Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 92 · 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 33 children, 6 like cricket, 21 like football and 3 like both. How many like at least one of the two? (a) 33 (b) 24 (c) 27 (d) 21
2. 2.In a class of 36 children, 18 like cricket, 22 like football and 2 like neither. How many like both? (a) 2 (b) 6 (c) 34 (d) 4
3. 3.In a class of 48 children, 21 like tea, 19 like coffee and 2 like both. How many like neither? (a) 10 (b) 12 (c) 2 (d) 8
4. 4.In a class of 23 children, 19 like cricket, 6 like football and 1 like neither. How many like both? (a) 2 (b) 1 (c) 3 (d) 22
5. 5.In a class of 44 children, 22 like tea, 25 like coffee and 6 like both. How many like at least one of the two? (a) 41 (b) 44 (c) 35 (d) 47
6. 6.In a class of 43 children, 27 like maths, 21 like science and 3 like neither. How many like both? (a) 8 (b) 3 (c) 5 (d) 40
7. 7.In a class of 42 children, 23 like tea, 25 like coffee and 10 like both. How many like at least one of the two? (a) 42 (b) 28 (c) 38 (d) 48
8. 8.In a class of 33 children, 8 like dance, 22 like music and 5 like neither. How many like both? (a) 28 (b) 3 (c) 5 (d) 2
9. 9.In a class of 27 children, 15 like mangoes, 9 like bananas and 3 like both. How many like neither? (a) 6 (b) 7 (c) 3 (d) 9
10. 10.In a class of 32 children, 10 like mangoes, 25 like bananas and 5 like both. How many like at least one of the two? (a) 32 (b) 35 (c) 25 (d) 30
11. 11.In a class of 24 children, 6 like dance, 19 like music and 1 like neither. How many like both? (a) 1 (b) 2 (c) 23 (d) 3
12. 12.In a class of 41 children, 14 like cricket, 20 like football and 3 like both. How many like neither? (a) 3 (b) 10 (c) 7 (d) 13
13. 13.In a class of 29 children, 10 like maths, 13 like science and 3 like both. How many like at least one of the two? (a) 20 (b) 29 (c) 17 (d) 23
14. 14.In a class of 29 children, 23 like dance, 10 like music and 7 like both. How many like at least one of the two? (a) 26 (b) 19 (c) 33 (d) 29
15. 15.In a class of 32 children, 9 like maths, 24 like science and 4 like both. How many like at least one of the two? (a) 29 (b) 25 (c) 33 (d) 32
16. 16.In a class of 32 children, 20 like mangoes, 16 like bananas and 6 like neither. How many like both? (a) 26 (b) 4 (c) 10 (d) 6
17. 17.In a class of 18 children, 11 like maths, 13 like science and 8 like both. How many like at least one of the two? (a) 24 (b) 8 (c) 18 (d) 16
18. 18.In a class of 39 children, 16 like cricket, 23 like football and 7 like neither. How many like both? (a) 8 (b) 6 (c) 7 (d) 32
19. 19.In a class of 32 children, 12 like dance, 18 like music and 4 like both. How many like neither? (a) 6 (b) 2 (c) 4 (d) 10
20. 20.In a class of 31 children, 20 like mangoes, 8 like bananas and 3 like both. How many like neither? (a) 9 (b) 6 (c) 7 (d) 3
21. 21.In a class of 39 children, 16 like cricket, 27 like football and 7 like both. How many like at least one of the two? (a) 39 (b) 29 (c) 43 (d) 36
22. 22.In a class of 46 children, 24 like dance, 28 like music and 9 like both. How many like neither? (a) 3 (b) 12 (c) 4 (d) 9
23. 23.In a class of 18 children, 11 like tea, 13 like coffee and 7 like both. How many like only tea? (a) 5 (b) 4 (c) 11 (d) 6
24. 24.In a class of 31 children, 9 like dance, 15 like music and 3 like both. How many like only dance? (a) 16 (b) 12 (c) 9 (d) 6
25. 25.In a class of 40 children, 24 like tea, 26 like coffee and 12 like both. How many like only tea? (a) 13 (b) 24 (c) 12 (d) 14
26. 26.In a class of 24 children, 12 like cricket, 7 like football and 2 like both. How many like neither? (a) 5 (b) 9 (c) 2 (d) 7
27. 27.In a class of 49 children, 28 like cricket, 21 like football and 9 like both. How many like neither? (a) 10 (b) 0 (c) 9 (d) 18
28. 28.In a class of 21 children, 9 like cricket, 15 like football and 1 like neither. How many like both? (a) 20 (b) 4 (c) 1 (d) 3
29. 29.In a class of 31 children, 9 like mangoes, 20 like bananas and 4 like both. How many like at least one of the two? (a) 21 (b) 25 (c) 31 (d) 29
30. 30.In a class of 39 children, 31 like maths, 19 like science and 12 like both. How many like at least one of the two? (a) 50 (b) 39 (c) 26 (d) 38
31. 31.In a class of 34 children, 18 like mangoes, 25 like bananas and 10 like both. How many like only mangoes? (a) 18 (b) 15 (c) 9 (d) 8
32. 32.In a class of 35 children, 22 like mangoes, 21 like bananas and 9 like both. How many like at least one of the two? (a) 34 (b) 25 (c) 35 (d) 43
33. 33.In a class of 41 children, 24 like tea, 17 like coffee and 9 like both. How many like neither? (a) 18 (b) 0 (c) 9 (d) 10
34. 34.In a class of 36 children, 24 like mangoes, 13 like bananas and 4 like both. How many like at least one of the two? (a) 37 (b) 33 (c) 29 (d) 36
35. 35.In a class of 36 children, 10 like cricket, 22 like football and 6 like both. How many like at least one of the two? (a) 32 (b) 20 (c) 36 (d) 26
36. 36.In a class of 33 children, 13 like dance, 28 like music and 1 like neither. How many like both? (a) 9 (b) 1 (c) 8 (d) 32
37. 37.In a class of 38 children, 19 like tea, 17 like coffee and 3 like both. How many like neither? (a) 3 (b) 5 (c) 8 (d) 2
38. 38.In a class of 17 children, 8 like tea, 8 like coffee and 5 like both. How many like neither? (a) 1 (b) 11 (c) 6 (d) 5
39. 39.In a class of 43 children, 15 like maths, 23 like science and 3 like both. How many like neither? (a) 11 (b) 5 (c) 8 (d) 3
40. 40.In a class of 24 children, 6 like mangoes, 15 like bananas and 5 like neither. How many like both? (a) 5 (b) 19 (c) 2 (d) 3

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