Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 83 · 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 21 children, 13 like tea, 13 like coffee and 7 like both. How many like only tea? (a) 7 (b) 13 (c) 8 (d) 6
2. 2.In a class of 32 children, 12 like dance, 26 like music and 9 like both. How many like at least one of the two? (a) 29 (b) 38 (c) 20 (d) 32
3. 3.In a class of 33 children, 13 like cricket, 23 like football and 6 like both. How many like only cricket? (a) 10 (b) 7 (c) 17 (d) 13
4. 4.In a class of 46 children, 24 like maths, 22 like science and 4 like both. How many like neither? (a) 8 (b) 5 (c) 0 (d) 4
5. 5.In a class of 33 children, 10 like mangoes, 22 like bananas and 4 like both. How many like only mangoes? (a) 11 (b) 18 (c) 10 (d) 6
6. 6.In a class of 45 children, 21 like tea, 22 like coffee and 2 like both. How many like neither? (a) 6 (b) 5 (c) 2 (d) 4
7. 7.In a class of 36 children, 10 like cricket, 27 like football and 7 like both. How many like at least one of the two? (a) 30 (b) 36 (c) 37 (d) 23
8. 8.In a class of 19 children, 8 like maths, 12 like science and 4 like both. How many like at least one of the two? (a) 12 (b) 19 (c) 16 (d) 20
9. 9.In a class of 22 children, 7 like dance, 18 like music and 4 like both. How many like only dance? (a) 3 (b) 14 (c) 7 (d) 4
10. 10.In a class of 44 children, 22 like maths, 21 like science and 2 like both. How many like at least one of the two? (a) 39 (b) 44 (c) 43 (d) 41
11. 11.In a class of 28 children, 18 like tea, 8 like coffee and 6 like neither. How many like both? (a) 22 (b) 5 (c) 4 (d) 6
12. 12.In a class of 43 children, 25 like dance, 19 like music and 9 like both. How many like at least one of the two? (a) 44 (b) 26 (c) 43 (d) 35
13. 13.In a class of 33 children, 23 like cricket, 13 like football and 7 like neither. How many like both? (a) 7 (b) 3 (c) 26 (d) 10
14. 14.In a class of 53 children, 28 like cricket, 28 like football and 6 like neither. How many like both? (a) 6 (b) 9 (c) 47 (d) 3
15. 15.In a class of 45 children, 26 like mangoes, 29 like bananas and 11 like both. How many like only mangoes? (a) 15 (b) 18 (c) 26 (d) 16
16. 16.In a class of 21 children, 12 like maths, 11 like science and 7 like both. How many like neither? (a) 6 (b) 5 (c) 12 (d) 7
17. 17.In a class of 24 children, 6 like dance, 19 like music and 3 like both. How many like at least one of the two? (a) 24 (b) 25 (c) 22 (d) 19
18. 18.In a class of 25 children, 12 like maths, 12 like science and 4 like both. How many like only maths? (a) 12 (b) 4 (c) 8 (d) 13
19. 19.In a class of 39 children, 22 like mangoes, 14 like bananas and 5 like both. How many like at least one of the two? (a) 26 (b) 36 (c) 39 (d) 31
20. 20.In a class of 23 children, 9 like cricket, 17 like football and 3 like neither. How many like both? (a) 3 (b) 7 (c) 20 (d) 6
21. 21.In a class of 18 children, 5 like dance, 11 like music and 2 like both. How many like only dance? (a) 7 (b) 3 (c) 9 (d) 5
22. 22.In a class of 31 children, 19 like tea, 10 like coffee and 7 like neither. How many like both? (a) 5 (b) 24 (c) 7 (d) 6
23. 23.In a class of 38 children, 10 like cricket, 26 like football and 6 like both. How many like neither? (a) 14 (b) 2 (c) 8 (d) 6
24. 24.In a class of 25 children, 6 like maths, 17 like science and 3 like both. How many like only maths? (a) 14 (b) 8 (c) 3 (d) 6
25. 25.In a class of 56 children, 27 like cricket, 28 like football and 9 like neither. How many like both? (a) 47 (b) 9 (c) 7 (d) 8
26. 26.In a class of 36 children, 12 like maths, 21 like science and 4 like both. How many like at least one of the two? (a) 33 (b) 29 (c) 36 (d) 25
27. 27.In a class of 25 children, 12 like dance, 10 like music and 2 like both. How many like at least one of the two? (a) 25 (b) 18 (c) 20 (d) 22
28. 28.In a class of 38 children, 23 like dance, 24 like music and 12 like both. How many like neither? (a) 4 (b) 12 (c) 3 (d) 15
29. 29.In a class of 39 children, 24 like maths, 14 like science and 6 like both. How many like at least one of the two? (a) 26 (b) 38 (c) 39 (d) 32
30. 30.In a class of 25 children, 15 like maths, 11 like science and 4 like both. How many like only maths? (a) 7 (b) 14 (c) 11 (d) 15
31. 31.In a class of 33 children, 7 like cricket, 19 like football and 2 like both. How many like neither? (a) 2 (b) 7 (c) 9 (d) 11
32. 32.In a class of 45 children, 29 like cricket, 20 like football and 11 like both. How many like only cricket? (a) 25 (b) 29 (c) 9 (d) 18
33. 33.In a class of 34 children, 27 like cricket, 14 like football and 10 like both. How many like neither? (a) 10 (b) 13 (c) 3 (d) 4
34. 34.In a class of 51 children, 24 like tea, 23 like coffee and 6 like both. How many like neither? (a) 10 (b) 6 (c) 4 (d) 16
35. 35.In a class of 35 children, 25 like dance, 13 like music and 6 like both. How many like only dance? (a) 7 (b) 22 (c) 25 (d) 19
36. 36.In a class of 40 children, 27 like tea, 19 like coffee and 10 like both. How many like neither? (a) 14 (b) 10 (c) 5 (d) 4
37. 37.In a class of 49 children, 23 like tea, 24 like coffee and 8 like both. How many like neither? (a) 18 (b) 2 (c) 8 (d) 10
38. 38.In a class of 30 children, 22 like tea, 8 like coffee and 5 like neither. How many like both? (a) 5 (b) 4 (c) 25 (d) 6
39. 39.In a class of 24 children, 14 like dance, 17 like music and 9 like both. How many like neither? (a) 2 (b) 11 (c) 9 (d) 3
40. 40.In a class of 34 children, 15 like cricket, 18 like football and 10 like neither. How many like both? (a) 8 (b) 9 (c) 10 (d) 24

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