CAT (QA) PYQs

Each of $74$ students in a class studies at least one of the three subjects $H, E$ and $P$. Ten students study all three subjects, while twenty study $H$ and $E$ , but not $P$ . Every student who studies $P$ also studies $H$ or $E$ or both. If the number of students studying $H$ equals that studying $E$, then the number of students studying $H$ 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

In a group of $250$ students, the percentage of girls was at least $44\%$ and at most $60\%$. The rest of the students were boys. Each student opted for either swimming or running or both. If $50\%$ of the boys and $80\%$ of the girls opted for swimming while $70\%$ of the boys and $60\%$ of the girls opted for running, then the minimum and maximum possible number of students who opted for both swimming and running, are