Question

34. A survey is conducted among 200 students in a college. 100 like Hiking, 120 like Rafting and 80 like Cycling. 60 students like Hiking and Rafting both, 40 like Rafting and Cycling both, 10 students liked all the three and 20 students did not like any of the three.
How many students liked at least two of the three?

• A. 90
• B. 100
• C. 120
• D. 80

Answer 1

The correct option is B 100

Let H = 100; R = 120; C = 80;
H R = 60; R C = 40; H R C=10

From above Venn Diagram: a + b + d + e = 100; b + c + e + f = 120; d + e + f + g = 80;
a + b + c + d + e + f + g = 180
b + e = 60; e + f = 40
e = 10
From these equations we can find;
a = 20; b = 50; c = 30; d = 20; e = 10; f = 30; g = 20
At least any two = b + d + e + g = 100