Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 362 · 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 39 children, 15 like dance, 20 like music and 2 like both. How many like neither? (a) 2 (b) 4 (c) 6 (d) 8
2. 2.In a class of 40 children, 23 like maths, 18 like science and 6 like neither. How many like both? (a) 7 (b) 1 (c) 34 (d) 6
3. 3.In a class of 49 children, 30 like mangoes, 24 like bananas and 11 like both. How many like neither? (a) 7 (b) 11 (c) 17 (d) 6
4. 4.In a class of 34 children, 15 like maths, 24 like science and 11 like both. How many like neither? (a) 7 (b) 11 (c) 17 (d) 6
5. 5.In a class of 26 children, 18 like cricket, 8 like football and 3 like both. How many like at least one of the two? (a) 24 (b) 26 (c) 20 (d) 23
6. 6.In a class of 23 children, 9 like tea, 8 like coffee and 4 like both. How many like at least one of the two? (a) 13 (b) 23 (c) 17 (d) 9
7. 7.In a class of 34 children, 14 like dance, 22 like music and 8 like both. How many like only dance? (a) 14 (b) 12 (c) 6 (d) 8
8. 8.In a class of 20 children, 7 like dance, 8 like music and 4 like both. How many like at least one of the two? (a) 7 (b) 15 (c) 11 (d) 20
9. 9.In a class of 40 children, 23 like dance, 10 like music and 3 like both. How many like only dance? (a) 20 (b) 7 (c) 23 (d) 30
10. 10.In a class of 27 children, 8 like maths, 17 like science and 5 like both. How many like neither? (a) 7 (b) 2 (c) 12 (d) 5
11. 11.In a class of 29 children, 17 like maths, 16 like science and 5 like neither. How many like both? (a) 9 (b) 4 (c) 5 (d) 24
12. 12.In a class of 39 children, 22 like cricket, 22 like football and 12 like both. How many like neither? (a) 12 (b) 19 (c) 8 (d) 7
13. 13.In a class of 34 children, 17 like dance, 21 like music and 11 like both. How many like neither? (a) 18 (b) 8 (c) 7 (d) 11
14. 14.In a class of 36 children, 23 like cricket, 20 like football and 12 like both. How many like neither? (a) 5 (b) 6 (c) 12 (d) 17
15. 15.In a class of 38 children, 16 like cricket, 21 like football and 7 like both. How many like only cricket? (a) 9 (b) 14 (c) 17 (d) 16
16. 16.In a class of 32 children, 26 like cricket, 13 like football and 9 like both. How many like at least one of the two? (a) 21 (b) 39 (c) 32 (d) 30
17. 17.In a class of 33 children, 14 like tea, 18 like coffee and 2 like both. How many like at least one of the two? (a) 28 (b) 33 (c) 30 (d) 32
18. 18.In a class of 42 children, 19 like mangoes, 29 like bananas and 9 like both. How many like at least one of the two? (a) 39 (b) 30 (c) 48 (d) 42
19. 19.In a class of 30 children, 15 like mangoes, 20 like bananas and 10 like both. How many like only mangoes? (a) 6 (b) 15 (c) 10 (d) 5
20. 20.In a class of 39 children, 22 like maths, 22 like science and 8 like both. How many like neither? (a) 8 (b) 4 (c) 3 (d) 11
21. 21.In a class of 31 children, 15 like mangoes, 16 like bananas and 3 like both. How many like at least one of the two? (a) 28 (b) 29 (c) 25 (d) 31
22. 22.In a class of 33 children, 14 like mangoes, 18 like bananas and 5 like both. How many like neither? (a) 1 (b) 11 (c) 6 (d) 5
23. 23.In a class of 43 children, 14 like maths, 26 like science and 6 like both. How many like neither? (a) 3 (b) 9 (c) 15 (d) 6
24. 24.In a class of 39 children, 19 like cricket, 24 like football and 7 like neither. How many like both? (a) 7 (b) 11 (c) 4 (d) 32
25. 25.In a class of 42 children, 24 like cricket, 15 like football and 5 like both. How many like only cricket? (a) 27 (b) 24 (c) 10 (d) 19
26. 26.In a class of 42 children, 21 like tea, 17 like coffee and 7 like neither. How many like both? (a) 7 (b) 35 (c) 4 (d) 3
27. 27.In a class of 39 children, 14 like cricket, 20 like football and 9 like neither. How many like both? (a) 4 (b) 30 (c) 9 (d) 5
28. 28.In a class of 34 children, 11 like cricket, 23 like football and 6 like both. How many like neither? (a) 12 (b) 6 (c) 7 (d) 0
29. 29.In a class of 34 children, 16 like dance, 15 like music and 5 like neither. How many like both? (a) 2 (b) 29 (c) 3 (d) 5
30. 30.In a class of 34 children, 26 like maths, 16 like science and 10 like both. How many like only maths? (a) 18 (b) 26 (c) 6 (d) 16
31. 31.In a class of 28 children, 11 like mangoes, 14 like bananas and 4 like both. How many like only mangoes? (a) 14 (b) 7 (c) 11 (d) 10
32. 32.In a class of 40 children, 18 like dance, 15 like music and 3 like both. How many like only dance? (a) 25 (b) 15 (c) 12 (d) 18
33. 33.In a class of 41 children, 26 like tea, 13 like coffee and 8 like both. How many like at least one of the two? (a) 41 (b) 23 (c) 31 (d) 39
34. 34.In a class of 36 children, 11 like tea, 22 like coffee and 5 like both. How many like neither? (a) 3 (b) 13 (c) 5 (d) 8
35. 35.In a class of 38 children, 22 like cricket, 18 like football and 5 like both. How many like at least one of the two? (a) 30 (b) 40 (c) 38 (d) 35
36. 36.In a class of 17 children, 8 like maths, 7 like science and 6 like neither. How many like both? (a) 4 (b) 11 (c) 5 (d) 6
37. 37.In a class of 40 children, 21 like maths, 16 like science and 4 like both. How many like at least one of the two? (a) 37 (b) 29 (c) 33 (d) 40
38. 38.In a class of 42 children, 12 like tea, 23 like coffee and 3 like both. How many like at least one of the two? (a) 35 (b) 29 (c) 42 (d) 32
39. 39.In a class of 34 children, 12 like dance, 28 like music and 8 like both. How many like at least one of the two? (a) 40 (b) 24 (c) 32 (d) 34
40. 40.In a class of 27 children, 10 like mangoes, 16 like bananas and 6 like both. How many like neither? (a) 1 (b) 6 (c) 7 (d) 13

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