Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 863 · 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 16 children, 8 like dance, 7 like music and 3 like both. How many like at least one of the two? (a) 12 (b) 15 (c) 16 (d) 9
2. 2.In a class of 48 children, 24 like maths, 28 like science and 8 like both. How many like at least one of the two? (a) 36 (b) 52 (c) 44 (d) 48
3. 3.In a class of 32 children, 19 like cricket, 10 like football and 4 like both. How many like only cricket? (a) 6 (b) 22 (c) 15 (d) 19
4. 4.In a class of 42 children, 17 like maths, 30 like science and 7 like neither. How many like both? (a) 7 (b) 12 (c) 35 (d) 5
5. 5.In a class of 37 children, 16 like cricket, 18 like football and 4 like both. How many like only cricket? (a) 12 (b) 16 (c) 19 (d) 14
6. 6.In a class of 29 children, 15 like maths, 15 like science and 7 like both. How many like at least one of the two? (a) 29 (b) 30 (c) 16 (d) 23
7. 7.In a class of 29 children, 18 like maths, 6 like science and 3 like both. How many like only maths? (a) 3 (b) 15 (c) 23 (d) 18
8. 8.In a class of 37 children, 20 like mangoes, 18 like bananas and 1 like neither. How many like both? (a) 2 (b) 36 (c) 3 (d) 1
9. 9.In a class of 45 children, 27 like tea, 25 like coffee and 8 like both. How many like at least one of the two? (a) 44 (b) 52 (c) 36 (d) 45
10. 10.In a class of 38 children, 19 like tea, 17 like coffee and 3 like both. How many like neither? (a) 2 (b) 5 (c) 3 (d) 8
11. 11.In a class of 50 children, 27 like maths, 28 like science and 10 like both. How many like neither? (a) 6 (b) 15 (c) 5 (d) 10
12. 12.In a class of 37 children, 19 like dance, 24 like music and 6 like neither. How many like both? (a) 12 (b) 13 (c) 31 (d) 6
13. 13.In a class of 39 children, 23 like mangoes, 14 like bananas and 6 like both. How many like at least one of the two? (a) 25 (b) 37 (c) 31 (d) 39
14. 14.In a class of 29 children, 16 like mangoes, 13 like bananas and 4 like both. How many like only mangoes? (a) 16 (b) 9 (c) 12 (d) 4
15. 15.In a class of 44 children, 25 like maths, 25 like science and 8 like both. How many like at least one of the two? (a) 34 (b) 42 (c) 50 (d) 44
16. 16.In a class of 25 children, 18 like cricket, 9 like football and 3 like both. How many like only cricket? (a) 18 (b) 15 (c) 6 (d) 16
17. 17.In a class of 38 children, 24 like tea, 16 like coffee and 2 like neither. How many like both? (a) 4 (b) 2 (c) 36 (d) 5
18. 18.In a class of 24 children, 8 like mangoes, 13 like bananas and 5 like neither. How many like both? (a) 19 (b) 5 (c) 3 (d) 2
19. 19.In a class of 38 children, 19 like tea, 24 like coffee and 8 like both. How many like only tea? (a) 19 (b) 16 (c) 14 (d) 11
20. 20.In a class of 45 children, 26 like tea, 17 like coffee and 7 like both. How many like neither? (a) 7 (b) 16 (c) 2 (d) 9
21. 21.In a class of 33 children, 12 like tea, 19 like coffee and 5 like both. How many like only tea? (a) 14 (b) 12 (c) 5 (d) 7
22. 22.In a class of 43 children, 16 like dance, 24 like music and 6 like both. How many like neither? (a) 6 (b) 9 (c) 15 (d) 3
23. 23.In a class of 54 children, 26 like maths, 25 like science and 6 like both. How many like neither? (a) 9 (b) 15 (c) 3 (d) 6
24. 24.In a class of 37 children, 15 like maths, 21 like science and 7 like both. How many like neither? (a) 7 (b) 15 (c) 8 (d) 1
25. 25.In a class of 49 children, 22 like cricket, 29 like football and 9 like both. How many like at least one of the two? (a) 51 (b) 33 (c) 42 (d) 49
26. 26.In a class of 37 children, 24 like cricket, 18 like football and 6 like both. How many like only cricket? (a) 18 (b) 19 (c) 24 (d) 12
27. 27.In a class of 43 children, 20 like cricket, 17 like football and 10 like neither. How many like both? (a) 5 (b) 10 (c) 4 (d) 33
28. 28.In a class of 45 children, 21 like tea, 26 like coffee and 7 like neither. How many like both? (a) 38 (b) 2 (c) 7 (d) 9
29. 29.In a class of 48 children, 31 like cricket, 26 like football and 11 like both. How many like neither? (a) 3 (b) 13 (c) 2 (d) 11
30. 30.In a class of 32 children, 11 like cricket, 18 like football and 3 like both. How many like neither? (a) 3 (b) 6 (c) 7 (d) 9
31. 31.In a class of 34 children, 19 like dance, 19 like music and 2 like neither. How many like both? (a) 4 (b) 32 (c) 2 (d) 6
32. 32.In a class of 26 children, 15 like cricket, 17 like football and 8 like both. How many like neither? (a) 10 (b) 8 (c) 2 (d) 3
33. 33.In a class of 56 children, 26 like maths, 26 like science and 6 like both. How many like neither? (a) 6 (b) 16 (c) 4 (d) 10
34. 34.In a class of 29 children, 18 like maths, 15 like science and 7 like both. How many like only maths? (a) 8 (b) 18 (c) 11 (d) 14
35. 35.In a class of 43 children, 21 like mangoes, 18 like bananas and 6 like neither. How many like both? (a) 37 (b) 6 (c) 2 (d) 3
36. 36.In a class of 45 children, 26 like mangoes, 23 like bananas and 4 like neither. How many like both? (a) 41 (b) 4 (c) 8 (d) 9
37. 37.In a class of 31 children, 22 like dance, 12 like music and 4 like both. How many like neither? (a) 2 (b) 1 (c) 5 (d) 4
38. 38.In a class of 47 children, 24 like dance, 22 like music and 9 like neither. How many like both? (a) 9 (b) 8 (c) 7 (d) 38
39. 39.In a class of 45 children, 21 like cricket, 21 like football and 10 like neither. How many like both? (a) 8 (b) 35 (c) 10 (d) 7
40. 40.In a class of 43 children, 24 like maths, 22 like science and 9 like both. How many like at least one of the two? (a) 46 (b) 43 (c) 28 (d) 37

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