Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 91 · 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 26 children, 15 like mangoes, 8 like bananas and 2 like both. How many like at least one of the two? (a) 23 (b) 19 (c) 26 (d) 21
2. 2.In a class of 34 children, 28 like mangoes, 13 like bananas and 1 like neither. How many like both? (a) 8 (b) 33 (c) 7 (d) 1
3. 3.In a class of 44 children, 22 like mangoes, 24 like bananas and 6 like both. How many like only mangoes? (a) 18 (b) 20 (c) 22 (d) 16
4. 4.In a class of 29 children, 15 like tea, 14 like coffee and 6 like both. How many like only tea? (a) 15 (b) 6 (c) 8 (d) 9
5. 5.In a class of 30 children, 23 like mangoes, 17 like bananas and 2 like neither. How many like both? (a) 12 (b) 28 (c) 2 (d) 10
6. 6.In a class of 38 children, 22 like mangoes, 24 like bananas and 10 like both. How many like neither? (a) 12 (b) 10 (c) 3 (d) 2
7. 7.In a class of 29 children, 14 like mangoes, 19 like bananas and 1 like neither. How many like both? (a) 1 (b) 5 (c) 28 (d) 4
8. 8.In a class of 38 children, 23 like cricket, 10 like football and 5 like both. How many like only cricket? (a) 23 (b) 5 (c) 18 (d) 28
9. 9.In a class of 27 children, 10 like cricket, 19 like football and 4 like both. How many like only cricket? (a) 15 (b) 8 (c) 6 (d) 10
10. 10.In a class of 20 children, 11 like tea, 14 like coffee and 2 like neither. How many like both? (a) 2 (b) 5 (c) 7 (d) 18
11. 11.In a class of 41 children, 16 like cricket, 28 like football and 10 like both. How many like at least one of the two? (a) 41 (b) 34 (c) 44 (d) 24
12. 12.In a class of 46 children, 22 like maths, 25 like science and 11 like both. How many like at least one of the two? (a) 46 (b) 36 (c) 25 (d) 47
13. 13.In a class of 41 children, 32 like maths, 17 like science and 4 like neither. How many like both? (a) 8 (b) 4 (c) 37 (d) 12
14. 14.In a class of 32 children, 11 like cricket, 22 like football and 4 like neither. How many like both? (a) 28 (b) 1 (c) 4 (d) 5
15. 15.In a class of 34 children, 24 like cricket, 14 like football and 5 like both. How many like neither? (a) 6 (b) 2 (c) 1 (d) 5
16. 16.In a class of 40 children, 24 like maths, 15 like science and 5 like both. How many like neither? (a) 11 (b) 5 (c) 1 (d) 6
17. 17.In a class of 22 children, 14 like cricket, 16 like football and 10 like both. How many like neither? (a) 12 (b) 3 (c) 10 (d) 2
18. 18.In a class of 40 children, 23 like maths, 15 like science and 3 like both. How many like only maths? (a) 25 (b) 23 (c) 20 (d) 12
19. 19.In a class of 26 children, 12 like cricket, 7 like football and 2 like both. How many like neither? (a) 11 (b) 7 (c) 2 (d) 9
20. 20.In a class of 26 children, 21 like mangoes, 10 like bananas and 6 like both. How many like at least one of the two? (a) 25 (b) 31 (c) 26 (d) 19
21. 21.In a class of 32 children, 9 like dance, 23 like music and 3 like both. How many like neither? (a) 3 (b) 0 (c) 6 (d) 4
22. 22.In a class of 40 children, 15 like tea, 21 like coffee and 5 like both. How many like at least one of the two? (a) 31 (b) 26 (c) 40 (d) 36
23. 23.In a class of 56 children, 29 like tea, 30 like coffee and 7 like neither. How many like both? (a) 3 (b) 49 (c) 7 (d) 10
24. 24.In a class of 20 children, 10 like tea, 11 like coffee and 2 like both. How many like only tea? (a) 2 (b) 8 (c) 10 (d) 9
25. 25.In a class of 28 children, 11 like mangoes, 16 like bananas and 4 like both. How many like at least one of the two? (a) 19 (b) 28 (c) 27 (d) 23
26. 26.In a class of 25 children, 12 like tea, 11 like coffee and 3 like both. How many like at least one of the two? (a) 17 (b) 20 (c) 25 (d) 23
27. 27.In a class of 29 children, 14 like dance, 20 like music and 9 like both. How many like only dance? (a) 14 (b) 11 (c) 9 (d) 5
28. 28.In a class of 31 children, 15 like maths, 13 like science and 5 like both. How many like only maths? (a) 18 (b) 15 (c) 10 (d) 8
29. 29.In a class of 34 children, 26 like mangoes, 14 like bananas and 7 like both. How many like neither? (a) 7 (b) 8 (c) 1 (d) 2
30. 30.In a class of 27 children, 15 like tea, 13 like coffee and 6 like neither. How many like both? (a) 6 (b) 1 (c) 7 (d) 21
31. 31.In a class of 40 children, 22 like dance, 21 like music and 7 like both. How many like only dance? (a) 22 (b) 19 (c) 14 (d) 15
32. 32.In a class of 33 children, 25 like tea, 13 like coffee and 7 like both. How many like at least one of the two? (a) 38 (b) 33 (c) 24 (d) 31
33. 33.In a class of 35 children, 18 like tea, 19 like coffee and 5 like both. How many like at least one of the two? (a) 35 (b) 37 (c) 27 (d) 32
34. 34.In a class of 30 children, 12 like cricket, 17 like football and 5 like both. How many like neither? (a) 6 (b) 5 (c) 11 (d) 1
35. 35.In a class of 25 children, 10 like tea, 15 like coffee and 7 like both. How many like neither? (a) 14 (b) 0 (c) 7 (d) 8
36. 36.In a class of 31 children, 20 like tea, 14 like coffee and 7 like both. How many like neither? (a) 5 (b) 7 (c) 11 (d) 4
37. 37.In a class of 19 children, 10 like cricket, 8 like football and 5 like both. How many like at least one of the two? (a) 19 (b) 13 (c) 8 (d) 18
38. 38.In a class of 25 children, 11 like maths, 12 like science and 5 like both. How many like neither? (a) 12 (b) 2 (c) 7 (d) 5
39. 39.In a class of 23 children, 9 like dance, 8 like music and 4 like both. How many like neither? (a) 4 (b) 14 (c) 10 (d) 6
40. 40.In a class of 41 children, 15 like dance, 24 like music and 7 like both. How many like only dance? (a) 7 (b) 15 (c) 17 (d) 8

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