Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 323 · 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 46 children, 23 like tea, 17 like coffee and 10 like neither. How many like both? (a) 36 (b) 10 (c) 4 (d) 5
2. 2.In a class of 32 children, 8 like cricket, 23 like football and 5 like both. How many like at least one of the two? (a) 26 (b) 31 (c) 32 (d) 21
3. 3.In a class of 36 children, 16 like maths, 19 like science and 8 like both. How many like neither? (a) 9 (b) 1 (c) 8 (d) 17
4. 4.In a class of 25 children, 15 like tea, 12 like coffee and 3 like both. How many like neither? (a) 2 (b) 3 (c) 4 (d) 1
5. 5.In a class of 46 children, 32 like tea, 22 like coffee and 12 like both. How many like only tea? (a) 24 (b) 32 (c) 20 (d) 10
6. 6.In a class of 32 children, 18 like mangoes, 14 like bananas and 10 like both. How many like only mangoes? (a) 8 (b) 10 (c) 18 (d) 4
7. 7.In a class of 35 children, 24 like dance, 14 like music and 11 like both. How many like neither? (a) 11 (b) 19 (c) 8 (d) 9
8. 8.In a class of 43 children, 25 like cricket, 24 like football and 3 like neither. How many like both? (a) 3 (b) 6 (c) 40 (d) 9
9. 9.In a class of 26 children, 8 like cricket, 14 like football and 4 like both. How many like only cricket? (a) 10 (b) 8 (c) 4 (d) 12
10. 10.In a class of 32 children, 17 like tea, 22 like coffee and 8 like both. How many like neither? (a) 2 (b) 1 (c) 8 (d) 9
11. 11.In a class of 17 children, 7 like dance, 9 like music and 3 like both. How many like at least one of the two? (a) 16 (b) 17 (c) 10 (d) 13
12. 12.In a class of 37 children, 24 like tea, 9 like coffee and 8 like neither. How many like both? (a) 8 (b) 5 (c) 29 (d) 4
13. 13.In a class of 39 children, 21 like dance, 16 like music and 8 like both. How many like at least one of the two? (a) 39 (b) 29 (c) 37 (d) 21
14. 14.In a class of 23 children, 15 like tea, 9 like coffee and 2 like both. How many like neither? (a) 2 (b) 1 (c) 3 (d) 0
15. 15.In a class of 34 children, 20 like mangoes, 14 like bananas and 5 like both. How many like at least one of the two? (a) 30 (b) 34 (c) 29 (d) 24
16. 16.In a class of 42 children, 24 like dance, 24 like music and 7 like both. How many like at least one of the two? (a) 42 (b) 34 (c) 41 (d) 48
17. 17.In a class of 18 children, 7 like tea, 12 like coffee and 4 like both. How many like at least one of the two? (a) 19 (b) 11 (c) 18 (d) 15
18. 18.In a class of 16 children, 12 like mangoes, 5 like bananas and 2 like both. How many like only mangoes? (a) 3 (b) 12 (c) 11 (d) 10
19. 19.In a class of 28 children, 18 like mangoes, 7 like bananas and 3 like both. How many like only mangoes? (a) 4 (b) 21 (c) 15 (d) 18
20. 20.In a class of 41 children, 17 like cricket, 25 like football and 10 like both. How many like only cricket? (a) 16 (b) 17 (c) 7 (d) 15
21. 21.In a class of 21 children, 9 like maths, 12 like science and 2 like both. How many like only maths? (a) 9 (b) 2 (c) 7 (d) 10
22. 22.In a class of 33 children, 21 like cricket, 8 like football and 2 like both. How many like only cricket? (a) 25 (b) 6 (c) 21 (d) 19
23. 23.In a class of 29 children, 15 like dance, 10 like music and 4 like both. How many like only dance? (a) 19 (b) 11 (c) 15 (d) 6
24. 24.In a class of 44 children, 19 like dance, 19 like music and 3 like both. How many like only dance? (a) 16 (b) 19 (c) 3 (d) 25
25. 25.In a class of 24 children, 13 like tea, 11 like coffee and 3 like both. How many like at least one of the two? (a) 24 (b) 22 (c) 21 (d) 18
26. 26.In a class of 48 children, 23 like dance, 26 like music and 8 like both. How many like neither? (a) 8 (b) 6 (c) 7 (d) 15
27. 27.In a class of 38 children, 24 like maths, 15 like science and 5 like both. How many like only maths? (a) 10 (b) 19 (c) 23 (d) 24
28. 28.In a class of 38 children, 23 like maths, 18 like science and 9 like neither. How many like both? (a) 12 (b) 9 (c) 3 (d) 29
29. 29.In a class of 43 children, 22 like tea, 23 like coffee and 6 like both. How many like at least one of the two? (a) 43 (b) 33 (c) 39 (d) 45
30. 30.In a class of 21 children, 14 like tea, 15 like coffee and 9 like both. How many like neither? (a) 10 (b) 9 (c) 2 (d) 1
31. 31.In a class of 38 children, 20 like maths, 15 like science and 7 like neither. How many like both? (a) 5 (b) 7 (c) 4 (d) 31
32. 32.In a class of 46 children, 18 like cricket, 23 like football and 3 like both. How many like at least one of the two? (a) 41 (b) 35 (c) 46 (d) 38
33. 33.In a class of 31 children, 20 like mangoes, 10 like bananas and 2 like both. How many like only mangoes? (a) 8 (b) 21 (c) 18 (d) 20
34. 34.In a class of 31 children, 10 like tea, 22 like coffee and 1 like neither. How many like both? (a) 2 (b) 1 (c) 30 (d) 3
35. 35.In a class of 41 children, 22 like maths, 27 like science and 10 like both. How many like neither? (a) 12 (b) 2 (c) 10 (d) 3
36. 36.In a class of 39 children, 14 like mangoes, 29 like bananas and 9 like both. How many like only mangoes? (a) 20 (b) 5 (c) 14 (d) 10
37. 37.In a class of 36 children, 25 like mangoes, 14 like bananas and 5 like both. How many like at least one of the two? (a) 36 (b) 29 (c) 39 (d) 34
38. 38.In a class of 36 children, 21 like maths, 14 like science and 9 like both. How many like only maths? (a) 5 (b) 22 (c) 12 (d) 21
39. 39.In a class of 47 children, 25 like mangoes, 25 like bananas and 10 like both. How many like only mangoes? (a) 25 (b) 10 (c) 22 (d) 15
40. 40.In a class of 36 children, 25 like tea, 13 like coffee and 7 like both. How many like only tea? (a) 23 (b) 6 (c) 25 (d) 18

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