Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 822 · 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 21 children, 13 like tea, 8 like coffee and 4 like both. How many like only tea? (a) 10 (b) 9 (c) 4 (d) 13
2. 2.In a class of 37 children, 13 like dance, 25 like music and 6 like both. How many like only dance? (a) 19 (b) 12 (c) 13 (d) 7
3. 3.In a class of 38 children, 19 like mangoes, 18 like bananas and 9 like both. How many like at least one of the two? (a) 38 (b) 37 (c) 28 (d) 19
4. 4.In a class of 24 children, 16 like mangoes, 17 like bananas and 3 like neither. How many like both? (a) 3 (b) 21 (c) 12 (d) 9
5. 5.In a class of 41 children, 15 like maths, 24 like science and 4 like both. How many like at least one of the two? (a) 41 (b) 39 (c) 35 (d) 31
6. 6.In a class of 32 children, 12 like cricket, 13 like football and 2 like both. How many like at least one of the two? (a) 23 (b) 25 (c) 32 (d) 21
7. 7.In a class of 41 children, 22 like tea, 23 like coffee and 10 like both. How many like neither? (a) 7 (b) 6 (c) 10 (d) 16
8. 8.In a class of 41 children, 17 like maths, 25 like science and 8 like neither. How many like both? (a) 33 (b) 1 (c) 8 (d) 9
9. 9.In a class of 35 children, 12 like mangoes, 22 like bananas and 6 like both. How many like neither? (a) 13 (b) 1 (c) 7 (d) 6
10. 10.In a class of 49 children, 21 like maths, 29 like science and 10 like both. How many like only maths? (a) 21 (b) 19 (c) 11 (d) 20
11. 11.In a class of 32 children, 25 like mangoes, 10 like bananas and 7 like both. How many like only mangoes? (a) 25 (b) 18 (c) 22 (d) 3
12. 12.In a class of 30 children, 18 like mangoes, 22 like bananas and 12 like both. How many like neither? (a) 14 (b) 2 (c) 3 (d) 12
13. 13.In a class of 41 children, 22 like tea, 17 like coffee and 3 like both. How many like at least one of the two? (a) 33 (b) 36 (c) 39 (d) 41
14. 14.In a class of 27 children, 16 like dance, 14 like music and 1 like neither. How many like both? (a) 26 (b) 3 (c) 4 (d) 1
15. 15.In a class of 36 children, 21 like cricket, 23 like football and 2 like neither. How many like both? (a) 34 (b) 2 (c) 8 (d) 10
16. 16.In a class of 24 children, 5 like dance, 14 like music and 2 like both. How many like only dance? (a) 3 (b) 10 (c) 12 (d) 5
17. 17.In a class of 41 children, 23 like tea, 17 like coffee and 3 like both. How many like at least one of the two? (a) 40 (b) 41 (c) 34 (d) 37
18. 18.In a class of 47 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) 47
19. 19.In a class of 50 children, 22 like tea, 23 like coffee and 4 like both. How many like only tea? (a) 19 (b) 18 (c) 27 (d) 22
20. 20.In a class of 25 children, 8 like dance, 13 like music and 3 like both. How many like at least one of the two? (a) 15 (b) 21 (c) 25 (d) 18
21. 21.In a class of 45 children, 26 like mangoes, 28 like bananas and 3 like neither. How many like both? (a) 42 (b) 3 (c) 9 (d) 12
22. 22.In a class of 47 children, 27 like mangoes, 24 like bananas and 7 like neither. How many like both? (a) 11 (b) 7 (c) 4 (d) 40
23. 23.In a class of 36 children, 11 like maths, 21 like science and 4 like both. How many like only maths? (a) 17 (b) 7 (c) 11 (d) 15
24. 24.In a class of 36 children, 13 like mangoes, 25 like bananas and 3 like neither. How many like both? (a) 2 (b) 33 (c) 5 (d) 3
25. 25.In a class of 41 children, 14 like tea, 23 like coffee and 4 like both. How many like neither? (a) 8 (b) 9 (c) 12 (d) 4
26. 26.In a class of 17 children, 7 like cricket, 12 like football and 4 like both. How many like neither? (a) 6 (b) 3 (c) 2 (d) 4
27. 27.In a class of 44 children, 21 like mangoes, 30 like bananas and 5 like neither. How many like both? (a) 7 (b) 39 (c) 5 (d) 12
28. 28.In a class of 39 children, 22 like cricket, 23 like football and 7 like both. How many like neither? (a) 8 (b) 1 (c) 2 (d) 7
29. 29.In a class of 47 children, 21 like mangoes, 21 like bananas and 2 like both. How many like neither? (a) 9 (b) 2 (c) 5 (d) 7
30. 30.In a class of 31 children, 16 like maths, 20 like science and 6 like both. How many like only maths? (a) 16 (b) 10 (c) 14 (d) 11
31. 31.In a class of 38 children, 20 like maths, 14 like science and 6 like neither. How many like both? (a) 3 (b) 32 (c) 2 (d) 6
32. 32.In a class of 21 children, 9 like cricket, 10 like football and 2 like both. How many like only cricket? (a) 9 (b) 8 (c) 11 (d) 7
33. 33.In a class of 33 children, 15 like mangoes, 17 like bananas and 5 like both. How many like only mangoes? (a) 12 (b) 16 (c) 15 (d) 10
34. 34.In a class of 35 children, 14 like maths, 23 like science and 6 like both. How many like only maths? (a) 14 (b) 8 (c) 17 (d) 12
35. 35.In a class of 39 children, 14 like dance, 21 like music and 2 like both. How many like neither? (a) 6 (b) 2 (c) 8 (d) 4
36. 36.In a class of 42 children, 19 like maths, 23 like science and 4 like both. How many like at least one of the two? (a) 34 (b) 39 (c) 38 (d) 42
37. 37.In a class of 35 children, 20 like tea, 8 like coffee and 2 like both. How many like only tea? (a) 27 (b) 20 (c) 6 (d) 18
38. 38.In a class of 34 children, 18 like cricket, 11 like football and 5 like both. How many like only cricket? (a) 13 (b) 23 (c) 18 (d) 6
39. 39.In a class of 37 children, 12 like mangoes, 21 like bananas and 4 like both. How many like at least one of the two? (a) 37 (b) 25 (c) 29 (d) 33
40. 40.In a class of 33 children, 24 like dance, 14 like music and 11 like both. How many like only dance? (a) 19 (b) 13 (c) 24 (d) 3

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