Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 628 · 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, 23 like cricket, 11 like football and 5 like both. How many like neither? (a) 15 (b) 10 (c) 5 (d) 11
2. 2.In a class of 38 children, 22 like cricket, 9 like football and 2 like both. How many like at least one of the two? (a) 31 (b) 27 (c) 38 (d) 29
3. 3.In a class of 23 children, 13 like dance, 10 like music and 4 like both. How many like neither? (a) 5 (b) 8 (c) 4 (d) 0
4. 4.In a class of 38 children, 19 like cricket, 19 like football and 8 like neither. How many like both? (a) 9 (b) 7 (c) 30 (d) 8
5. 5.In a class of 27 children, 17 like mangoes, 9 like bananas and 3 like both. How many like only mangoes? (a) 17 (b) 14 (c) 18 (d) 6
6. 6.In a class of 31 children, 16 like dance, 18 like music and 11 like both. How many like only dance? (a) 7 (b) 5 (c) 16 (d) 13
7. 7.In a class of 29 children, 9 like maths, 17 like science and 6 like both. How many like only maths? (a) 9 (b) 3 (c) 12 (d) 11
8. 8.In a class of 28 children, 16 like cricket, 6 like football and 2 like both. How many like neither? (a) 10 (b) 2 (c) 8 (d) 6
9. 9.In a class of 15 children, 7 like dance, 9 like music and 2 like neither. How many like both? (a) 1 (b) 2 (c) 3 (d) 13
10. 10.In a class of 34 children, 20 like cricket, 14 like football and 7 like both. How many like neither? (a) 7 (b) 0 (c) 14 (d) 8
11. 11.In a class of 39 children, 31 like mangoes, 14 like bananas and 11 like both. How many like neither? (a) 11 (b) 16 (c) 5 (d) 6
12. 12.In a class of 45 children, 26 like tea, 21 like coffee and 8 like both. How many like neither? (a) 14 (b) 7 (c) 8 (d) 6
13. 13.In a class of 39 children, 27 like maths, 12 like science and 7 like both. How many like at least one of the two? (a) 33 (b) 25 (c) 32 (d) 39
14. 14.In a class of 35 children, 27 like dance, 11 like music and 4 like neither. How many like both? (a) 3 (b) 7 (c) 31 (d) 4
15. 15.In a class of 24 children, 9 like cricket, 10 like football and 5 like both. How many like only cricket? (a) 5 (b) 14 (c) 9 (d) 4
16. 16.In a class of 29 children, 16 like maths, 14 like science and 6 like neither. How many like both? (a) 23 (b) 7 (c) 6 (d) 1
17. 17.In a class of 36 children, 22 like dance, 17 like music and 5 like neither. How many like both? (a) 5 (b) 3 (c) 31 (d) 8
18. 18.In a class of 27 children, 12 like maths, 16 like science and 5 like both. How many like at least one of the two? (a) 28 (b) 23 (c) 18 (d) 27
19. 19.In a class of 45 children, 16 like cricket, 29 like football and 10 like both. How many like only cricket? (a) 10 (b) 19 (c) 16 (d) 6
20. 20.In a class of 41 children, 27 like maths, 11 like science and 7 like both. How many like at least one of the two? (a) 38 (b) 41 (c) 24 (d) 31
21. 21.In a class of 37 children, 11 like mangoes, 22 like bananas and 4 like both. How many like neither? (a) 8 (b) 4 (c) 9 (d) 12
22. 22.In a class of 21 children, 14 like mangoes, 10 like bananas and 6 like both. How many like at least one of the two? (a) 24 (b) 21 (c) 18 (d) 12
23. 23.In a class of 41 children, 28 like dance, 20 like music and 5 like neither. How many like both? (a) 7 (b) 5 (c) 36 (d) 12
24. 24.In a class of 37 children, 26 like maths, 16 like science and 6 like both. How many like neither? (a) 6 (b) 7 (c) 2 (d) 1
25. 25.In a class of 45 children, 24 like maths, 24 like science and 1 like neither. How many like both? (a) 44 (b) 4 (c) 3 (d) 1
26. 26.In a class of 30 children, 11 like mangoes, 22 like bananas and 8 like both. How many like at least one of the two? (a) 17 (b) 33 (c) 25 (d) 30
27. 27.In a class of 26 children, 7 like tea, 22 like coffee and 4 like both. How many like neither? (a) 4 (b) 5 (c) 2 (d) 1
28. 28.In a class of 25 children, 10 like dance, 9 like music and 2 like both. How many like only dance? (a) 8 (b) 7 (c) 16 (d) 10
29. 29.In a class of 42 children, 19 like mangoes, 19 like bananas and 6 like both. How many like only mangoes? (a) 6 (b) 13 (c) 23 (d) 19
30. 30.In a class of 20 children, 11 like tea, 9 like coffee and 5 like both. How many like only tea? (a) 5 (b) 4 (c) 11 (d) 6
31. 31.In a class of 30 children, 14 like tea, 13 like coffee and 6 like neither. How many like both? (a) 24 (b) 4 (c) 6 (d) 3
32. 32.In a class of 41 children, 22 like tea, 22 like coffee and 4 like neither. How many like both? (a) 3 (b) 37 (c) 4 (d) 7
33. 33.In a class of 32 children, 8 like cricket, 17 like football and 2 like both. How many like neither? (a) 2 (b) 9 (c) 7 (d) 11
34. 34.In a class of 42 children, 19 like cricket, 23 like football and 8 like both. How many like neither? (a) 8 (b) 9 (c) 16 (d) 0
35. 35.In a class of 24 children, 7 like mangoes, 16 like bananas and 3 like both. How many like neither? (a) 1 (b) 7 (c) 4 (d) 3
36. 36.In a class of 15 children, 8 like maths, 7 like science and 3 like both. How many like neither? (a) 0 (b) 4 (c) 6 (d) 3
37. 37.In a class of 37 children, 29 like dance, 18 like music and 11 like both. How many like neither? (a) 2 (b) 12 (c) 1 (d) 11
38. 38.In a class of 29 children, 11 like mangoes, 23 like bananas and 6 like both. How many like neither? (a) 6 (b) 1 (c) 2 (d) 7
39. 39.In a class of 41 children, 21 like maths, 23 like science and 9 like both. How many like only maths? (a) 21 (b) 18 (c) 14 (d) 12
40. 40.In a class of 33 children, 15 like maths, 11 like science and 9 like neither. How many like both? (a) 3 (b) 24 (c) 2 (d) 9

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