IPMAT Indore (MCQ) PYQs

Out of 80 students who appeared for the school exams in Mathematics (M), Physics (P) and Chemistry (C), 50 passed M, 30 passed P and 40 passed C. At most 20 students passed M and P, at most 20 students passed P and C, and at most 20 students passed C and M. The maximum number of students who could have passed all three exams is __________.

Let A and B be two finite sets such that $n(A - B)$, $n(A\cap B)$, $n(B - A)$ are in an arithmetic progression. Here $n(X)$ denotes the number of elements in a finite set $X$. If $n(A\cup B) = 18$, then $n(A) + n(B)$ is ____

In a group of 150 students, 52 like tea, 48 like juice and 62 like coffee. If each student in the group likes at least one among tea, juice and coffee, then the maximum number of students that like more than one drink is: