Answer

4 students watched all three films. 40 students each watched exactly one film or all three films (no student watched exactly two). Given the counts for each individual film, we use the fact that the total across all film-viewings must equal 40 plus twice the number who watched all three (since all-three viewers are counted in three film totals). Setting up the equation lets us find how many watched all three.

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? A. 0 B. 2 C. 4 D. 8