CAT 2022 Slot 1 QA Question 15: 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 maxim

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 maxim

Accepted Answer

The maximum number who can like all three is limited by the smallest group, lemonade.
Maximum = $52$
For the minimum, use the standard lower bound for three-set intersection.
Minimum = $73 + 80 + 52 - 2(100)$
$= 205 - 200 = 5$
Required difference = $52 - 5 = 47$
Answer: (4) 47

In a class of 100100100 students, 737373 like coffee, 808080 like tea and 525252 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

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