# Set Theory, Clocks, Calendars and Binomial Theorem

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Set Theory (especially consructing venn diagrams) is a frequently tested topic. Make sure you know the basics from this chapter.
1. ### Set Theory - Number Theory

Set Fn gives all factors of n. Set Mn gives all multiples of n less than 1000. Which of the following statements is/are true?

i. ${F_{108} \cap F_{84}=F_{12}}$
ii. ${M_{12} \cup M_{18}=M_{36}}$
iii. ${M_{12} \cap M_{18}=M_{36}}$
iv. ${M_{12} \subset (M_{6}\cap M_{4})}$

1. i, ii and iii only
2. i, iii and iv only
3. i and iii only
4. All statements are true
• Set Theory and Number Theory
• Hard
2. ### Set Theory - De Morgan's Laws

A´ is defined as the complement of A, as in, set of all elements that are part of the universal set but not in A. How many of the following have to be true?

i. ${n(A \cup B)' =n(A' \cap B')}$
ii. If ${A \cap B=0}$, then ${A' \cup B'}$ is equal to the universal set
iii. If ${A \cup B}$ = universal set, then ${A' \cap B'}$ should be the null set.
iv. If ${A \subset B}$ then ${A' \cup B'=(A \cap B)'}$

1. 1
2. 2
3. 3
4. 4
All four statements are true
• De Morgan's Laws
• Hard
3. ### Set Theory: Venn Diagrams

Of 60 students in a class, anyone who has chosen to study maths elects to do physics as well. But no one does maths and chemistry, 16 do physics and chemistry. All the students do at least one of the three subjects and the number of people who do exactly one of the three is more than the number who do more than one of the three. What are the maximum and minimum number of people who could have done Chemistry only?

1. 40, 0
2. 28, 0
3. 38, 2
4. 44, 0
• Correct AnswerChoice (D), 44 is the Max, 0 is the min. Correct answer
• Venn Diagrams - Max, Min
• Hard
4. ### Calendars - Counting Birthdays

John was born on Feb 29th of 2012 which happened to be a Wednesday. If he lives to be 101 years old, how many birthdays would he celebrate on a Wednesday?

1. 3
2. 4
3. 5
4. 1
5. ### Calendars - Recurring Days

How many of the following statements have to be true?

i. No year can have 5 Sundays in the month of May and 5 Thursdays in the month of June.
ii. If Feb 14th of a certain year is a Friday, May 14th of the same year cannot be a Thursday
iii. If a year has 53 Sundays, it can have 5 Mondays in the month of May.

1. 0
2. 1
3. 2
4. 3
One statement only
• Recurring Days
• Hard
6. ### Set Theory: Number Of Elements

Set P comprises all multiples of 4 less than 500. Set Q comprises all odd multiples of 7 less than 500, Set R comprises all multiples of 6 less than 500. How many elements are present in ${P\cup Q\cup R}$ ?

1. 202
2. 243
3. 228
4. 186
7. ### Set Theory: Min and Max % of people

95% of the students in a class have taken Marketing, 80% have chosen Finance, 84% have chosen operations (ops), and 90% have chosen Human Resources (HR). What is the maximum and minimum percentage of people who have chosen all of the four?

1. 80% and 56%
2. 95% and 53%
3. 80% and 49%
4. 80% and 51%
• Min and Max % of people
• Medium
8. ### Set Theory: Number of Elements

Set A comprises all three digit numbers that are multiples of 5, Set B comprises all three–digit even numbers that are multiples of 3 and Set C comprises all three–digit numbers that are multiples of 4. How many elements are present in ${A\cup B\cup C}$?

1. 420
2. 405
3. 555
4. 480
9. ### Set Theory and Combinatorics

Set A = {2, 3, 5, 6, 7}, Set B = {a, b, c}. How many onto functions can be defined from Set B to Set A?

1. 2
2. 3
3. 4
4. None of the above
• Set Theory and Combinatorics
• Medium
10. ### Bijective Functions

If set A and set B are bijective and set C and set D are bijective too, State whether there exist a bijection between AC + BD or not

1. Yes
2. No
3. Data insufficient
4. Cannot be determined
11. ### Sets and Unions

Sonu started a new business with accounts in two different banks (i.e. Axis and SBI).He deposited the earnings of each day in either of the two banks. However he does not deposit his earnings in both the banks simultaneously on any given day. However somehow he could not carry the business for long and had to shut it down. Find the total no of days Sonu carried on the business if… 1) He did not deposited in axis bank on 20 days and in SBI on 24 days.
2) He deposited on either axis bank or SBI on 28 days.

1. 36
2. 18
3. 13
4. 24
12. ### Sets and Unions

A class in college has 150 students numbered from 1 to 150 , in which all the even numbered students are doing CA, whose number are divisible by 54 are doing Actuarial and those whose numbers are divisible by 7 are preparing for MBA. How many of the students are doing nothing?

