Venn Diagram Worksheet for Maths Olympiad

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

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