IPMAT Indore (MCQ) PYQs

Let $S = \{1, 2, \ldots, 180\}$. Define $A$ as the set of all multiples of 4 in $S$, $B$ as the set of all multiples of 6 in $S$, and $C$ as the set of all multiples of 9 in $S$. The number of elements in $S$ that belong to exactly one of $A, B, C$ is

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 __________.

In a survey of 500 people, it was found that 250 owned a 4-wheeler but not a 2-wheeler, 100 owned a 2-wheeler but not a 4-wheeler, and 100 owned neither a 4-wheeler nor a 2-wheeler. Then the number of people who owned both is