Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 512 · 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 29 children, 9 like maths, 24 like science and 2 like neither. How many like both? (a) 2 (b) 6 (c) 4 (d) 27
2. 2.In a class of 49 children, 28 like maths, 22 like science and 9 like both. How many like at least one of the two? (a) 50 (b) 49 (c) 32 (d) 41
3. 3.In a class of 32 children, 15 like tea, 20 like coffee and 9 like both. How many like at least one of the two? (a) 17 (b) 35 (c) 26 (d) 32
4. 4.In a class of 37 children, 30 like maths, 16 like science and 11 like both. How many like neither? (a) 3 (b) 11 (c) 13 (d) 2
5. 5.In a class of 29 children, 8 like mangoes, 24 like bananas and 5 like both. How many like at least one of the two? (a) 29 (b) 22 (c) 27 (d) 32
6. 6.In a class of 41 children, 25 like tea, 13 like coffee and 7 like both. How many like only tea? (a) 28 (b) 25 (c) 18 (d) 6
7. 7.In a class of 25 children, 7 like tea, 13 like coffee and 9 like neither. How many like both? (a) 16 (b) 5 (c) 9 (d) 4
8. 8.In a class of 42 children, 18 like maths, 22 like science and 3 like both. How many like neither? (a) 8 (b) 3 (c) 5 (d) 2
9. 9.In a class of 34 children, 19 like mangoes, 23 like bananas and 10 like both. How many like neither? (a) 10 (b) 2 (c) 3 (d) 12
10. 10.In a class of 34 children, 16 like tea, 18 like coffee and 8 like both. How many like only tea? (a) 10 (b) 8 (c) 9 (d) 16
11. 11.In a class of 21 children, 7 like cricket, 14 like football and 3 like both. How many like only cricket? (a) 7 (b) 4 (c) 3 (d) 11
12. 12.In a class of 36 children, 15 like mangoes, 23 like bananas and 5 like neither. How many like both? (a) 31 (b) 2 (c) 5 (d) 7
13. 13.In a class of 40 children, 19 like cricket, 28 like football and 4 like neither. How many like both? (a) 11 (b) 36 (c) 4 (d) 7
14. 14.In a class of 25 children, 10 like maths, 13 like science and 6 like neither. How many like both? (a) 4 (b) 6 (c) 19 (d) 5
15. 15.In a class of 34 children, 23 like mangoes, 15 like bananas and 2 like neither. How many like both? (a) 2 (b) 32 (c) 6 (d) 4
16. 16.In a class of 27 children, 11 like cricket, 15 like football and 6 like both. How many like at least one of the two? (a) 14 (b) 27 (c) 20 (d) 26
17. 17.In a class of 19 children, 8 like dance, 10 like music and 5 like both. How many like neither? (a) 1 (b) 11 (c) 6 (d) 5
18. 18.In a class of 41 children, 21 like tea, 17 like coffee and 3 like both. How many like neither? (a) 7 (b) 9 (c) 3 (d) 6
19. 19.In a class of 28 children, 9 like cricket, 13 like football and 4 like both. How many like only cricket? (a) 4 (b) 9 (c) 5 (d) 15
20. 20.In a class of 17 children, 7 like maths, 9 like science and 3 like neither. How many like both? (a) 2 (b) 3 (c) 1 (d) 14
21. 21.In a class of 39 children, 13 like tea, 25 like coffee and 9 like neither. How many like both? (a) 8 (b) 9 (c) 7 (d) 30
22. 22.In a class of 29 children, 18 like cricket, 11 like football and 3 like both. How many like only cricket? (a) 3 (b) 8 (c) 15 (d) 18
23. 23.In a class of 40 children, 20 like tea, 24 like coffee and 5 like both. How many like only tea? (a) 20 (b) 15 (c) 19 (d) 16
24. 24.In a class of 37 children, 24 like dance, 11 like music and 7 like both. How many like only dance? (a) 17 (b) 4 (c) 24 (d) 26
25. 25.In a class of 29 children, 20 like dance, 14 like music and 11 like both. How many like neither? (a) 17 (b) 7 (c) 11 (d) 6
26. 26.In a class of 34 children, 11 like maths, 23 like science and 6 like both. How many like at least one of the two? (a) 34 (b) 22 (c) 29 (d) 28
27. 27.In a class of 43 children, 26 like cricket, 25 like football and 9 like both. How many like at least one of the two? (a) 42 (b) 51 (c) 43 (d) 33
28. 28.In a class of 42 children, 19 like tea, 24 like coffee and 11 like both. How many like only tea? (a) 18 (b) 19 (c) 13 (d) 8
29. 29.In a class of 31 children, 22 like mangoes, 15 like bananas and 12 like both. How many like neither? (a) 7 (b) 18 (c) 6 (d) 12
30. 30.In a class of 25 children, 10 like tea, 18 like coffee and 4 like both. How many like neither? (a) 1 (b) 4 (c) 2 (d) 5
31. 31.In a class of 40 children, 24 like tea, 23 like coffee and 1 like neither. How many like both? (a) 39 (b) 1 (c) 8 (d) 7
32. 32.In a class of 36 children, 22 like dance, 16 like music and 10 like both. How many like only dance? (a) 22 (b) 6 (c) 20 (d) 12
33. 33.In a class of 49 children, 22 like tea, 24 like coffee and 4 like both. How many like only tea? (a) 20 (b) 25 (c) 18 (d) 22
34. 34.In a class of 28 children, 23 like cricket, 12 like football and 9 like both. How many like only cricket? (a) 23 (b) 14 (c) 3 (d) 16
35. 35.In a class of 35 children, 24 like maths, 19 like science and 9 like both. How many like at least one of the two? (a) 25 (b) 35 (c) 34 (d) 43
36. 36.In a class of 51 children, 27 like maths, 25 like science and 10 like both. How many like only maths? (a) 27 (b) 17 (c) 26 (d) 15
37. 37.In a class of 42 children, 30 like dance, 16 like music and 12 like both. How many like neither? (a) 20 (b) 9 (c) 12 (d) 8
38. 38.In a class of 34 children, 23 like cricket, 18 like football and 11 like both. How many like neither? (a) 5 (b) 15 (c) 4 (d) 11
39. 39.In a class of 31 children, 15 like tea, 13 like coffee and 6 like both. How many like only tea? (a) 15 (b) 9 (c) 18 (d) 7
40. 40.In a class of 37 children, 14 like tea, 22 like coffee and 8 like both. How many like at least one of the two? (a) 20 (b) 28 (c) 37 (d) 36

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