Venn Diagrams Questions for CAT

In a group of students taking Physics, Chemistry and Math, the ratio of (only Physics) : (only Chemistry) : (only Math) is 3 : 2 : 1. The exactly-two total is 30, all three is 10, and the union is 100 (no one is outside).

Three sets satisfy n(A) = 80, n(B) = 70, n(C) = 60. Exactly two of the three is 40, all three is 20, and no element lies outside the three sets. Use the identity n(A) + n(B) + n(C) = E1 + 2(E2) + 3(E3), where E1, E2, E3 are the exactly-one, exactly-two, exactly-three totals.

The number of students playing football and cricket in class 8 of ABC school is 48 and 65 respectively. The total number of students playing football and cricket in ABC school is 126 and 135 respectively. The number of students in class 8 is 95 and total number of students in ABC school is 220.

In a group of 150 people, 120 own a phone, 110 own a laptop, and 100 own a tablet. We examine the possible range for the number who own all three devices, using the complement (do-not-own) method.

In a survey, 120 people like tea, 90 like coffee, and 40 like both. It is also given that the number who like neither beverage is exactly equal to the number who like both. The total number surveyed is to be found.