Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 65 · 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, 22 like mangoes, 19 like bananas and 2 like both. How many like at least one of the two? (a) 37 (b) 41 (c) 46 (d) 39
2. 2.In a class of 24 children, 11 like dance, 10 like music and 4 like both. How many like at least one of the two? (a) 24 (b) 21 (c) 13 (d) 17
3. 3.In a class of 45 children, 28 like cricket, 25 like football and 2 like neither. How many like both? (a) 8 (b) 2 (c) 43 (d) 10
4. 4.In a class of 35 children, 22 like maths, 11 like science and 2 like both. How many like at least one of the two? (a) 35 (b) 29 (c) 33 (d) 31
5. 5.In a class of 47 children, 23 like mangoes, 20 like bananas and 4 like both. How many like at least one of the two? (a) 43 (b) 47 (c) 35 (d) 39
6. 6.In a class of 21 children, 16 like dance, 9 like music and 6 like both. How many like neither? (a) 3 (b) 2 (c) 6 (d) 8
7. 7.In a class of 27 children, 16 like cricket, 18 like football and 8 like both. How many like only cricket? (a) 9 (b) 8 (c) 10 (d) 16
8. 8.In a class of 36 children, 21 like cricket, 13 like football and 5 like both. How many like only cricket? (a) 23 (b) 21 (c) 8 (d) 16
9. 9.In a class of 33 children, 17 like cricket, 16 like football and 5 like neither. How many like both? (a) 5 (b) 6 (c) 28 (d) 4
10. 10.In a class of 34 children, 18 like cricket, 16 like football and 4 like both. How many like only cricket? (a) 4 (b) 12 (c) 18 (d) 14
11. 11.In a class of 48 children, 26 like mangoes, 28 like bananas and 12 like both. How many like neither? (a) 7 (b) 12 (c) 6 (d) 18
12. 12.In a class of 30 children, 13 like maths, 20 like science and 10 like both. How many like neither? (a) 10 (b) 17 (c) 7 (d) 8
13. 13.In a class of 47 children, 22 like tea, 27 like coffee and 8 like both. How many like at least one of the two? (a) 33 (b) 47 (c) 49 (d) 41
14. 14.In a class of 41 children, 24 like maths, 24 like science and 5 like neither. How many like both? (a) 7 (b) 12 (c) 5 (d) 36
15. 15.In a class of 20 children, 10 like mangoes, 10 like bananas and 3 like both. How many like neither? (a) 0 (b) 3 (c) 4 (d) 6
16. 16.In a class of 32 children, 10 like mangoes, 21 like bananas and 2 like both. How many like only mangoes? (a) 8 (b) 11 (c) 10 (d) 19
17. 17.In a class of 22 children, 11 like cricket, 13 like football and 7 like both. How many like neither? (a) 6 (b) 5 (c) 12 (d) 7
18. 18.In a class of 36 children, 13 like dance, 23 like music and 6 like both. How many like neither? (a) 7 (b) 6 (c) 0 (d) 12
19. 19.In a class of 31 children, 22 like tea, 19 like coffee and 11 like both. How many like only tea? (a) 12 (b) 8 (c) 22 (d) 11
20. 20.In a class of 29 children, 14 like dance, 12 like music and 7 like both. How many like at least one of the two? (a) 26 (b) 29 (c) 12 (d) 19
21. 21.In a class of 34 children, 13 like dance, 22 like music and 2 like both. How many like neither? (a) 3 (b) 2 (c) 0 (d) 1
22. 22.In a class of 33 children, 17 like cricket, 21 like football and 12 like both. How many like neither? (a) 7 (b) 19 (c) 8 (d) 12
23. 23.In a class of 33 children, 21 like mangoes, 17 like bananas and 8 like both. How many like neither? (a) 8 (b) 11 (c) 4 (d) 3
24. 24.In a class of 31 children, 11 like maths, 20 like science and 4 like both. How many like only maths? (a) 7 (b) 11 (c) 4 (d) 16
25. 25.In a class of 24 children, 10 like tea, 6 like coffee and 2 like both. How many like only tea? (a) 18 (b) 4 (c) 10 (d) 8
26. 26.In a class of 30 children, 19 like maths, 8 like science and 4 like both. How many like neither? (a) 4 (b) 7 (c) 11 (d) 3
27. 27.In a class of 37 children, 21 like cricket, 16 like football and 9 like both. How many like neither? (a) 18 (b) 9 (c) 0 (d) 10
28. 28.In a class of 29 children, 15 like dance, 20 like music and 7 like both. How many like at least one of the two? (a) 35 (b) 29 (c) 28 (d) 21
29. 29.In a class of 32 children, 14 like dance, 13 like music and 5 like both. How many like neither? (a) 10 (b) 11 (c) 15 (d) 5
30. 30.In a class of 23 children, 12 like tea, 10 like coffee and 5 like both. How many like at least one of the two? (a) 23 (b) 12 (c) 17 (d) 22
31. 31.In a class of 55 children, 29 like mangoes, 29 like bananas and 9 like neither. How many like both? (a) 9 (b) 12 (c) 46 (d) 3
32. 32.In a class of 42 children, 27 like dance, 17 like music and 9 like both. How many like neither? (a) 16 (b) 8 (c) 9 (d) 7
33. 33.In a class of 34 children, 16 like mangoes, 24 like bananas and 8 like both. How many like neither? (a) 8 (b) 2 (c) 10 (d) 3
34. 34.In a class of 37 children, 21 like cricket, 24 like football and 4 like neither. How many like both? (a) 4 (b) 12 (c) 33 (d) 8
35. 35.In a class of 32 children, 5 like tea, 19 like coffee and 2 like both. How many like at least one of the two? (a) 24 (b) 20 (c) 32 (d) 22
36. 36.In a class of 37 children, 22 like tea, 20 like coffee and 6 like both. How many like only tea? (a) 16 (b) 14 (c) 22 (d) 17
37. 37.In a class of 38 children, 28 like dance, 12 like music and 7 like neither. How many like both? (a) 7 (b) 31 (c) 2 (d) 9
38. 38.In a class of 25 children, 15 like maths, 12 like science and 7 like neither. How many like both? (a) 18 (b) 2 (c) 9 (d) 7
39. 39.In a class of 21 children, 7 like maths, 9 like science and 8 like neither. How many like both? (a) 4 (b) 13 (c) 3 (d) 8
40. 40.In a class of 35 children, 11 like cricket, 20 like football and 3 like both. How many like neither? (a) 10 (b) 7 (c) 4 (d) 3

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