Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 36 · 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 29 children, 18 like dance, 17 like music and 11 like both. How many like only dance? (a) 12 (b) 18 (c) 6 (d) 7
2. 2.In a class of 31 children, 15 like tea, 27 like coffee and 1 like neither. How many like both? (a) 11 (b) 30 (c) 1 (d) 12
3. 3.In a class of 43 children, 24 like mangoes, 21 like bananas and 5 like both. How many like only mangoes? (a) 22 (b) 16 (c) 19 (d) 24
4. 4.In a class of 35 children, 20 like cricket, 18 like football and 12 like both. How many like neither? (a) 21 (b) 12 (c) 9 (d) 10
5. 5.In a class of 19 children, 14 like cricket, 9 like football and 6 like both. How many like only cricket? (a) 10 (b) 14 (c) 8 (d) 3
6. 6.In a class of 32 children, 10 like dance, 21 like music and 4 like both. How many like at least one of the two? (a) 32 (b) 27 (c) 23 (d) 31
7. 7.In a class of 23 children, 9 like maths, 13 like science and 3 like neither. How many like both? (a) 20 (b) 1 (c) 2 (d) 3
8. 8.In a class of 37 children, 21 like dance, 27 like music and 12 like both. How many like only dance? (a) 10 (b) 9 (c) 21 (d) 15
9. 9.In a class of 37 children, 22 like dance, 18 like music and 6 like both. How many like only dance? (a) 19 (b) 16 (c) 22 (d) 12
10. 10.In a class of 38 children, 19 like cricket, 18 like football and 9 like neither. How many like both? (a) 9 (b) 29 (c) 8 (d) 7
11. 11.In a class of 13 children, 5 like tea, 6 like coffee and 2 like both. How many like neither? (a) 4 (b) 2 (c) 6 (d) 5
12. 12.In a class of 46 children, 22 like tea, 26 like coffee and 7 like both. How many like at least one of the two? (a) 48 (b) 34 (c) 41 (d) 46
13. 13.In a class of 28 children, 18 like mangoes, 19 like bananas and 12 like both. How many like neither? (a) 3 (b) 4 (c) 12 (d) 15
14. 14.In a class of 21 children, 7 like dance, 13 like music and 3 like both. How many like at least one of the two? (a) 17 (b) 20 (c) 21 (d) 14
15. 15.In a class of 28 children, 13 like maths, 10 like science and 2 like both. How many like neither? (a) 9 (b) 2 (c) 5 (d) 7
16. 16.In a class of 39 children, 18 like mangoes, 20 like bananas and 3 like both. How many like neither? (a) 1 (b) 3 (c) 7 (d) 4
17. 17.In a class of 46 children, 20 like dance, 21 like music and 5 like both. How many like only dance? (a) 16 (b) 20 (c) 15 (d) 25
18. 18.In a class of 40 children, 20 like cricket, 20 like football and 4 like neither. How many like both? (a) 3 (b) 5 (c) 36 (d) 4
19. 19.In a class of 48 children, 19 like tea, 31 like coffee and 11 like both. How many like neither? (a) 11 (b) 10 (c) 20 (d) 9
20. 20.In a class of 31 children, 7 like maths, 22 like science and 3 like both. How many like at least one of the two? (a) 26 (b) 31 (c) 29 (d) 23
21. 21.In a class of 44 children, 20 like dance, 18 like music and 3 like both. How many like at least one of the two? (a) 38 (b) 44 (c) 32 (d) 35
22. 22.In a class of 31 children, 17 like mangoes, 8 like bananas and 2 like both. How many like only mangoes? (a) 17 (b) 6 (c) 15 (d) 23
23. 23.In a class of 40 children, 25 like maths, 12 like science and 10 like neither. How many like both? (a) 10 (b) 8 (c) 7 (d) 30
24. 24.In a class of 40 children, 19 like mangoes, 20 like bananas and 5 like both. How many like at least one of the two? (a) 29 (b) 39 (c) 40 (d) 34
25. 25.In a class of 41 children, 19 like maths, 25 like science and 2 like neither. How many like both? (a) 39 (b) 2 (c) 3 (d) 5
26. 26.In a class of 48 children, 22 like cricket, 24 like football and 8 like both. How many like at least one of the two? (a) 46 (b) 38 (c) 30 (d) 48
27. 27.In a class of 27 children, 17 like tea, 15 like coffee and 7 like both. How many like neither? (a) 7 (b) 9 (c) 2 (d) 3
28. 28.In a class of 30 children, 24 like cricket, 13 like football and 8 like both. How many like only cricket? (a) 24 (b) 5 (c) 16 (d) 17
29. 29.In a class of 27 children, 8 like mangoes, 13 like bananas and 3 like both. How many like at least one of the two? (a) 18 (b) 15 (c) 27 (d) 21
30. 30.In a class of 35 children, 11 like dance, 25 like music and 7 like neither. How many like both? (a) 8 (b) 1 (c) 28 (d) 7
31. 31.In a class of 23 children, 9 like maths, 19 like science and 6 like both. How many like at least one of the two? (a) 16 (b) 28 (c) 23 (d) 22
32. 32.In a class of 35 children, 21 like cricket, 17 like football and 11 like both. How many like at least one of the two? (a) 27 (b) 38 (c) 35 (d) 16
33. 33.In a class of 37 children, 20 like cricket, 14 like football and 5 like both. How many like at least one of the two? (a) 34 (b) 29 (c) 24 (d) 37
34. 34.In a class of 36 children, 22 like cricket, 24 like football and 1 like neither. How many like both? (a) 1 (b) 10 (c) 11 (d) 35
35. 35.In a class of 14 children, 7 like mangoes, 7 like bananas and 2 like both. How many like only mangoes? (a) 5 (b) 2 (c) 6 (d) 7
36. 36.In a class of 42 children, 29 like dance, 22 like music and 11 like both. How many like neither? (a) 11 (b) 3 (c) 13 (d) 2
37. 37.In a class of 34 children, 18 like maths, 24 like science and 12 like both. How many like only maths? (a) 10 (b) 18 (c) 6 (d) 12
38. 38.In a class of 43 children, 14 like dance, 31 like music and 9 like neither. How many like both? (a) 34 (b) 2 (c) 9 (d) 11
39. 39.In a class of 41 children, 16 like cricket, 20 like football and 9 like neither. How many like both? (a) 4 (b) 32 (c) 5 (d) 9
40. 40.In a class of 34 children, 26 like cricket, 11 like football and 5 like neither. How many like both? (a) 8 (b) 3 (c) 5 (d) 29

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad