List of top Quantitative Aptitude Questions on Set Theory asked in CAT

Consider two sets A = {2, 3, 5, 7, 11, 13} and B = {1, 8, 27}. Let f be a function from A to B such that for every element b in B, there is at least one element a in A such that f(a) = b. Then, the total number of such functions f is

Let a,b,c be non-zero real numbers such that \(b^2<4ac\), and \(f(x)=ax^2+bx+c\). If the set S consists of all integers m such that \(f(m)<0\), then the set S must necessarily be

A club has 256 members of whom 144 can play football, 123 can play tennis, and 132 can play cricket. Moreover, 58 members can play both football and tennis, 25 can play both cricket and tennis, while 63 can play both football and cricket. If every member can play at least one game, then the number of members who can play only tennis is

In a class of 50 students, 23 speak English, 15 speak Hindi, and 18 speak Tamil. 8 speak both English and Hindi, 11 speak both Hindi and Tamil, 6 speak both English and Tamil, and 5 speak all three languages. How many students speak exactly two languages?

A set \( S = \{1, 2, 3, \ldots, n\} \) is partitioned into \( n \) disjoint subsets \( A_1, A_2, \ldots, A_n \), each containing four elements. It is given that in each subset, one element is the arithmetic mean of the other three. Which of the following statements is true?

In a certain zoo, there are 42 animals in one sector, 34 in the second sector and 20 in the third sector. Out of this, 24 graze in sector one and also in sector two. 10 graze in sector two and sector three, 12 graze in sector one and sector three. These figures also include four animals grazing in all the three sectors are now transported to another zoo. Find the total number of animals.

A survey of 100 people was conducted to find out whether they had read recent issues of Golmal magazine in July, August, and September. Data:

• Only September: 18
• September but not August: 23
• September and July: 8
• September: 28
• July: 48
• July and August: 10
• None: 24

Find the number who read exactly two consecutive issues out of the three months.

A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of the three popular options — air conditioning, radio and power windows were already installed. Following were the observation of the survey:
I. 15 had air conditioning
II. 2 had air conditioning and power windows but no radios
III. 12 had radio
IV. 6 had air conditioning and radio but no power windows
V. 11 had power windows
VI. 4 had radio and power windows
VII. 3 had all three options
What is the number of cars that had none of the options?

In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals I, II and III. If 50% favoured the first proposal, 30% the second and 20% the third, 5% favoured all the three, what is the percentage of those asked favoured more than one of the three proposals?

Which of the following is true?

A survey of 200 people in a community who watched at least one of the three channels — BBC, CNN and DD —showedthat 80% of the people watched DD, 22% watched BBC and 15% watched CNN

In a locality of 100 families: 45 have radios, 75 have TVs, 25 have VCRs. 10 have all three. Every VCR owner has TV. 25 have radio only. How many families have only TV?

Fifty college teachers are surveyed as to their possession of colour TV, VCR and tape recorder. Of them, 22 own colour TV, 15 own VCR and 14 own tape recorders. Nine of these college teachers own exactly two items out of colour TV, VCR and tape recorder; and, one college teacher owns all three. How many of the 50 teachers own none of the three, colour TV, VCR or tape recorder?

There are 3 clubs A, B \& C in a town with 40, 50 \& 60 members respectively. While 10 people are members of all 3 clubs, 70 are members in only one club. How many belong to exactly two clubs?

Let a,b,c be non-zero real numbers such that b2<4ac, and f(x)=ax2+bx+c. If the set S consists of all integers m such that f(m)<0, then the set S must necessarily be