CAT 2022Slot 1QAQuestion & Solution
AlgebraHard
Question
In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks is
Options
47
53
52
48
Solution
Let n, s, d and t be the number of students who likes none of the drinks, exactly one drink, exactly 2 drinks and all three drinks, respectively.
It is given,
n + s + d + t = 100 ...... (1)
s + 2d + 3t = 73 + 80 + 52
s + 2d + 3t = 205 ...... (2)
(2)-(1), we get
d + 2t - n = 105
Maximum value t can take is 52, i.e. t = 52, d = 1 and n = 0
Minimum value t can take is 5, i.e. t = 5, d = 95 and n = 0 (This also satisfies equation (1))
Difference = 52 - 5 = 47
The answer is option A.