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­Correct option is E


­We have our equation set as:
F+B-a+y = 100 (y = number of students who like neither of the games)
=> a-y = 68+57-100 = 25
We can have y=0 in which case we shall have a=25 which is the minimum

Or We can have a scenario in which there is a possibility that all the students who like football also like basketball, in which case we shall have the intersection value = a = 57 which is the maximum

So difference = 57 - 25 = 32

Correct option is E

We can approach it in another beautiful way:


From fig 1 we can say the maximum value of a=57
From fig 2 we can say minimum value of a = 25
(shaded region is the intersection = a)

So difference = 57-25 = 32
­­­­­
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