Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 975 · 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 23 children, 16 like dance, 18 like music and 1 like neither. How many like both? (a) 1 (b) 11 (c) 22 (d) 12
2. 2.In a class of 28 children, 12 like maths, 20 like science and 9 like both. How many like neither? (a) 14 (b) 6 (c) 5 (d) 9
3. 3.In a class of 35 children, 15 like cricket, 21 like football and 9 like both. How many like at least one of the two? (a) 35 (b) 27 (c) 36 (d) 18
4. 4.In a class of 39 children, 15 like maths, 24 like science and 5 like both. How many like at least one of the two? (a) 34 (b) 39 (c) 29 (d) 35
5. 5.In a class of 16 children, 9 like cricket, 5 like football and 2 like both. How many like at least one of the two? (a) 16 (b) 12 (c) 14 (d) 10
6. 6.In a class of 32 children, 16 like tea, 15 like coffee and 4 like both. How many like at least one of the two? (a) 23 (b) 27 (c) 31 (d) 32
7. 7.In a class of 29 children, 11 like tea, 19 like coffee and 8 like both. How many like at least one of the two? (a) 30 (b) 29 (c) 22 (d) 14
8. 8.In a class of 13 children, 8 like dance, 8 like music and 5 like both. How many like at least one of the two? (a) 11 (b) 13 (c) 16 (d) 6
9. 9.In a class of 46 children, 27 like dance, 20 like music and 11 like both. How many like at least one of the two? (a) 47 (b) 25 (c) 36 (d) 46
10. 10.In a class of 45 children, 22 like tea, 21 like coffee and 3 like both. How many like only tea? (a) 22 (b) 19 (c) 18 (d) 24
11. 11.In a class of 30 children, 16 like mangoes, 15 like bananas and 2 like both. How many like at least one of the two? (a) 29 (b) 30 (c) 27 (d) 31
12. 12.In a class of 31 children, 21 like cricket, 11 like football and 3 like both. How many like at least one of the two? (a) 26 (b) 29 (c) 32 (d) 31
13. 13.In a class of 43 children, 29 like maths, 17 like science and 11 like both. How many like at least one of the two? (a) 35 (b) 24 (c) 46 (d) 43
14. 14.In a class of 38 children, 16 like maths, 27 like science and 7 like neither. How many like both? (a) 7 (b) 31 (c) 12 (d) 5
15. 15.In a class of 17 children, 13 like mangoes, 9 like bananas and 1 like neither. How many like both? (a) 5 (b) 16 (c) 6 (d) 1
16. 16.In a class of 30 children, 15 like dance, 24 like music and 11 like both. How many like at least one of the two? (a) 30 (b) 28 (c) 17 (d) 39
17. 17.In a class of 50 children, 28 like dance, 29 like music and 9 like both. How many like at least one of the two? (a) 50 (b) 57 (c) 48 (d) 39
18. 18.In a class of 40 children, 14 like maths, 31 like science and 11 like both. How many like only maths? (a) 20 (b) 3 (c) 9 (d) 14
19. 19.In a class of 23 children, 16 like mangoes, 10 like bananas and 6 like both. How many like neither? (a) 4 (b) 9 (c) 6 (d) 3
20. 20.In a class of 15 children, 7 like dance, 6 like music and 2 like both. How many like only dance? (a) 9 (b) 5 (c) 7 (d) 4
21. 21.In a class of 39 children, 30 like dance, 13 like music and 10 like both. How many like neither? (a) 7 (b) 6 (c) 16 (d) 10
22. 22.In a class of 47 children, 17 like tea, 24 like coffee and 4 like both. How many like at least one of the two? (a) 41 (b) 47 (c) 33 (d) 37
23. 23.In a class of 21 children, 11 like dance, 11 like music and 6 like both. How many like only dance? (a) 11 (b) 10 (c) 6 (d) 5
24. 24.In a class of 29 children, 18 like maths, 12 like science and 7 like both. How many like only maths? (a) 11 (b) 5 (c) 18 (d) 17
25. 25.In a class of 43 children, 26 like cricket, 24 like football and 3 like neither. How many like both? (a) 7 (b) 10 (c) 40 (d) 3
26. 26.In a class of 29 children, 19 like tea, 11 like coffee and 4 like both. How many like only tea? (a) 19 (b) 15 (c) 18 (d) 7
27. 27.In a class of 52 children, 28 like mangoes, 32 like bananas and 12 like both. How many like only mangoes? (a) 12 (b) 16 (c) 20 (d) 28
28. 28.In a class of 27 children, 13 like cricket, 8 like football and 10 like neither. How many like both? (a) 5 (b) 4 (c) 10 (d) 17
29. 29.In a class of 20 children, 10 like cricket, 10 like football and 5 like neither. How many like both? (a) 15 (b) 6 (c) 5 (d) 4
30. 30.In a class of 45 children, 22 like tea, 23 like coffee and 10 like both. How many like neither? (a) 20 (b) 10 (c) 0 (d) 11
31. 31.In a class of 30 children, 7 like dance, 21 like music and 6 like neither. How many like both? (a) 4 (b) 5 (c) 6 (d) 24
32. 32.In a class of 27 children, 16 like cricket, 11 like football and 6 like neither. How many like both? (a) 6 (b) 7 (c) 21 (d) 5
33. 33.In a class of 36 children, 13 like dance, 20 like music and 5 like both. How many like only dance? (a) 8 (b) 13 (c) 16 (d) 15
34. 34.In a class of 32 children, 13 like dance, 12 like music and 9 like neither. How many like both? (a) 9 (b) 3 (c) 23 (d) 2
35. 35.In a class of 25 children, 11 like mangoes, 12 like bananas and 4 like both. How many like only mangoes? (a) 8 (b) 7 (c) 11 (d) 13
36. 36.In a class of 21 children, 14 like maths, 11 like science and 8 like both. How many like only maths? (a) 3 (b) 14 (c) 6 (d) 10
37. 37.In a class of 25 children, 14 like tea, 15 like coffee and 6 like both. How many like at least one of the two? (a) 25 (b) 29 (c) 23 (d) 17
38. 38.In a class of 54 children, 28 like mangoes, 26 like bananas and 10 like both. How many like at least one of the two? (a) 34 (b) 54 (c) 44 (d) 45
39. 39.In a class of 17 children, 5 like tea, 9 like coffee and 2 like both. How many like only tea? (a) 8 (b) 5 (c) 3 (d) 7
40. 40.In a class of 36 children, 19 like tea, 22 like coffee and 1 like neither. How many like both? (a) 6 (b) 5 (c) 35 (d) 1

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