Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 652 · 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 41 children, 22 like cricket, 18 like football and 9 like neither. How many like both? (a) 9 (b) 32 (c) 7 (d) 8
2. 2.In a class of 26 children, 14 like cricket, 13 like football and 7 like both. How many like at least one of the two? (a) 13 (b) 20 (c) 27 (d) 26
3. 3.In a class of 31 children, 16 like maths, 13 like science and 4 like both. How many like only maths? (a) 12 (b) 18 (c) 16 (d) 9
4. 4.In a class of 38 children, 9 like cricket, 23 like football and 4 like both. How many like only cricket? (a) 19 (b) 5 (c) 9 (d) 15
5. 5.In a class of 42 children, 17 like cricket, 27 like football and 7 like both. How many like neither? (a) 7 (b) 6 (c) 12 (d) 5
6. 6.In a class of 39 children, 16 like cricket, 24 like football and 8 like both. How many like only cricket? (a) 16 (b) 15 (c) 8 (d) 9
7. 7.In a class of 34 children, 15 like maths, 23 like science and 9 like both. How many like neither? (a) 6 (b) 5 (c) 9 (d) 14
8. 8.In a class of 27 children, 15 like mangoes, 11 like bananas and 4 like neither. How many like both? (a) 2 (b) 4 (c) 23 (d) 3
9. 9.In a class of 23 children, 13 like dance, 14 like music and 6 like both. How many like at least one of the two? (a) 21 (b) 27 (c) 15 (d) 23
10. 10.In a class of 31 children, 13 like cricket, 14 like football and 3 like both. How many like at least one of the two? (a) 27 (b) 21 (c) 24 (d) 31
11. 11.In a class of 31 children, 11 like mangoes, 20 like bananas and 8 like neither. How many like both? (a) 23 (b) 8 (c) 7 (d) 9
12. 12.In a class of 37 children, 25 like mangoes, 20 like bananas and 9 like both. How many like only mangoes? (a) 25 (b) 17 (c) 16 (d) 11
13. 13.In a class of 35 children, 11 like dance, 25 like music and 5 like both. How many like at least one of the two? (a) 36 (b) 35 (c) 26 (d) 31
14. 14.In a class of 38 children, 14 like mangoes, 18 like bananas and 8 like neither. How many like both? (a) 8 (b) 30 (c) 3 (d) 2
15. 15.In a class of 26 children, 16 like dance, 10 like music and 3 like both. How many like neither? (a) 6 (b) 0 (c) 3 (d) 4
16. 16.In a class of 33 children, 20 like mangoes, 10 like bananas and 6 like neither. How many like both? (a) 3 (b) 6 (c) 4 (d) 27
17. 17.In a class of 39 children, 15 like maths, 21 like science and 7 like both. How many like only maths? (a) 18 (b) 8 (c) 15 (d) 14
18. 18.In a class of 41 children, 26 like cricket, 19 like football and 12 like both. How many like neither? (a) 12 (b) 9 (c) 8 (d) 20
19. 19.In a class of 33 children, 15 like cricket, 17 like football and 3 like both. How many like only cricket? (a) 16 (b) 15 (c) 14 (d) 12
20. 20.In a class of 35 children, 17 like tea, 16 like coffee and 2 like both. How many like neither? (a) 6 (b) 4 (c) 5 (d) 2
21. 21.In a class of 43 children, 24 like cricket, 25 like football and 11 like both. How many like neither? (a) 6 (b) 16 (c) 5 (d) 11
22. 22.In a class of 30 children, 14 like dance, 18 like music and 10 like both. How many like neither? (a) 9 (b) 8 (c) 10 (d) 18
23. 23.In a class of 32 children, 15 like mangoes, 17 like bananas and 2 like both. How many like at least one of the two? (a) 31 (b) 28 (c) 30 (d) 32
24. 24.In a class of 31 children, 10 like dance, 20 like music and 4 like both. How many like only dance? (a) 10 (b) 6 (c) 16 (d) 11
25. 25.In a class of 25 children, 5 like mangoes, 16 like bananas and 2 like both. How many like at least one of the two? (a) 17 (b) 21 (c) 19 (d) 25
26. 26.In a class of 36 children, 17 like maths, 21 like science and 8 like both. How many like at least one of the two? (a) 22 (b) 36 (c) 30 (d) 38
27. 27.In a class of 30 children, 19 like tea, 17 like coffee and 8 like both. How many like neither? (a) 2 (b) 8 (c) 10 (d) 3
28. 28.In a class of 25 children, 8 like maths, 15 like science and 2 like both. How many like only maths? (a) 10 (b) 13 (c) 8 (d) 6
29. 29.In a class of 35 children, 15 like cricket, 13 like football and 2 like both. How many like at least one of the two? (a) 35 (b) 28 (c) 24 (d) 26
30. 30.In a class of 43 children, 21 like mangoes, 19 like bananas and 7 like both. How many like neither? (a) 17 (b) 3 (c) 7 (d) 10
31. 31.In a class of 36 children, 20 like cricket, 8 like football and 2 like both. How many like neither? (a) 10 (b) 2 (c) 8 (d) 12
32. 32.In a class of 36 children, 21 like mangoes, 18 like bananas and 9 like neither. How many like both? (a) 9 (b) 27 (c) 12 (d) 3
33. 33.In a class of 27 children, 21 like tea, 15 like coffee and 1 like neither. How many like both? (a) 9 (b) 10 (c) 26 (d) 1
34. 34.In a class of 27 children, 21 like maths, 15 like science and 12 like both. How many like neither? (a) 3 (b) 4 (c) 15 (d) 12
35. 35.In a class of 29 children, 16 like maths, 11 like science and 8 like neither. How many like both? (a) 6 (b) 21 (c) 7 (d) 8
36. 36.In a class of 37 children, 22 like dance, 15 like music and 5 like both. How many like at least one of the two? (a) 33 (b) 27 (c) 32 (d) 37
37. 37.In a class of 36 children, 18 like maths, 17 like science and 5 like both. How many like only maths? (a) 12 (b) 18 (c) 13 (d) 19
38. 38.In a class of 36 children, 20 like tea, 16 like coffee and 10 like both. How many like only tea? (a) 10 (b) 6 (c) 11 (d) 20
39. 39.In a class of 34 children, 15 like tea, 18 like coffee and 2 like both. How many like neither? (a) 2 (b) 5 (c) 1 (d) 3
40. 40.In a class of 20 children, 8 like mangoes, 8 like bananas and 2 like both. How many like neither? (a) 6 (b) 2 (c) 8 (d) 4

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