Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 156 · 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 31 children, 15 like cricket, 12 like football and 2 like both. How many like neither? (a) 4 (b) 6 (c) 8 (d) 2
2. 2.In a class of 20 children, 9 like mangoes, 6 like bananas and 2 like both. How many like only mangoes? (a) 7 (b) 9 (c) 14 (d) 4
3. 3.In a class of 22 children, 14 like maths, 13 like science and 8 like both. How many like at least one of the two? (a) 27 (b) 22 (c) 19 (d) 11
4. 4.In a class of 44 children, 18 like tea, 27 like coffee and 6 like neither. How many like both? (a) 7 (b) 1 (c) 6 (d) 38
5. 5.In a class of 40 children, 24 like maths, 14 like science and 10 like neither. How many like both? (a) 30 (b) 8 (c) 10 (d) 9
6. 6.In a class of 42 children, 23 like mangoes, 27 like bananas and 10 like both. How many like at least one of the two? (a) 50 (b) 30 (c) 42 (d) 40
7. 7.In a class of 34 children, 11 like tea, 21 like coffee and 3 like both. How many like at least one of the two? (a) 34 (b) 32 (c) 29 (d) 26
8. 8.In a class of 38 children, 17 like dance, 23 like music and 3 like both. How many like neither? (a) 1 (b) 3 (c) 4 (d) 2
9. 9.In a class of 37 children, 27 like dance, 17 like music and 11 like both. How many like only dance? (a) 16 (b) 6 (c) 20 (d) 27
10. 10.In a class of 21 children, 7 like tea, 10 like coffee and 2 like both. How many like neither? (a) 4 (b) 8 (c) 2 (d) 6
11. 11.In a class of 27 children, 16 like mangoes, 15 like bananas and 12 like both. How many like only mangoes? (a) 12 (b) 16 (c) 3 (d) 4
12. 12.In a class of 18 children, 12 like cricket, 14 like football and 9 like both. How many like only cricket? (a) 5 (b) 3 (c) 12 (d) 4
13. 13.In a class of 22 children, 5 like dance, 17 like music and 2 like both. How many like neither? (a) 3 (b) 0 (c) 4 (d) 2
14. 14.In a class of 35 children, 18 like tea, 14 like coffee and 5 like neither. How many like both? (a) 5 (b) 30 (c) 2 (d) 3
15. 15.In a class of 52 children, 24 like maths, 24 like science and 4 like both. How many like neither? (a) 9 (b) 8 (c) 4 (d) 12
16. 16.In a class of 33 children, 23 like maths, 15 like science and 10 like both. How many like at least one of the two? (a) 38 (b) 18 (c) 28 (d) 33
17. 17.In a class of 23 children, 12 like dance, 14 like music and 5 like neither. How many like both? (a) 5 (b) 18 (c) 3 (d) 8
18. 18.In a class of 25 children, 19 like cricket, 8 like football and 3 like both. How many like neither? (a) 4 (b) 1 (c) 3 (d) 2
19. 19.In a class of 44 children, 18 like cricket, 24 like football and 4 like both. How many like neither? (a) 2 (b) 10 (c) 6 (d) 4
20. 20.In a class of 29 children, 16 like mangoes, 11 like bananas and 7 like both. How many like neither? (a) 2 (b) 9 (c) 16 (d) 7
21. 21.In a class of 33 children, 9 like tea, 23 like coffee and 4 like neither. How many like both? (a) 2 (b) 4 (c) 29 (d) 3
22. 22.In a class of 21 children, 12 like cricket, 13 like football and 2 like neither. How many like both? (a) 19 (b) 2 (c) 4 (d) 6
23. 23.In a class of 33 children, 21 like cricket, 17 like football and 3 like neither. How many like both? (a) 3 (b) 30 (c) 5 (d) 8
24. 24.In a class of 44 children, 29 like cricket, 19 like football and 11 like both. How many like neither? (a) 18 (b) 11 (c) 8 (d) 7
25. 25.In a class of 37 children, 16 like cricket, 19 like football and 4 like neither. How many like both? (a) 2 (b) 4 (c) 3 (d) 33
26. 26.In a class of 34 children, 14 like tea, 22 like coffee and 6 like both. How many like at least one of the two? (a) 34 (b) 30 (c) 24 (d) 36
27. 27.In a class of 13 children, 7 like tea, 5 like coffee and 2 like both. How many like at least one of the two? (a) 12 (b) 8 (c) 10 (d) 13
28. 28.In a class of 38 children, 8 like cricket, 22 like football and 2 like both. How many like neither? (a) 12 (b) 8 (c) 2 (d) 10
29. 29.In a class of 45 children, 22 like mangoes, 24 like bananas and 5 like neither. How many like both? (a) 6 (b) 5 (c) 1 (d) 40
30. 30.In a class of 27 children, 22 like tea, 13 like coffee and 1 like neither. How many like both? (a) 8 (b) 26 (c) 1 (d) 9
31. 31.In a class of 47 children, 26 like cricket, 25 like football and 8 like both. How many like only cricket? (a) 26 (b) 18 (c) 22 (d) 17
32. 32.In a class of 28 children, 19 like cricket, 13 like football and 10 like both. How many like neither? (a) 10 (b) 7 (c) 16 (d) 6
33. 33.In a class of 44 children, 19 like maths, 18 like science and 10 like neither. How many like both? (a) 4 (b) 3 (c) 34 (d) 10
34. 34.In a class of 39 children, 15 like dance, 24 like music and 7 like both. How many like only dance? (a) 7 (b) 15 (c) 8 (d) 17
35. 35.In a class of 40 children, 25 like tea, 18 like coffee and 10 like both. How many like neither? (a) 8 (b) 10 (c) 7 (d) 17
36. 36.In a class of 49 children, 27 like tea, 28 like coffee and 8 like both. How many like neither? (a) 8 (b) 10 (c) 3 (d) 2
37. 37.In a class of 47 children, 25 like tea, 17 like coffee and 5 like both. How many like at least one of the two? (a) 37 (b) 42 (c) 32 (d) 47
38. 38.In a class of 34 children, 19 like cricket, 15 like football and 3 like both. How many like neither? (a) 6 (b) 0 (c) 4 (d) 3
39. 39.In a class of 35 children, 12 like tea, 16 like coffee and 3 like both. How many like at least one of the two? (a) 35 (b) 25 (c) 22 (d) 28
40. 40.In a class of 16 children, 7 like maths, 10 like science and 4 like both. How many like at least one of the two? (a) 9 (b) 16 (c) 13 (d) 17

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