Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 1 · 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 39 children, 21 like mangoes, 20 like bananas and 3 like both. How many like only mangoes? (a) 19 (b) 21 (c) 18 (d) 17
2. 2.In a class of 44 children, 23 like maths, 25 like science and 6 like both. How many like neither? (a) 3 (b) 8 (c) 6 (d) 2
3. 3.In a class of 15 children, 6 like dance, 5 like music and 2 like both. How many like only dance? (a) 3 (b) 10 (c) 4 (d) 6
4. 4.In a class of 22 children, 12 like mangoes, 6 like bananas and 2 like both. How many like at least one of the two? (a) 14 (b) 18 (c) 16 (d) 22
5. 5.In a class of 22 children, 16 like mangoes, 12 like bananas and 9 like both. How many like only mangoes? (a) 10 (b) 7 (c) 3 (d) 16
6. 6.In a class of 22 children, 13 like tea, 10 like coffee and 2 like both. How many like neither? (a) 2 (b) 3 (c) 0 (d) 1
7. 7.In a class of 24 children, 13 like mangoes, 16 like bananas and 8 like both. How many like only mangoes? (a) 13 (b) 8 (c) 6 (d) 5
8. 8.In a class of 22 children, 9 like cricket, 12 like football and 6 like neither. How many like both? (a) 5 (b) 16 (c) 4 (d) 6
9. 9.In a class of 29 children, 13 like maths, 12 like science and 8 like neither. How many like both? (a) 5 (b) 21 (c) 8 (d) 4
10. 10.In a class of 34 children, 16 like cricket, 22 like football and 8 like both. How many like only cricket? (a) 8 (b) 14 (c) 16 (d) 12
11. 11.In a class of 26 children, 13 like mangoes, 9 like bananas and 4 like both. How many like at least one of the two? (a) 14 (b) 26 (c) 18 (d) 22
12. 12.In a class of 46 children, 19 like maths, 25 like science and 6 like both. How many like neither? (a) 2 (b) 8 (c) 6 (d) 14
13. 13.In a class of 32 children, 18 like dance, 10 like music and 6 like both. How many like at least one of the two? (a) 16 (b) 22 (c) 32 (d) 28
14. 14.In a class of 26 children, 15 like cricket, 13 like football and 7 like both. How many like only cricket? (a) 13 (b) 15 (c) 6 (d) 8
15. 15.In a class of 48 children, 20 like cricket, 32 like football and 12 like both. How many like only cricket? (a) 8 (b) 16 (c) 12 (d) 20
16. 16.In a class of 37 children, 15 like mangoes, 26 like bananas and 5 like neither. How many like both? (a) 32 (b) 9 (c) 4 (d) 5
17. 17.In a class of 32 children, 10 like dance, 18 like music and 9 like neither. How many like both? (a) 9 (b) 6 (c) 5 (d) 23
18. 18.In a class of 48 children, 19 like cricket, 23 like football and 3 like both. How many like only cricket? (a) 20 (b) 19 (c) 25 (d) 16
19. 19.In a class of 31 children, 25 like mangoes, 16 like bananas and 11 like both. How many like at least one of the two? (a) 30 (b) 41 (c) 31 (d) 19
20. 20.In a class of 21 children, 15 like maths, 16 like science and 11 like both. How many like neither? (a) 12 (b) 11 (c) 2 (d) 1
21. 21.In a class of 35 children, 7 like tea, 23 like coffee and 4 like both. How many like at least one of the two? (a) 35 (b) 30 (c) 26 (d) 22
22. 22.In a class of 35 children, 22 like dance, 7 like music and 10 like neither. How many like both? (a) 5 (b) 25 (c) 4 (d) 10
23. 23.In a class of 32 children, 12 like mangoes, 28 like bananas and 9 like both. How many like at least one of the two? (a) 31 (b) 22 (c) 32 (d) 40
24. 24.In a class of 27 children, 17 like mangoes, 16 like bananas and 7 like both. How many like neither? (a) 1 (b) 8 (c) 7 (d) 2
25. 25.In a class of 46 children, 16 like dance, 32 like music and 12 like both. How many like only dance? (a) 16 (b) 14 (c) 20 (d) 4
26. 26.In a class of 21 children, 5 like mangoes, 15 like bananas and 3 like neither. How many like both? (a) 1 (b) 2 (c) 3 (d) 18
27. 27.In a class of 38 children, 11 like dance, 24 like music and 5 like both. How many like only dance? (a) 6 (b) 19 (c) 11 (d) 14
28. 28.In a class of 28 children, 20 like dance, 12 like music and 2 like neither. How many like both? (a) 6 (b) 2 (c) 4 (d) 26
29. 29.In a class of 20 children, 11 like dance, 13 like music and 6 like both. How many like neither? (a) 3 (b) 2 (c) 6 (d) 8
30. 30.In a class of 40 children, 15 like mangoes, 26 like bananas and 11 like both. How many like only mangoes? (a) 14 (b) 11 (c) 4 (d) 15
31. 31.In a class of 28 children, 6 like dance, 22 like music and 3 like both. How many like neither? (a) 0 (b) 6 (c) 4 (d) 3
32. 32.In a class of 30 children, 19 like cricket, 10 like football and 4 like both. How many like at least one of the two? (a) 21 (b) 29 (c) 30 (d) 25
33. 33.In a class of 29 children, 14 like maths, 23 like science and 2 like neither. How many like both? (a) 27 (b) 10 (c) 8 (d) 2
34. 34.In a class of 28 children, 18 like cricket, 14 like football and 11 like both. How many like at least one of the two? (a) 28 (b) 32 (c) 10 (d) 21
35. 35.In a class of 21 children, 12 like tea, 11 like coffee and 4 like both. How many like only tea? (a) 8 (b) 12 (c) 7 (d) 10
36. 36.In a class of 46 children, 31 like mangoes, 21 like bananas and 12 like both. How many like only mangoes? (a) 9 (b) 25 (c) 31 (d) 19
37. 37.In a class of 52 children, 31 like cricket, 29 like football and 4 like neither. How many like both? (a) 4 (b) 8 (c) 48 (d) 12
38. 38.In a class of 26 children, 15 like cricket, 7 like football and 2 like both. How many like only cricket? (a) 13 (b) 15 (c) 5 (d) 19
39. 39.In a class of 44 children, 25 like tea, 26 like coffee and 11 like both. How many like at least one of the two? (a) 40 (b) 29 (c) 44 (d) 51
40. 40.In a class of 43 children, 27 like mangoes, 25 like bananas and 10 like both. How many like at least one of the two? (a) 43 (b) 42 (c) 52 (d) 32

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