Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 292 · 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, 14 like dance, 16 like music and 8 like both. How many like neither? (a) 4 (b) 12 (c) 8 (d) 5
2. 2.In a class of 29 children, 12 like tea, 21 like coffee and 5 like neither. How many like both? (a) 4 (b) 24 (c) 9 (d) 5
3. 3.In a class of 50 children, 28 like cricket, 27 like football and 6 like neither. How many like both? (a) 6 (b) 44 (c) 5 (d) 11
4. 4.In a class of 33 children, 9 like mangoes, 22 like bananas and 5 like neither. How many like both? (a) 4 (b) 3 (c) 28 (d) 5
5. 5.In a class of 31 children, 17 like cricket, 11 like football and 6 like both. How many like neither? (a) 6 (b) 15 (c) 3 (d) 9
6. 6.In a class of 34 children, 12 like maths, 23 like science and 3 like neither. How many like both? (a) 4 (b) 31 (c) 3 (d) 1
7. 7.In a class of 27 children, 10 like maths, 13 like science and 2 like both. How many like only maths? (a) 10 (b) 8 (c) 14 (d) 11
8. 8.In a class of 29 children, 15 like mangoes, 17 like bananas and 4 like both. How many like at least one of the two? (a) 29 (b) 32 (c) 28 (d) 24
9. 9.In a class of 34 children, 9 like maths, 23 like science and 5 like both. How many like at least one of the two? (a) 32 (b) 27 (c) 22 (d) 34
10. 10.In a class of 27 children, 17 like dance, 10 like music and 4 like both. How many like at least one of the two? (a) 23 (b) 24 (c) 19 (d) 27
11. 11.In a class of 34 children, 18 like tea, 19 like coffee and 5 like neither. How many like both? (a) 3 (b) 8 (c) 29 (d) 5
12. 12.In a class of 38 children, 14 like dance, 20 like music and 3 like both. How many like at least one of the two? (a) 34 (b) 28 (c) 38 (d) 31
13. 13.In a class of 24 children, 10 like dance, 9 like music and 4 like both. How many like at least one of the two? (a) 19 (b) 24 (c) 11 (d) 15
14. 14.In a class of 28 children, 9 like cricket, 20 like football and 1 like neither. How many like both? (a) 2 (b) 1 (c) 3 (d) 27
15. 15.In a class of 25 children, 8 like maths, 13 like science and 5 like both. How many like only maths? (a) 8 (b) 5 (c) 3 (d) 12
16. 16.In a class of 46 children, 25 like cricket, 26 like football and 8 like both. How many like at least one of the two? (a) 46 (b) 51 (c) 43 (d) 35
17. 17.In a class of 32 children, 12 like cricket, 23 like football and 6 like both. How many like neither? (a) 4 (b) 9 (c) 3 (d) 6
18. 18.In a class of 45 children, 19 like mangoes, 20 like bananas and 2 like both. How many like only mangoes? (a) 19 (b) 25 (c) 18 (d) 17
19. 19.In a class of 48 children, 25 like dance, 29 like music and 12 like both. How many like only dance? (a) 25 (b) 17 (c) 13 (d) 19
20. 20.In a class of 29 children, 14 like maths, 23 like science and 9 like both. How many like neither? (a) 1 (b) 10 (c) 2 (d) 9
21. 21.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) 39 (b) 42 (c) 43 (d) 41
22. 22.In a class of 22 children, 15 like cricket, 9 like football and 5 like both. How many like neither? (a) 3 (b) 8 (c) 4 (d) 5
23. 23.In a class of 40 children, 29 like dance, 21 like music and 12 like both. How many like only dance? (a) 19 (b) 17 (c) 29 (d) 9
24. 24.In a class of 41 children, 18 like tea, 19 like coffee and 6 like both. How many like only tea? (a) 22 (b) 12 (c) 13 (d) 18
25. 25.In a class of 36 children, 22 like mangoes, 12 like bananas and 3 like both. How many like at least one of the two? (a) 36 (b) 28 (c) 34 (d) 31
26. 26.In a class of 47 children, 21 like mangoes, 23 like bananas and 6 like both. How many like only mangoes? (a) 15 (b) 17 (c) 24 (d) 21
27. 27.In a class of 27 children, 11 like maths, 16 like science and 6 like both. How many like at least one of the two? (a) 15 (b) 27 (c) 21 (d) 22
28. 28.In a class of 33 children, 11 like mangoes, 25 like bananas and 6 like both. How many like neither? (a) 6 (b) 9 (c) 3 (d) 4
29. 29.In a class of 39 children, 26 like tea, 11 like coffee and 8 like both. How many like only tea? (a) 28 (b) 18 (c) 3 (d) 26
30. 30.In a class of 42 children, 19 like mangoes, 21 like bananas and 3 like both. How many like at least one of the two? (a) 40 (b) 42 (c) 37 (d) 34
31. 31.In a class of 34 children, 23 like tea, 10 like coffee and 3 like both. How many like only tea? (a) 24 (b) 7 (c) 23 (d) 20
32. 32.In a class of 40 children, 13 like maths, 27 like science and 9 like both. How many like at least one of the two? (a) 32 (b) 22 (c) 40 (d) 31
33. 33.In a class of 40 children, 26 like maths, 15 like science and 11 like both. How many like only maths? (a) 25 (b) 26 (c) 4 (d) 15
34. 34.In a class of 21 children, 15 like tea, 13 like coffee and 10 like both. How many like neither? (a) 13 (b) 3 (c) 4 (d) 10
35. 35.In a class of 31 children, 10 like tea, 20 like coffee and 7 like both. How many like only tea? (a) 10 (b) 13 (c) 11 (d) 3
36. 36.In a class of 46 children, 25 like tea, 24 like coffee and 9 like neither. How many like both? (a) 12 (b) 9 (c) 3 (d) 37
37. 37.In a class of 40 children, 28 like dance, 12 like music and 9 like both. How many like only dance? (a) 9 (b) 3 (c) 19 (d) 28
38. 38.In a class of 29 children, 18 like cricket, 7 like football and 3 like both. How many like at least one of the two? (a) 22 (b) 29 (c) 19 (d) 25
39. 39.In a class of 43 children, 15 like mangoes, 23 like bananas and 4 like both. How many like at least one of the two? (a) 34 (b) 30 (c) 38 (d) 43
40. 40.In a class of 38 children, 19 like maths, 22 like science and 3 like neither. How many like both? (a) 7 (b) 35 (c) 3 (d) 6

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