Venn diagrams and drawing inferences - Question Bank

1. In a group of 80 professionals, 50 are Engineers, 40 are Managers, and 20 are both. How many are only Engineers?
A) 80
B) 60
C) 50
D) 30
2. Consider the statement: 'All squares are quadrilaterals. All quadrilaterals have four sides.' What can be inferred?
A) All squares have four sides.
B) All things with four sides are squares.
C) Some squares do not have four sides.
D) No squares have four sides.
3. If 95% of students passed Physics and 85% passed Chemistry, and 80% passed both, what percentage passed only Physics?
A) 5%
B) 10%
C) 15%
D) 20%
4. Which Venn diagram represents 'Teachers', 'Male Teachers', and 'Female Teachers'?
A) Three separate circles.
B) Overlapping circles.
C) 'Male Teachers' and 'Female Teachers' are mutually exclusive categories within 'Teachers'.
D) 'Teachers' is a subset of 'Male Teachers' and 'Female Teachers'.
5. In a survey of 100 people, 70 own a Car, 60 own a Bike, and 40 own both. How many own only a Car?
A) 70
B) 60
C) 30
D) 20
6. Consider the statement: 'All dogs are mammals. Some mammals are black.' What can be inferred?
A) All dogs are black.
B) Some dogs are black.
C) Some dogs are not black.
D) No dogs are black.
7. If 60% of people like Tea and 40% like Coffee, and 20% like both, what percentage likes at least one?
A) 70%
B) 80%
C) 90%
D) 100%
8. Which Venn diagram represents 'Students', 'Boys', and 'Girls'?
A) Overlapping circles.
B) Three separate circles.
C) 'Boys' and 'Girls' are mutually exclusive categories within 'Students'.
D) 'Students' is a subset of 'Boys' and 'Girls'.
9. In a group of 50 singers, 30 sing classical music, 25 sing folk music, and 10 sing both. How many sing only folk music?
A) 50
B) 40
C) 25
D) 15
10. Consider the statement: 'Some animals are pets. All pets are domesticated.' What can be inferred?
A) All animals are domesticated.
B) Some animals are not domesticated.
C) Some animals are domesticated.
D) No animals are domesticated.
11. If 80% of students passed in English and 70% passed in Hindi, and 60% passed in both, what percentage passed only Hindi?
A) 10%
B) 20%
C) 30%
D) 40%
12. Which Venn diagram shows the relationship between 'Furniture', 'Chairs', and 'Tables'?
A) Three separate circles.
B) 'Chairs' and 'Tables' are distinct categories within 'Furniture'.
C) Overlapping circles for 'Chairs' and 'Tables' within 'Furniture'.
D) 'Furniture' circle inside 'Chairs' and 'Tables'.
13. In a group of 90 students, 50 play Chess, 40 play Ludo, and 20 play both. How many play only Chess?
A) 50
B) 40
C) 30
D) 20
14. Consider the statement: 'All cars have wheels. All things with wheels move.' What can be inferred?
A) All cars move.
B) All things that move are cars.
C) Some cars do not move.
D) No cars move.
15. If 70% of people like Apples and 50% like Bananas, and 30% like both, what percentage likes neither?
A) 10%
B) 20%
C) 30%
D) 40%
16. Which Venn diagram best represents 'Doctors', 'Gynaecologists', and 'Paediatricians'?
A) Three separate circles.
B) 'Gynaecologists' and 'Paediatricians' are distinct within 'Doctors'.
C) Overlapping circles for 'Gynaecologists' and 'Paediatricians' within 'Doctors'.
D) 'Doctors' circle inside 'Gynaecologists' and 'Paediatricians'.
17. In a survey of 200 athletes, 120 play Football, 100 play Basketball, and 60 play both. How many play only Basketball?
A) 120
B) 100
C) 60
D) 40
18. Consider the statement: 'Some leaders are honest. All honest people are respected.' What can be inferred?
A) All leaders are respected.
B) Some leaders are not respected.
C) Some leaders are respected.
D) No leaders are respected.
19. If Set P = {Prime Numbers} and Set Q = {Even Numbers}, what is P ∩ Q?
A) {2}
B) {}
C) {Prime numbers greater than 2}
D) {All even numbers}
20. Which Venn diagram represents 'Students', 'Passes', and 'Fails'?
A) Overlapping circles.
B) Two separate circles within 'Students'.
C) 'Passes' and 'Fails' are mutually exclusive categories within 'Students'.
D) 'Students' is a subset of 'Passes' and 'Fails'.
21. In a group of 60 people, 30 like Apples, 25 like Bananas, and 10 like both. How many like neither?
A) 10
B) 15
C) 20
D) 25
22. Consider the statement: 'All squares are rectangles. All rectangles have four sides.' What can be inferred?
A) All squares have four sides.
B) All things with four sides are squares.
C) Some squares do not have four sides.
D) No squares have four sides.
23. If 50% of candidates cleared Paper 1, 60% cleared Paper 2, and 30% cleared both, what percentage cleared at least one paper?
A) 70%
B) 80%
C) 90%
D) 100%
24. Which Venn diagram shows the relationship between 'Mammals', 'Whales', and 'Fish'?
A) Whales are mammals, and fish are separate.
B) All three are separate.
C) Mammals and Fish overlap, with Whales inside Mammals.
D) Whales and Fish overlap, both within Mammals.
25. In a group of 75 students, 40 play Hockey, 35 play Cricket, and 15 play both. How many play only Cricket?
A) 40
B) 35
C) 20
D) 15
26. Consider the statement: 'Some workers are efficient. All efficient people are disciplined.' What can be inferred?
A) All workers are disciplined.
B) Some workers are not disciplined.
C) Some workers are disciplined.
D) No workers are disciplined.
