What is the maximum possible number of students who like at least two of the three games?
Explanation:
Let the number of people liking
exactly 1 game = a (all orange areas together) = 90 exactly 2 games = b (all green areas together) all three games = c (blur area) none of the three games = n
⇒ n + a + b + c = 130 ⇒ n + b + c = 40 ...(1)
Also, When we add those who like Cricket (60), Football (45) and TT (45), we add 'a' once, 'b' twice and 'c' thrice. ∴ a + 2b + 3c = 60 + 50 + 45 ⇒ 2b + 3c = 65 ...(2)
Now, to maximise 'b + c', we should maximise the variable with lesser coefficient and to minimise 'b + c', we should maximise the variable with higher coefficient.
Here, we need to maximise 'b + c', hence we will maximise 'b' and minimise 'c'. For, 'b' and 'c' to be integers, least value 'c' can take is 1.
Hence, 2b + 3 = 65 ⇒ b = 31
∴ Maximum possible value of 'b + c' = 31 + 1 = 32.
Hence, option (b).
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