Two Sets Venn Diagram

Q. What is the maximum number of customers who could like exactly two out of the three soaps?

1. 31
2. 33
3. 29
4. 23

Q. Out of 180 students in a class 7 students failed in all the three subjects viz, Physics, Chemistry, Maths. only 144 students pass in only one subject and 21 students pass in only two subjects.
(a) How many studens passed in all the three subjects?
(b) How many students passed in atleast two subjects?
(c) How many students passed in at most two subjects but atleast in one subject?

1. 8, 25, 150
2. 8, 29, 145
3. 8, 29, 165
4. 8, 25, 130

Q. A survey of 500 television watchers produced the following information; 285 watch badminton, 195 watch chess, 115 watch cricket, 45 watch badminton and cricket, 70 watch badminton and chess, 50 watch chess and cricket 50 do not watch any of the three games. How many watch all the three games? How many watch exactly one of the three games?

1. 10, 360
2. 24, 352
3. 20, 325
4. 40, 440

Q. In a pollution study of 1500 Indian canals the following data were reported. 520 were polluted by sulphur compounds, 335 polluted by phosphate 425 were polluted by crude oil, 100 were polluted by both crude oil and sulphur compounds, 180 were polluted by both sulphur compounds and phosphate, 150 were polluted by both phosphates and crude oil and 28 were polluted by sulphur compounds, phosphates and crude oil. How many of the canals were polluted by at least one of the three impurities? How many of the canals were polluted by exactly one of the three impurities?

1. 678, 512
2. 768, 504
3. 878, 504
4. 916, 496

Q. A group of people like - Khus, Mango or Orange. 60 like Khus, 50 like Orange, 48 like Mango. 12 like Khus and Mango, 15 like Mango and Orange and 20 like Orange and Khus. What is the minimum and maximum number of people in the group respectively?

1. 115, 119
2. 111, 123
3. 123, 135
4. 111, 121

Q. A survey was conducted at a coaching institution and it was found that there were 34 students who appeared in MAT. There were 37 students who appeared in CAT of which 17 students appeared in MAT. 30 students appeared in XAT of which 13 students appeared in MAT. of the XAT applications (i.e., appeared students) 14 appeared in CAT and these 6 appeared in MAT. How many students appeared in CAT but not in MAT or XAT?

1. 9
2. 10
3. 12
4. none of these

Q. In the year 222 B.C. 100 CAT aspirants appeared in CAT- (Common Admission Test for MBA in some prestigious institutions.) They had to show their competency in all the following four areas viz-Maths, Data Interpretation (DI), Logical Reasoning (LR) and English.
Number of aspirants who had qualified Maths is 55.
Number of aspirants who had qualified LR is 38
Number of aspirants who had qualified Maths and English is 30.
Number of aspirants who had qualified LR and English is 15.
Number of aspirants who had qualified Maths and LR is 20.
Number of aspiration who had qualified Maths, L.R and English is 5.
Number of aspirants who had qualified DI is 22.
Number of aspirants who had qualified DI and LR is 5.
Number of aspirants who had qualified DI and Maths is 5.
Number of aspirants who had qualified DI maths LR is 5.
Number of aspirants who had qualified English is 50.
Number of aspirants who had qualified English could not qualify DI section.

Find the number of aspirants who had qualified none of the sections

1. 12
2. 17
3. 18
4. 0

Q. In the year 222 B.C. 100 CAT aspirants appeared in CAT- (Common Admission Test for MBA in some prestigious institutions.) They had to show their competency in all the following four areas viz-Maths, Data Interpretation (DI), Logical Reasoning (LR) and English.
Number of aspirants who had qualified Maths is 55.
Number of aspirants who had qualified LR is 38
Number of aspirants who had qualified Maths and English is 30.
Number of aspirants who had qualified LR and English is 15.
Number of aspirants who had qualified Maths and LR is 20.
Number of aspiration who had qualified Maths, L.R and English is 5.
Number of aspirants who had qualified DI is 22.
Number of aspirants who had qualified DI and LR is 5.
Number of aspirants who had qualified DI and Maths is 5.
Number of aspirants who had qualified DI maths LR is 5.
Number of aspirants who had qualified English is 50.
Number of aspirants who had qualified English could not qualify DI section.

Find the number of aspirants who had qualified in at least two sections out of 4 sections.

1. 45
2. 35
3. 55
4. can't be determined

Q. What is the minimum number of customers who could like exactly two out of the three soaps?

1. 3
2. 7
3. 19
4. 23

Q. In a group of 132 people 50, 60, 70 people like three different sweets-Berfi, Jalebi, Rasgulla, respectively, The number of people who like all the three sweets is half the number of people who like exactly two sweets. The number of people who like exactly any two out of the three sweets is the same as those who like exactly any other two of the three sweets. The number of people who like the three sweets:

1. 12
2. 6
3. 8
4. none of these