CAT (QA) PYQs

Students in a college have to choose at least two subjects from Chemistry, Mathematics and Physics. The number of students choosing all three subjects is $18$, choosing Mathematics as one of their subjects is $23$ and choosing Physics as one of their subjects is $25$. The smallest possible number of students who could choose Chemistry as one of their subjects is

For two sets $A$ and $B$, let $A \Delta B$ denote the set of elements which belong to $A$ or $B$ but not both. If $P=\{1,2,3,4\}, Q=\{2,3,5,6\},, R=\{1,3,7,8,9\}, S=$ $\{2,4,9,10\}$, then the number of elements in $(P \Delta Q) \Delta(R \Delta S)$ 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