Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 139 · 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 35 children, 28 like cricket, 16 like football and 10 like both. How many like only cricket? (a) 28 (b) 19 (c) 6 (d) 18
2. 2.In a class of 41 children, 28 like cricket, 19 like football and 11 like both. How many like neither? (a) 11 (b) 5 (c) 16 (d) 6
3. 3.In a class of 40 children, 31 like dance, 19 like music and 2 like neither. How many like both? (a) 2 (b) 10 (c) 12 (d) 38
4. 4.In a class of 49 children, 23 like mangoes, 21 like bananas and 5 like both. How many like at least one of the two? (a) 49 (b) 39 (c) 44 (d) 34
5. 5.In a class of 46 children, 22 like dance, 25 like music and 10 like both. How many like neither? (a) 8 (b) 19 (c) 10 (d) 9
6. 6.In a class of 29 children, 20 like mangoes, 6 like bananas and 3 like both. How many like only mangoes? (a) 23 (b) 17 (c) 20 (d) 3
7. 7.In a class of 28 children, 17 like tea, 8 like coffee and 2 like both. How many like neither? (a) 3 (b) 2 (c) 7 (d) 5
8. 8.In a class of 38 children, 11 like cricket, 20 like football and 9 like neither. How many like both? (a) 2 (b) 3 (c) 29 (d) 9
9. 9.In a class of 23 children, 6 like maths, 11 like science and 8 like neither. How many like both? (a) 15 (b) 2 (c) 3 (d) 8
10. 10.In a class of 34 children, 12 like mangoes, 14 like bananas and 2 like both. How many like at least one of the two? (a) 22 (b) 26 (c) 34 (d) 24
11. 11.In a class of 32 children, 20 like cricket, 14 like football and 7 like both. How many like only cricket? (a) 18 (b) 20 (c) 13 (d) 7
12. 12.In a class of 27 children, 18 like tea, 18 like coffee and 11 like both. How many like only tea? (a) 9 (b) 11 (c) 18 (d) 7
13. 13.In a class of 58 children, 30 like mangoes, 29 like bananas and 9 like neither. How many like both? (a) 10 (b) 1 (c) 9 (d) 49
14. 14.In a class of 23 children, 6 like tea, 18 like coffee and 2 like both. How many like neither? (a) 3 (b) 0 (c) 2 (d) 1
15. 15.In a class of 30 children, 7 like cricket, 15 like football and 2 like both. How many like at least one of the two? (a) 22 (b) 20 (c) 18 (d) 30
16. 16.In a class of 32 children, 16 like tea, 14 like coffee and 7 like neither. How many like both? (a) 7 (b) 5 (c) 25 (d) 6
17. 17.In a class of 37 children, 8 like maths, 24 like science and 4 like both. How many like at least one of the two? (a) 37 (b) 32 (c) 24 (d) 28
18. 18.In a class of 32 children, 17 like mangoes, 25 like bananas and 1 like neither. How many like both? (a) 11 (b) 31 (c) 1 (d) 10
19. 19.In a class of 29 children, 18 like tea, 21 like coffee and 11 like both. How many like only tea? (a) 8 (b) 18 (c) 7 (d) 10
20. 20.In a class of 46 children, 18 like dance, 21 like music and 3 like both. How many like at least one of the two? (a) 33 (b) 36 (c) 46 (d) 39
21. 21.In a class of 42 children, 20 like dance, 22 like music and 2 like both. How many like neither? (a) 3 (b) 2 (c) 4 (d) 0
22. 22.In a class of 48 children, 26 like maths, 19 like science and 7 like both. How many like at least one of the two? (a) 48 (b) 38 (c) 45 (d) 31
23. 23.In a class of 31 children, 9 like mangoes, 19 like bananas and 6 like both. How many like at least one of the two? (a) 28 (b) 16 (c) 31 (d) 22
24. 24.In a class of 41 children, 19 like mangoes, 18 like bananas and 3 like both. How many like neither? (a) 10 (b) 7 (c) 3 (d) 4
25. 25.In a class of 50 children, 23 like cricket, 21 like football and 9 like neither. How many like both? (a) 3 (b) 4 (c) 9 (d) 41
26. 26.In a class of 36 children, 23 like cricket, 20 like football and 8 like both. How many like only cricket? (a) 16 (b) 23 (c) 12 (d) 15
27. 27.In a class of 36 children, 19 like tea, 14 like coffee and 4 like both. How many like neither? (a) 11 (b) 7 (c) 4 (d) 3
28. 28.In a class of 30 children, 22 like cricket, 18 like football and 12 like both. How many like neither? (a) 2 (b) 3 (c) 14 (d) 12
29. 29.In a class of 27 children, 8 like maths, 19 like science and 2 like neither. How many like both? (a) 1 (b) 3 (c) 25 (d) 2
30. 30.In a class of 40 children, 15 like tea, 23 like coffee and 5 like neither. How many like both? (a) 35 (b) 5 (c) 4 (d) 3
31. 31.In a class of 17 children, 7 like maths, 7 like science and 4 like both. How many like only maths? (a) 4 (b) 3 (c) 10 (d) 7
32. 32.In a class of 29 children, 20 like tea, 10 like coffee and 4 like both. How many like neither? (a) 3 (b) 7 (c) 2 (d) 4
33. 33.In a class of 33 children, 20 like cricket, 20 like football and 10 like both. How many like only cricket? (a) 20 (b) 11 (c) 10 (d) 13
34. 34.In a class of 29 children, 14 like cricket, 18 like football and 6 like both. How many like only cricket? (a) 14 (b) 11 (c) 12 (d) 8
35. 35.In a class of 33 children, 26 like tea, 18 like coffee and 12 like both. How many like neither? (a) 1 (b) 2 (c) 12 (d) 13
36. 36.In a class of 29 children, 18 like dance, 13 like music and 2 like neither. How many like both? (a) 2 (b) 4 (c) 27 (d) 5
37. 37.In a class of 40 children, 20 like mangoes, 23 like bananas and 6 like both. How many like at least one of the two? (a) 43 (b) 40 (c) 37 (d) 31
38. 38.In a class of 39 children, 16 like cricket, 22 like football and 3 like both. How many like only cricket? (a) 16 (b) 17 (c) 13 (d) 19
39. 39.In a class of 22 children, 10 like tea, 9 like coffee and 4 like both. How many like only tea? (a) 6 (b) 10 (c) 13 (d) 5
40. 40.In a class of 24 children, 6 like mangoes, 11 like bananas and 3 like both. How many like neither? (a) 3 (b) 7 (c) 13 (d) 10

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