Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 30 · 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 30 children, 13 like maths, 13 like science and 10 like neither. How many like both? (a) 20 (b) 7 (c) 10 (d) 6
2. 2.In a class of 46 children, 31 like cricket, 22 like football and 12 like both. How many like at least one of the two? (a) 29 (b) 53 (c) 46 (d) 41
3. 3.In a class of 36 children, 20 like mangoes, 10 like bananas and 3 like both. How many like neither? (a) 9 (b) 6 (c) 12 (d) 3
4. 4.In a class of 30 children, 16 like mangoes, 14 like bananas and 10 like both. How many like neither? (a) 11 (b) 20 (c) 0 (d) 10
5. 5.In a class of 23 children, 18 like cricket, 15 like football and 1 like neither. How many like both? (a) 1 (b) 10 (c) 22 (d) 11
6. 6.In a class of 42 children, 16 like cricket, 25 like football and 8 like both. How many like only cricket? (a) 9 (b) 17 (c) 8 (d) 16
7. 7.In a class of 41 children, 20 like maths, 28 like science and 11 like both. How many like neither? (a) 11 (b) 15 (c) 4 (d) 5
8. 8.In a class of 30 children, 17 like cricket, 19 like football and 6 like neither. How many like both? (a) 13 (b) 6 (c) 24 (d) 12
9. 9.In a class of 49 children, 24 like maths, 19 like science and 4 like both. How many like at least one of the two? (a) 49 (b) 35 (c) 43 (d) 39
10. 10.In a class of 46 children, 27 like maths, 26 like science and 8 like both. How many like neither? (a) 9 (b) 2 (c) 8 (d) 1
11. 11.In a class of 25 children, 13 like tea, 11 like coffee and 8 like neither. How many like both? (a) 17 (b) 6 (c) 7 (d) 8
12. 12.In a class of 29 children, 10 like maths, 20 like science and 5 like neither. How many like both? (a) 24 (b) 5 (c) 6 (d) 1
13. 13.In a class of 27 children, 22 like cricket, 12 like football and 8 like both. How many like at least one of the two? (a) 27 (b) 26 (c) 18 (d) 34
14. 14.In a class of 30 children, 20 like maths, 16 like science and 8 like both. How many like at least one of the two? (a) 36 (b) 28 (c) 20 (d) 30
15. 15.In a class of 21 children, 16 like maths, 9 like science and 5 like both. How many like only maths? (a) 16 (b) 11 (c) 4 (d) 12
16. 16.In a class of 33 children, 18 like cricket, 19 like football and 8 like neither. How many like both? (a) 25 (b) 12 (c) 4 (d) 8
17. 17.In a class of 43 children, 26 like mangoes, 18 like bananas and 8 like neither. How many like both? (a) 1 (b) 8 (c) 35 (d) 9
18. 18.In a class of 22 children, 8 like cricket, 18 like football and 5 like both. How many like neither? (a) 5 (b) 2 (c) 6 (d) 1
19. 19.In a class of 19 children, 14 like mangoes, 12 like bananas and 9 like both. How many like only mangoes? (a) 7 (b) 3 (c) 14 (d) 5
20. 20.In a class of 34 children, 23 like cricket, 13 like football and 7 like neither. How many like both? (a) 2 (b) 27 (c) 9 (d) 7
21. 21.In a class of 45 children, 29 like dance, 23 like music and 10 like both. How many like at least one of the two? (a) 42 (b) 32 (c) 45 (d) 52
22. 22.In a class of 25 children, 10 like maths, 16 like science and 4 like both. How many like only maths? (a) 6 (b) 12 (c) 10 (d) 9
23. 23.In a class of 37 children, 23 like mangoes, 13 like bananas and 9 like both. How many like at least one of the two? (a) 37 (b) 36 (c) 27 (d) 18
24. 24.In a class of 35 children, 17 like maths, 26 like science and 10 like both. How many like only maths? (a) 16 (b) 17 (c) 9 (d) 7
25. 25.In a class of 14 children, 10 like tea, 8 like coffee and 1 like neither. How many like both? (a) 5 (b) 1 (c) 4 (d) 13
26. 26.In a class of 32 children, 20 like cricket, 16 like football and 7 like both. How many like only cricket? (a) 13 (b) 16 (c) 20 (d) 9
27. 27.In a class of 28 children, 20 like cricket, 9 like football and 3 like both. How many like only cricket? (a) 17 (b) 19 (c) 20 (d) 6
28. 28.In a class of 38 children, 25 like tea, 14 like coffee and 11 like both. How many like only tea? (a) 25 (b) 14 (c) 3 (d) 24
29. 29.In a class of 25 children, 9 like tea, 18 like coffee and 5 like both. How many like only tea? (a) 4 (b) 9 (c) 13 (d) 7
30. 30.In a class of 26 children, 12 like dance, 12 like music and 7 like both. How many like only dance? (a) 5 (b) 14 (c) 7 (d) 12
31. 31.In a class of 26 children, 5 like maths, 17 like science and 2 like both. How many like at least one of the two? (a) 18 (b) 26 (c) 20 (d) 22
32. 32.In a class of 21 children, 12 like maths, 12 like science and 5 like neither. How many like both? (a) 5 (b) 3 (c) 16 (d) 8
33. 33.In a class of 22 children, 10 like cricket, 7 like football and 2 like both. How many like at least one of the two? (a) 17 (b) 22 (c) 15 (d) 13
34. 34.In a class of 27 children, 10 like tea, 17 like coffee and 2 like neither. How many like both? (a) 2 (b) 25 (c) 1 (d) 3
35. 35.In a class of 56 children, 27 like maths, 32 like science and 12 like both. How many like neither? (a) 9 (b) 10 (c) 21 (d) 12
36. 36.In a class of 22 children, 10 like maths, 8 like science and 4 like both. How many like at least one of the two? (a) 14 (b) 18 (c) 22 (d) 10
37. 37.In a class of 33 children, 18 like maths, 12 like science and 8 like neither. How many like both? (a) 25 (b) 6 (c) 8 (d) 5
38. 38.In a class of 46 children, 29 like mangoes, 22 like bananas and 11 like both. How many like at least one of the two? (a) 29 (b) 46 (c) 51 (d) 40
39. 39.In a class of 32 children, 18 like mangoes, 19 like bananas and 7 like neither. How many like both? (a) 7 (b) 12 (c) 5 (d) 25
40. 40.In a class of 14 children, 9 like dance, 7 like music and 1 like neither. How many like both? (a) 2 (b) 3 (c) 1 (d) 13

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