Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 809 · 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 24 children, 13 like dance, 6 like music and 8 like neither. How many like both? (a) 3 (b) 8 (c) 16 (d) 4
2. 2.In a class of 22 children, 14 like cricket, 10 like football and 4 like both. How many like at least one of the two? (a) 16 (b) 22 (c) 20 (d) 24
3. 3.In a class of 28 children, 17 like maths, 20 like science and 10 like both. How many like neither? (a) 2 (b) 1 (c) 10 (d) 11
4. 4.In a class of 30 children, 23 like tea, 7 like coffee and 3 like both. How many like neither? (a) 6 (b) 0 (c) 4 (d) 3
5. 5.In a class of 41 children, 14 like dance, 24 like music and 8 like neither. How many like both? (a) 5 (b) 33 (c) 8 (d) 6
6. 6.In a class of 39 children, 26 like mangoes, 11 like bananas and 8 like both. How many like neither? (a) 18 (b) 8 (c) 2 (d) 10
7. 7.In a class of 33 children, 21 like dance, 16 like music and 9 like both. How many like neither? (a) 14 (b) 9 (c) 6 (d) 5
8. 8.In a class of 34 children, 24 like tea, 16 like coffee and 4 like neither. How many like both? (a) 10 (b) 6 (c) 30 (d) 4
9. 9.In a class of 20 children, 8 like maths, 14 like science and 3 like both. How many like neither? (a) 3 (b) 2 (c) 1 (d) 4
10. 10.In a class of 41 children, 21 like cricket, 23 like football and 9 like both. How many like at least one of the two? (a) 44 (b) 35 (c) 26 (d) 41
11. 11.In a class of 36 children, 24 like maths, 11 like science and 6 like both. How many like only maths? (a) 25 (b) 18 (c) 24 (d) 5
12. 12.In a class of 39 children, 16 like maths, 23 like science and 6 like both. How many like neither? (a) 6 (b) 7 (c) 0 (d) 12
13. 13.In a class of 43 children, 23 like dance, 16 like music and 5 like both. How many like at least one of the two? (a) 29 (b) 43 (c) 39 (d) 34
14. 14.In a class of 30 children, 15 like dance, 15 like music and 9 like both. How many like at least one of the two? (a) 22 (b) 30 (c) 12 (d) 21
15. 15.In a class of 46 children, 26 like mangoes, 19 like bananas and 8 like both. How many like only mangoes? (a) 26 (b) 27 (c) 11 (d) 18
16. 16.In a class of 29 children, 15 like cricket, 15 like football and 4 like neither. How many like both? (a) 4 (b) 5 (c) 25 (d) 1
17. 17.In a class of 28 children, 16 like tea, 10 like coffee and 2 like both. How many like at least one of the two? (a) 28 (b) 26 (c) 22 (d) 24
18. 18.In a class of 29 children, 19 like maths, 19 like science and 11 like both. How many like only maths? (a) 11 (b) 19 (c) 8 (d) 10
19. 19.In a class of 35 children, 26 like dance, 11 like music and 7 like both. How many like only dance? (a) 24 (b) 4 (c) 19 (d) 26
20. 20.In a class of 20 children, 10 like maths, 9 like science and 4 like both. How many like at least one of the two? (a) 15 (b) 11 (c) 19 (d) 20
21. 21.In a class of 26 children, 16 like mangoes, 19 like bananas and 3 like neither. How many like both? (a) 9 (b) 3 (c) 12 (d) 23
22. 22.In a class of 34 children, 24 like maths, 13 like science and 3 like neither. How many like both? (a) 3 (b) 7 (c) 6 (d) 31
23. 23.In a class of 22 children, 14 like tea, 12 like coffee and 6 like both. How many like neither? (a) 3 (b) 2 (c) 6 (d) 8
24. 24.In a class of 27 children, 12 like cricket, 9 like football and 3 like both. How many like at least one of the two? (a) 18 (b) 27 (c) 21 (d) 15
25. 25.In a class of 39 children, 11 like tea, 28 like coffee and 8 like both. How many like at least one of the two? (a) 23 (b) 32 (c) 39 (d) 31
26. 26.In a class of 29 children, 15 like maths, 14 like science and 6 like both. How many like only maths? (a) 9 (b) 6 (c) 8 (d) 15
27. 27.In a class of 42 children, 22 like mangoes, 24 like bananas and 10 like both. How many like only mangoes? (a) 18 (b) 22 (c) 14 (d) 12
28. 28.In a class of 29 children, 21 like tea, 9 like coffee and 1 like neither. How many like both? (a) 28 (b) 3 (c) 2 (d) 1
29. 29.In a class of 47 children, 18 like dance, 25 like music and 6 like both. How many like at least one of the two? (a) 43 (b) 37 (c) 47 (d) 31
30. 30.In a class of 27 children, 15 like dance, 16 like music and 12 like both. How many like only dance? (a) 4 (b) 3 (c) 15 (d) 11
31. 31.In a class of 29 children, 25 like cricket, 14 like football and 11 like both. How many like only cricket? (a) 25 (b) 3 (c) 15 (d) 14
32. 32.In a class of 29 children, 17 like tea, 13 like coffee and 2 like both. How many like neither? (a) 3 (b) 0 (c) 1 (d) 2
33. 33.In a class of 25 children, 10 like tea, 13 like coffee and 8 like neither. How many like both? (a) 6 (b) 17 (c) 8 (d) 7
34. 34.In a class of 22 children, 12 like tea, 9 like coffee and 4 like both. How many like neither? (a) 1 (b) 5 (c) 4 (d) 9
35. 35.In a class of 30 children, 13 like dance, 21 like music and 7 like both. How many like only dance? (a) 14 (b) 9 (c) 6 (d) 13
36. 36.In a class of 27 children, 20 like cricket, 8 like football and 4 like neither. How many like both? (a) 4 (b) 23 (c) 5 (d) 1
37. 37.In a class of 28 children, 5 like dance, 22 like music and 2 like both. How many like only dance? (a) 6 (b) 3 (c) 5 (d) 20
38. 38.In a class of 19 children, 13 like maths, 14 like science and 9 like both. How many like only maths? (a) 13 (b) 5 (c) 4 (d) 9
39. 39.In a class of 25 children, 15 like tea, 16 like coffee and 7 like both. How many like only tea? (a) 15 (b) 7 (c) 9 (d) 8
40. 40.In a class of 39 children, 14 like dance, 25 like music and 7 like both. How many like at least one of the two? (a) 33 (b) 39 (c) 32 (d) 25

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