Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 984 · 40 questions

How to solve it (Do not count twice): n(A or B) = n(A) + n(B) − n(both) — otherwise the “both” group is counted twice. Only A = n(A) − n(both). Neither = total − n(A or B). Both = n(A) + n(B) − n(A or B).

1. 1.In a class of 42 children, 20 like mangoes, 16 like bananas and 4 like both. How many like neither? (a) 10 (b) 4 (c) 6 (d) 14
2. 2.In a class of 33 children, 21 like tea, 23 like coffee and 12 like both. How many like neither? (a) 12 (b) 1 (c) 2 (d) 13
3. 3.In a class of 40 children, 18 like cricket, 28 like football and 2 like neither. How many like both? (a) 38 (b) 2 (c) 8 (d) 6
4. 4.In a class of 37 children, 21 like dance, 9 like music and 3 like both. How many like only dance? (a) 6 (b) 21 (c) 28 (d) 18
5. 5.In a class of 39 children, 14 like cricket, 23 like football and 10 like neither. How many like both? (a) 10 (b) 29 (c) 8 (d) 9
6. 6.In a class of 50 children, 24 like maths, 27 like science and 11 like both. How many like neither? (a) 9 (b) 21 (c) 10 (d) 11
7. 7.In a class of 23 children, 6 like dance, 11 like music and 9 like neither. How many like both? (a) 14 (b) 3 (c) 9 (d) 4
8. 8.In a class of 35 children, 24 like dance, 13 like music and 9 like both. How many like neither? (a) 7 (b) 9 (c) 8 (d) 16
9. 9.In a class of 32 children, 21 like dance, 11 like music and 7 like both. How many like only dance? (a) 4 (b) 21 (c) 14 (d) 7
10. 10.In a class of 38 children, 15 like cricket, 23 like football and 9 like both. How many like neither? (a) 0 (b) 10 (c) 9 (d) 18
11. 11.In a class of 36 children, 28 like cricket, 15 like football and 4 like neither. How many like both? (a) 4 (b) 32 (c) 7 (d) 11
12. 12.In a class of 34 children, 20 like cricket, 13 like football and 3 like both. How many like at least one of the two? (a) 27 (b) 34 (c) 30 (d) 33
13. 13.In a class of 28 children, 24 like cricket, 15 like football and 12 like both. How many like only cricket? (a) 24 (b) 3 (c) 13 (d) 12
14. 14.In a class of 39 children, 19 like dance, 22 like music and 5 like both. How many like neither? (a) 4 (b) 3 (c) 5 (d) 8
15. 15.In a class of 23 children, 8 like dance, 11 like music and 3 like both. How many like neither? (a) 7 (b) 3 (c) 10 (d) 4
16. 16.In a class of 34 children, 21 like dance, 15 like music and 12 like both. How many like only dance? (a) 19 (b) 3 (c) 21 (d) 9
17. 17.In a class of 33 children, 15 like dance, 17 like music and 4 like both. How many like at least one of the two? (a) 28 (b) 24 (c) 32 (d) 33
18. 18.In a class of 38 children, 8 like tea, 24 like coffee and 10 like neither. How many like both? (a) 4 (b) 5 (c) 10 (d) 28
19. 19.In a class of 38 children, 22 like tea, 19 like coffee and 7 like neither. How many like both? (a) 3 (b) 7 (c) 10 (d) 31
20. 20.In a class of 24 children, 13 like mangoes, 14 like bananas and 6 like both. How many like neither? (a) 6 (b) 3 (c) 4 (d) 9
21. 21.In a class of 42 children, 16 like maths, 23 like science and 6 like both. How many like neither? (a) 6 (b) 3 (c) 9 (d) 15
22. 22.In a class of 30 children, 25 like tea, 9 like coffee and 6 like both. How many like neither? (a) 6 (b) 8 (c) 2 (d) 3
23. 23.In a class of 33 children, 20 like dance, 13 like music and 8 like neither. How many like both? (a) 9 (b) 7 (c) 25 (d) 8
24. 24.In a class of 25 children, 9 like mangoes, 13 like bananas and 6 like both. How many like neither? (a) 6 (b) 3 (c) 15 (d) 9
25. 25.In a class of 23 children, 15 like tea, 17 like coffee and 10 like both. How many like neither? (a) 2 (b) 11 (c) 10 (d) 1
26. 26.In a class of 30 children, 17 like dance, 8 like music and 2 like both. How many like only dance? (a) 6 (b) 15 (c) 22 (d) 17
27. 27.In a class of 34 children, 24 like mangoes, 14 like bananas and 6 like both. How many like only mangoes? (a) 24 (b) 18 (c) 8 (d) 20
28. 28.In a class of 19 children, 10 like maths, 9 like science and 4 like both. How many like neither? (a) 4 (b) 5 (c) 0 (d) 8
29. 29.In a class of 27 children, 12 like dance, 23 like music and 1 like neither. How many like both? (a) 8 (b) 26 (c) 9 (d) 1
30. 30.In a class of 23 children, 13 like mangoes, 14 like bananas and 9 like both. How many like at least one of the two? (a) 9 (b) 18 (c) 23 (d) 27
31. 31.In a class of 41 children, 26 like dance, 15 like music and 9 like both. How many like only dance? (a) 6 (b) 26 (c) 9 (d) 17
32. 32.In a class of 48 children, 21 like mangoes, 24 like bananas and 9 like neither. How many like both? (a) 39 (b) 9 (c) 6 (d) 7
33. 33.In a class of 42 children, 16 like cricket, 25 like football and 7 like both. How many like only cricket? (a) 9 (b) 18 (c) 17 (d) 16
34. 34.In a class of 44 children, 20 like dance, 28 like music and 9 like both. How many like neither? (a) 5 (b) 6 (c) 9 (d) 14
35. 35.In a class of 42 children, 21 like dance, 16 like music and 4 like both. How many like neither? (a) 4 (b) 13 (c) 5 (d) 9
36. 36.In a class of 24 children, 13 like cricket, 16 like football and 7 like both. How many like only cricket? (a) 9 (b) 6 (c) 8 (d) 13
37. 37.In a class of 29 children, 16 like cricket, 14 like football and 11 like both. How many like only cricket? (a) 3 (b) 5 (c) 15 (d) 16
38. 38.In a class of 46 children, 20 like mangoes, 22 like bananas and 6 like both. How many like neither? (a) 4 (b) 6 (c) 16 (d) 10
39. 39.In a class of 42 children, 20 like maths, 24 like science and 8 like both. How many like at least one of the two? (a) 28 (b) 36 (c) 42 (d) 44
40. 40.In a class of 36 children, 24 like dance, 11 like music and 9 like neither. How many like both? (a) 27 (b) 9 (c) 7 (d) 8

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