1. 37
2. 45
3. 51
4. 62
13. ### Sets and Unions

In a class of 345 students, the students who took English, Math and Science are equal in number. There are 30 students who took both English and Math, 26 who took both Math and Science, 28 who took Science and English and 14 who took all the 3 subjects.There are 43 students who didn’t take any of the subjects. Answer the following question according to the data given above.
How many students have taken English as a subject ?

1. 286
2. 124
3. 246
4. 108
14. ### Sets and Unions

In a class of 345 students, the students who took English, Math and Science are equal in number. There are 30 students who took both English and math, 26 who took both math and science, 28 who took science and English and 14 who took all the 3 subjects. Answer the following question according to the data given above.
How many students have taken only one subject?

1. 286
2. 124
3. 246
4. 108
15. ### Sets and Unions

In a class of 345 students, the students who took English, Math and Science are equal in number. There are 30 students who took both English and math, 26 who took both math and science, 28 who took science and English and 14 who took all the 3 subjects. Answer the following question according to the data given above.
What percent of students took English and Math but not Science ?

1. Less than 55%
2. approx. 59%
3. 72%
4. 79%
16. ### Sets and Unions

In a survey conducted to know people’s preference for android phones and I phones, 80 person preferred android phones while 60 person preferred I phones. There were 20 who liked both and may prefer any. If there was no one who didn’t prefer at least one of the phones,then on how many people was the survey conducted?

1. 120
2. 40
3. 80
4. 60
17. ### Sets and Unions

In Grand Oberoi hotel, 1160 guests are present currently. The hotel provides the following extra facilities: Gym, Swimming, Fun park, Food. During a regular survey the management team of Oberoi noticed something quite extraordinary about the extra facilities provided by them. They noticed that for every person who uses ‘F’ no. of facilities, there are exactly 3 persons who uses at least (F-1) no. of facilities, F= 2,3,4. They also found that the no. of persons who used no extra facilities is twice the no of person that used all the 4 facilities. Help the management team to find out how many persons used exactly 3 facilities.

1. 40
2. 60
3. 80
4. 100
18. ### Sets and Unions

In its annual fest, a college is organizing three events: B-quiz, Finance & Marketing. The college has a strength of 510 students.The students were allowed to participate in any no. of events they liked. While viewing the statistics of the performance, the general secretary noticed:-
1. The number of students who participated in atleast two events were 52% more than those who participated in exactly one game.
2. The no. of students participating in 1,2 or 3 events respectively was atleast equal to 1.
3. The number of students who did not participate in any of the three events was the minimum possible integral value under these conditions.
What can be the maximum no. of students who participated in exactly 3 games?

1. 200
2. 300
3. 303
4. 304
19. ### Sets and Unions

A factory has 80 workers and 3 machines. Each worker knows to operate atleast 1 machine. If there are 65 persons who knows to operate machine 1, 60 who knows to operate machine 2 and 55 who knows to operate machine 3,what can be the minimum number of persons who knows to operate all the three machines?

1. 15
2. 20
3. 30
4. 40
20. ### Sets and Unions

In a survey it was found that 10% people don’t use Facebook, Twitter or Whatsapp.8% uses all the three. There are 15% who usesFacebook and Twitter, 20% who use Twitter and Whatsapp and 20% who useFacebook and Whatsapp. Number of people that use only Facebook, only Twitter and only Whatsapp are equal. If the survey was conducted on 1000 people, answer the following:
1.) How many people use Whatsapp only?
a)20 b)9 c)15 d)90
2.) What is the ratio of number of people that uses Whatsapp only to the people using either Whats app or Facebook or both?
a)1/6 b)25/75 c)1/3 d)1/9

21. ### Sets and Unions

In class of 260 students, each student needs to choose between the three extra subject (i.e IT, Hindi and Sanskrit) offered along with the course. The students that choose each of these subjects are 160, 130, 110. The number of students who choose more than one of the three is 40% more than the number of students who choose all the three subjects If there are no students who choose none of the 3 subjects, how many students study all the three subjects?

1. 40
2. 50
3. 80
4. 100
22. ### Sets and Unions

A shop sells three type of products i.e. Pen, Pencil & Notebook. On a survey for checking the sales of each product of the shop he found that the no. of people who bought only pen, only pencil, & only notebook are in A.P. in no particular order. Similarly, the number of people who bought exactly two of the three products are in A.P. too.
It was also found that the no. of people who bought all the products is 1/20th of the number of people who bought pencil only which in turn is equal to half of the number of people who bought notebook only. The number of people that bought both pen & pencil is 15, whereas that of those who bought pencil & notebook is 19. The number of people who bought notebook are 120, which is more than the no. of people who bought pen (which is a 2 digit no above 50).
1) What is the total no people that visits the shop?
a) 220 b) 231 c) 233 d) 240
2) How many people bought both pen and notebook?
a) 15 b) 17 c) 19 d) 21

23. ### Sets and Unions

In a survey it was found that, the number of people that like only Pepsi, only Coke, both Coke and Pepsi and neither of them are 2n, 3n, 69/n, 69/3n respectively.

1. 72
2. 49
3. Both a and b
4. cannot be determined

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