Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 19 · 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 54 children, 26 like maths, 27 like science and 9 like both. How many like at least one of the two? (a) 53 (b) 44 (c) 54 (d) 35
2. 2.In a class of 18 children, 8 like maths, 8 like science and 3 like both. How many like neither? (a) 8 (b) 2 (c) 3 (d) 5
3. 3.In a class of 31 children, 11 like dance, 15 like music and 4 like both. How many like only dance? (a) 4 (b) 11 (c) 16 (d) 7
4. 4.In a class of 36 children, 17 like dance, 26 like music and 8 like both. How many like only dance? (a) 9 (b) 18 (c) 10 (d) 17
5. 5.In a class of 41 children, 13 like maths, 24 like science and 6 like both. How many like neither? (a) 6 (b) 4 (c) 10 (d) 16
6. 6.In a class of 54 children, 27 like maths, 30 like science and 10 like both. How many like at least one of the two? (a) 37 (b) 57 (c) 54 (d) 47
7. 7.In a class of 27 children, 17 like cricket, 16 like football and 11 like both. How many like neither? (a) 16 (b) 6 (c) 11 (d) 5
8. 8.In a class of 48 children, 27 like cricket, 25 like football and 9 like both. How many like at least one of the two? (a) 34 (b) 48 (c) 52 (d) 43
9. 9.In a class of 41 children, 13 like cricket, 20 like football and 2 like both. How many like at least one of the two? (a) 33 (b) 29 (c) 41 (d) 31
10. 10.In a class of 32 children, 20 like dance, 12 like music and 6 like neither. How many like both? (a) 5 (b) 7 (c) 26 (d) 6
11. 11.In a class of 50 children, 25 like mangoes, 25 like bananas and 5 like both. How many like neither? (a) 6 (b) 5 (c) 0 (d) 10
12. 12.In a class of 24 children, 15 like mangoes, 15 like bananas and 11 like both. How many like at least one of the two? (a) 24 (b) 30 (c) 19 (d) 8
13. 13.In a class of 41 children, 21 like dance, 19 like music and 9 like neither. How many like both? (a) 32 (b) 8 (c) 9 (d) 7
14. 14.In a class of 30 children, 17 like dance, 11 like music and 8 like neither. How many like both? (a) 7 (b) 6 (c) 22 (d) 8
15. 15.In a class of 40 children, 19 like tea, 27 like coffee and 12 like both. How many like neither? (a) 18 (b) 6 (c) 7 (d) 12
16. 16.In a class of 27 children, 19 like maths, 8 like science and 5 like both. How many like at least one of the two? (a) 17 (b) 23 (c) 27 (d) 22
17. 17.In a class of 24 children, 15 like cricket, 16 like football and 11 like both. How many like at least one of the two? (a) 31 (b) 20 (c) 24 (d) 9
18. 18.In a class of 32 children, 21 like mangoes, 14 like bananas and 1 like neither. How many like both? (a) 31 (b) 4 (c) 1 (d) 3
19. 19.In a class of 18 children, 12 like cricket, 9 like football and 5 like both. How many like at least one of the two? (a) 11 (b) 21 (c) 18 (d) 16
20. 20.In a class of 33 children, 12 like mangoes, 22 like bananas and 1 like neither. How many like both? (a) 1 (b) 32 (c) 2 (d) 3
21. 21.In a class of 50 children, 21 like tea, 30 like coffee and 11 like both. How many like neither? (a) 9 (b) 10 (c) 21 (d) 11
22. 22.In a class of 29 children, 12 like tea, 15 like coffee and 5 like both. How many like neither? (a) 2 (b) 5 (c) 7 (d) 12
23. 23.In a class of 29 children, 15 like maths, 19 like science and 6 like neither. How many like both? (a) 6 (b) 23 (c) 5 (d) 11
24. 24.In a class of 38 children, 25 like cricket, 19 like football and 9 like both. How many like at least one of the two? (a) 44 (b) 38 (c) 26 (d) 35
25. 25.In a class of 24 children, 15 like mangoes, 8 like bananas and 3 like both. How many like only mangoes? (a) 16 (b) 5 (c) 12 (d) 15
26. 26.In a class of 47 children, 28 like cricket, 25 like football and 9 like both. How many like at least one of the two? (a) 35 (b) 44 (c) 47 (d) 53
27. 27.In a class of 27 children, 16 like dance, 15 like music and 5 like both. How many like only dance? (a) 16 (b) 10 (c) 11 (d) 12
28. 28.In a class of 44 children, 28 like maths, 22 like science and 10 like both. How many like only maths? (a) 28 (b) 18 (c) 22 (d) 12
29. 29.In a class of 46 children, 26 like dance, 28 like music and 10 like both. How many like at least one of the two? (a) 34 (b) 44 (c) 46 (d) 54
30. 30.In a class of 49 children, 30 like mangoes, 29 like bananas and 2 like neither. How many like both? (a) 47 (b) 12 (c) 10 (d) 2
31. 31.In a class of 28 children, 12 like dance, 20 like music and 5 like neither. How many like both? (a) 5 (b) 9 (c) 23 (d) 4
32. 32.In a class of 41 children, 15 like maths, 25 like science and 6 like both. How many like only maths? (a) 15 (b) 19 (c) 9 (d) 16
33. 33.In a class of 24 children, 15 like tea, 10 like coffee and 5 like neither. How many like both? (a) 5 (b) 1 (c) 19 (d) 6
34. 34.In a class of 48 children, 26 like mangoes, 24 like bananas and 9 like neither. How many like both? (a) 39 (b) 2 (c) 9 (d) 11
35. 35.In a class of 23 children, 10 like mangoes, 16 like bananas and 4 like both. How many like neither? (a) 2 (b) 1 (c) 4 (d) 5
36. 36.In a class of 33 children, 19 like tea, 11 like coffee and 2 like both. How many like only tea? (a) 22 (b) 17 (c) 9 (d) 19
37. 37.In a class of 41 children, 21 like dance, 28 like music and 9 like both. How many like only dance? (a) 12 (b) 21 (c) 19 (d) 13
38. 38.In a class of 45 children, 28 like maths, 20 like science and 12 like both. How many like at least one of the two? (a) 36 (b) 45 (c) 48 (d) 24
39. 39.In a class of 29 children, 13 like cricket, 14 like football and 7 like both. How many like at least one of the two? (a) 29 (b) 20 (c) 13 (d) 27
40. 40.In a class of 30 children, 19 like tea, 16 like coffee and 11 like both. How many like at least one of the two? (a) 30 (b) 35 (c) 24 (d) 13

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