Discussion
In a society with 100 members, each member plays at least one sport amongst cricket, hockey and volleyball. If 20 members play cricket only, 30 play hockey only, 25 play volleyball only, 12 play both cricket and hockey, 7 play both hockey and volleyball and 3 members play all the sports, then how many members play at least two sports ?
Answer: A
The number who play at least two sports is 25.
Every one of the 100 members plays at least one sport, so each member is in exactly one of two groups: those who play exactly one sport and those who play two or more.
\[ \begin{aligned} \text{exactly one} &= 20 + 30 + 25 = 75 \\ \text{at least two} &= 100 - 75 = 25 \end{aligned} \]
The pairwise figures are not needed: everyone who does not play exactly one sport plays at least two. Option 22 is the number who play exactly two sports, \(25 - 3\), which leaves out the 3 who play all three.
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