CAT 2022 Set Theory Question (Hard)

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

Accepted Answer

Step 1 Minimum number of students who like all three Maximum possible overlap minimum all-three Apply inclusion-exclusion Max total if all sets are disjoint 73 80 52 205 But only 100 students exist So minimum number of students who like all three excess Thus, minimum number liking all three at least

CAT 2022

Quantitative

Set Theory

Hard

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

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