Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 479 · 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 27 children, 15 like maths, 11 like science and 8 like both. How many like neither? (a) 1 (b) 17 (c) 8 (d) 9
2. 2.In a class of 44 children, 26 like dance, 21 like music and 12 like both. How many like neither? (a) 12 (b) 9 (c) 10 (d) 21
3. 3.In a class of 36 children, 20 like cricket, 16 like football and 4 like both. How many like only cricket? (a) 4 (b) 20 (c) 16 (d) 12
4. 4.In a class of 43 children, 19 like tea, 24 like coffee and 5 like both. How many like neither? (a) 6 (b) 0 (c) 10 (d) 5
5. 5.In a class of 39 children, 17 like dance, 26 like music and 3 like neither. How many like both? (a) 4 (b) 7 (c) 3 (d) 36
6. 6.In a class of 36 children, 30 like dance, 14 like music and 2 like neither. How many like both? (a) 8 (b) 2 (c) 34 (d) 10
7. 7.In a class of 16 children, 12 like maths, 9 like science and 6 like both. How many like at least one of the two? (a) 16 (b) 15 (c) 21 (d) 9
8. 8.In a class of 32 children, 25 like maths, 12 like science and 7 like both. How many like at least one of the two? (a) 32 (b) 23 (c) 30 (d) 37
9. 9.In a class of 38 children, 16 like mangoes, 17 like bananas and 8 like neither. How many like both? (a) 4 (b) 8 (c) 3 (d) 30
10. 10.In a class of 55 children, 30 like dance, 30 like music and 12 like both. How many like only dance? (a) 12 (b) 25 (c) 18 (d) 30
11. 11.In a class of 44 children, 22 like maths, 20 like science and 6 like both. How many like only maths? (a) 14 (b) 24 (c) 22 (d) 16
12. 12.In a class of 27 children, 23 like maths, 11 like science and 8 like both. How many like neither? (a) 2 (b) 8 (c) 1 (d) 9
13. 13.In a class of 37 children, 22 like tea, 21 like coffee and 9 like both. How many like only tea? (a) 13 (b) 12 (c) 16 (d) 22
14. 14.In a class of 37 children, 18 like cricket, 14 like football and 5 like both. How many like at least one of the two? (a) 22 (b) 27 (c) 37 (d) 32
15. 15.In a class of 38 children, 16 like mangoes, 17 like bananas and 4 like both. How many like at least one of the two? (a) 33 (b) 38 (c) 29 (d) 25
16. 16.In a class of 25 children, 12 like cricket, 13 like football and 6 like both. How many like at least one of the two? (a) 20 (b) 13 (c) 19 (d) 25
17. 17.In a class of 23 children, 14 like cricket, 7 like football and 3 like both. How many like neither? (a) 3 (b) 8 (c) 2 (d) 5
18. 18.In a class of 21 children, 10 like dance, 11 like music and 2 like both. How many like at least one of the two? (a) 21 (b) 20 (c) 17 (d) 19
19. 19.In a class of 31 children, 20 like dance, 13 like music and 4 like both. How many like at least one of the two? (a) 25 (b) 29 (c) 31 (d) 33
20. 20.In a class of 30 children, 10 like dance, 19 like music and 5 like both. How many like neither? (a) 11 (b) 1 (c) 5 (d) 6
21. 21.In a class of 30 children, 21 like maths, 18 like science and 11 like both. How many like only maths? (a) 7 (b) 12 (c) 10 (d) 21
22. 22.In a class of 38 children, 26 like mangoes, 17 like bananas and 7 like both. How many like neither? (a) 9 (b) 7 (c) 2 (d) 3
23. 23.In a class of 48 children, 28 like dance, 27 like music and 5 like neither. How many like both? (a) 5 (b) 43 (c) 12 (d) 7
24. 24.In a class of 33 children, 19 like tea, 7 like coffee and 3 like both. How many like only tea? (a) 26 (b) 19 (c) 16 (d) 4
25. 25.In a class of 43 children, 24 like dance, 17 like music and 5 like both. How many like neither? (a) 2 (b) 7 (c) 5 (d) 12
26. 26.In a class of 31 children, 14 like cricket, 10 like football and 2 like both. How many like only cricket? (a) 8 (b) 21 (c) 14 (d) 12
27. 27.In a class of 37 children, 25 like tea, 10 like coffee and 7 like both. How many like neither? (a) 2 (b) 9 (c) 16 (d) 7
28. 28.In a class of 34 children, 20 like cricket, 16 like football and 3 like both. How many like neither? (a) 2 (b) 3 (c) 1 (d) 4
29. 29.In a class of 31 children, 21 like dance, 11 like music and 4 like both. How many like at least one of the two? (a) 32 (b) 28 (c) 31 (d) 24
30. 30.In a class of 37 children, 25 like maths, 12 like science and 6 like both. How many like at least one of the two? (a) 31 (b) 25 (c) 32 (d) 37
31. 31.In a class of 26 children, 20 like maths, 14 like science and 2 like neither. How many like both? (a) 24 (b) 2 (c) 8 (d) 10
32. 32.In a class of 46 children, 19 like maths, 26 like science and 7 like neither. How many like both? (a) 5 (b) 6 (c) 39 (d) 7
33. 33.In a class of 39 children, 13 like mangoes, 22 like bananas and 7 like neither. How many like both? (a) 7 (b) 32 (c) 3 (d) 4
34. 34.In a class of 38 children, 22 like dance, 24 like music and 1 like neither. How many like both? (a) 9 (b) 8 (c) 37 (d) 1
35. 35.In a class of 25 children, 8 like tea, 9 like coffee and 2 like both. How many like neither? (a) 10 (b) 8 (c) 12 (d) 2
36. 36.In a class of 32 children, 10 like cricket, 20 like football and 4 like both. How many like at least one of the two? (a) 26 (b) 22 (c) 32 (d) 30
37. 37.In a class of 37 children, 14 like cricket, 15 like football and 2 like both. How many like at least one of the two? (a) 37 (b) 25 (c) 29 (d) 27
38. 38.In a class of 20 children, 6 like tea, 14 like coffee and 3 like both. How many like neither? (a) 0 (b) 6 (c) 3 (d) 4
39. 39.In a class of 37 children, 25 like cricket, 14 like football and 9 like both. How many like at least one of the two? (a) 37 (b) 21 (c) 39 (d) 30
40. 40.In a class of 47 children, 29 like maths, 17 like science and 9 like both. How many like at least one of the two? (a) 47 (b) 46 (c) 28 (d) 37

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