Misc. 2 || Quantitative Aptitude || CAT 2021 || 30 October

There are 100 students in a class. in an examination, 50 of them failed in Mathematics, 45 failed in Physics and 40 failed in Biology. 32 failed in exactly two of the three subjects. Only one student passed in all the subjects. The number of students failing in all the three subjects is

In a society, 90% of boys play at least one of the three games among Cricket, Football and Hockey. The number of boys who play Hockey and Football but not Cricket is the average of the number of boys who play Hockey and Cricket but not Football and Football and Cricket but not Hockey. The number of boys who play all the three games is one-third of the numbers of boys who play exactly two games. The number of boys who play only Cricket, only Hockey and only Football is 10 each. The number of boys who play Hockey but not Football is 6 more than the number of boys who play Football but not Hockey. If the number of boys who do not play any of the three games is 10, then how many boys play Football?

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 AΔB 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 (PΔQ)Δ(RΔS) is

In a survey of 200 students of a school, it was found that 120 study Mathematics, 90 study Physics and 70 study Chemistry, 40 study Mathematics and Physics, 30 study Physics and Chemistry, 50 study Mathematics and Chemistry and if students who study none of these subjects is a multiple of 11.Find the minimum number of students who study all the three subjects. (TITA)

For any two sets A and B, A # B is defined as the set of elements which belong to either of the sets A or B but not both. X, Y and Z are subsets of the set of natural numbers, containing all the multiples of 2, 3 and 5 respectively, that are not greater than 100 . Find the number of elements in (X # Y) # Z.

In a certain school, out of every seven students who like eating Apple, three like Cherry as well. For every student liking among these at least one of these two fruits, there are three students who like none of these. If 10% of the students eat only Apple, then what percentage of students eat only Cherry?

A club has 60 members and anyone who has chosen to play Cricket choose to play TT as well. But no one play Cricket and Soccer, 16 play TT and Soccer. All the members play at least one of the three sports and the number of people who play exactly one of the three is more than the number who play more than one of the three. What are the maximum and minimum number of people who could have played Soccer only?

In a survey among 120 people, 70 people like Potato Chips and 100 people like Pasta. What is the minimum and maximum number of people like both Potato Chips and Pasta
respectively?