27. If 85% of students passed English and 75% passed Maths, and 70% passed both, what percentage passed only English?
A) 10%
B) 15%
C) 20%
D) 25%
28. Which Venn diagram represents 'Writers', 'Novelists', and 'Poets'?
A) Three separate circles.
B) 'Novelists' and 'Poets' are distinct categories within 'Writers'.
C) Overlapping circles for 'Novelists' and 'Poets' within 'Writers'.
D) 'Writers' circle inside 'Novelists' and 'Poets'.
29. In a survey of 150 students, 80 play Tennis, 70 play Badminton, and 40 play both. How many play at least one sport?
A) 110
B) 120
C) 130
D) 150
30. If Set A = {Even Numbers} and Set B = {Multiples of 4}, which statement is true?
A) A is a subset of B.
B) B is a subset of A.
C) A and B are disjoint.
D) A and B are identical.
31. Consider the statement: 'All poets are dreamers. All dreamers are imaginative.' What can be inferred?
A) Some poets are not imaginative.
B) All imaginative people are poets.
C) All poets are imaginative.
D) No poets are imaginative.
32. In a village, 60% of families have a TV, 40% have a radio, and 20% have both. What percentage have neither?
A) 10%
B) 20%
C) 30%
D) 40%
33. If 90% of students passed Physics and 80% passed Chemistry, and 75% passed both, what percentage failed both?
A) 5%
B) 10%
C) 15%
D) 25%
34. Which Venn diagram illustrates the relationship between 'Musicians', 'Pianists', and 'Guitarists'?
A) Three separate circles.
B) 'Pianists' and 'Guitarists' are distinct within 'Musicians'.
C) Overlapping circles for 'Pianists' and 'Guitarists' within 'Musicians'.
D) 'Musicians' circle inside 'Pianists' and 'Guitarists'.
35. In a group of 80 people, 50 like Tea, 40 like Coffee, and 20 like both. How many like only Tea?
A) 50
B) 30
C) 20
D) 10
36. Consider the statement: 'Some cats are black. All black things are not white.' What can be inferred?
A) All cats are white.
B) Some cats are not white.
C) No cats are black.
D) All white things are cats.
37. If the set of 'Professors' is a subset of 'Academicians', and 'Doctors' are also 'Academicians', what is the inference?
A) All Professors are Doctors.
B) Some Professors might be Doctors, and both are Academicians.
C) No Professor can be a Doctor.
D) All Doctors are Professors.
38. In a class of 60 students, 35 have a bicycle, 45 have a scooter, and 20 have both. How many students have neither a bicycle nor a scooter?
A) 5
B) 10
C) 15
D) 20
39. Which Venn diagram correctly depicts the relationship between 'Vegetables', 'Carrots', and 'Potatoes'?
A) Three separate circles.
B) 'Carrots' and 'Potatoes' are distinct categories within the 'Vegetables' circle.
C) A circle for 'Vegetables' inside 'Carrots' and 'Potatoes'.
D) Overlapping circles for 'Carrots' and 'Potatoes' within 'Vegetables'.
40. Consider the statement: 'All men are mortal. Socrates is a man.' What inference can be drawn?
A) Socrates is not mortal.
B) All mortals are men.
C) Socrates is mortal.
D) Some men are not mortal.
41. In a group of 50 people, 30 play Cricket, 25 play Football, and 10 play both. How many play only Football?
A) 15
B) 20
C) 25
D) 10
42. If 70% of students passed in Math and 60% passed in Science, and 40% passed in both, what percentage passed in at least one subject?
A) 100%
B) 90%
C) 80%
D) 70%
43. Which Venn diagram represents 'Animals', 'Mammals', and 'Dogs'?
A) Three overlapping circles.
B) 'Mammals' circle inside 'Animals', and 'Dogs' circle inside 'Mammals'.
C) 'Animals' circle inside 'Mammals', and 'Mammals' inside 'Dogs'.
D) Two separate circles for 'Animals' and 'Mammals', with 'Dogs' overlapping both.
44. In a survey of 200 people, 120 read Newspaper X, 90 read Newspaper Y, and 50 read both. How many read neither newspaper?
A) 20
B) 30
C) 40
D) 10
45. If a Venn diagram shows 'Birds', 'Sparrows', and 'Eagles', what is the typical representation?
A) Sparrows and Eagles are separate, both within the 'Birds' circle.
B) Birds are a subset of Sparrows and Eagles.
C) Three completely separate circles.
D) Sparrows and Eagles overlap, and both are within the 'Birds' circle.
46. Consider the sets: A = {1, 2, 3, 4}, B = {3, 4, 5, 6}. What does the intersection A ∩ B represent?
A) Elements common to both A and B
B) All elements in A or B or both
C) Elements in A but not in B
D) Elements in B but not in A
47. In a class, 50 students like Coffee, 60 like Tea, and 20 like both. How many students like only Coffee?
A) 50
B) 30
C) 20
D) 40
48. If 'Doctors', 'Surgeons', and 'Physicians' are represented in a Venn diagram, which relationship is most likely?
A) Surgeons and Physicians are separate categories, both falling under Doctors.
B) All Surgeons are Doctors, and all Physicians are Doctors, with some overlap between Surgeons and Physicians.
C) Doctors is a subset of Surgeons and Physicians.
D) Surgeons and Physicians are entirely distinct from Doctors.
49. Which of the following Venn diagrams best represents the relationship between 'Fruits', 'Apples', and 'Oranges'?
A) Three separate circles
B) One circle inside another, with a third separate circle
C) Three overlapping circles
D) Two overlapping circles, with a third separate circle
50. In a group of 100 students, 70 passed in English, 60 passed in Hindi, and 40 passed in both. How many students passed in at least one subject?
A) 130
B) 90
C) 110
D) 100
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