Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 5 · 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, 6 like cricket, 22 like football and 3 like both. How many like only cricket? (a) 19 (b) 4 (c) 3 (d) 6
2. 2.In a class of 23 children, 14 like maths, 5 like science and 2 like both. How many like neither? (a) 2 (b) 4 (c) 6 (d) 8
3. 3.In a class of 35 children, 15 like cricket, 17 like football and 6 like both. How many like only cricket? (a) 11 (b) 9 (c) 15 (d) 18
4. 4.In a class of 26 children, 7 like dance, 12 like music and 3 like both. How many like only dance? (a) 9 (b) 4 (c) 14 (d) 7
5. 5.In a class of 54 children, 31 like maths, 27 like science and 11 like both. How many like at least one of the two? (a) 36 (b) 58 (c) 47 (d) 54
6. 6.In a class of 20 children, 12 like dance, 9 like music and 5 like both. How many like at least one of the two? (a) 16 (b) 11 (c) 20 (d) 21
7. 7.In a class of 40 children, 26 like dance, 21 like music and 10 like both. How many like at least one of the two? (a) 40 (b) 47 (c) 37 (d) 27
8. 8.In a class of 27 children, 7 like cricket, 21 like football and 2 like both. How many like only cricket? (a) 5 (b) 6 (c) 19 (d) 7
9. 9.In a class of 31 children, 10 like maths, 20 like science and 7 like both. How many like only maths? (a) 3 (b) 10 (c) 11 (d) 13
10. 10.In a class of 38 children, 13 like tea, 21 like coffee and 2 like both. How many like only tea? (a) 11 (b) 19 (c) 13 (d) 17
11. 11.In a class of 33 children, 19 like dance, 16 like music and 5 like both. How many like at least one of the two? (a) 35 (b) 33 (c) 30 (d) 25
12. 12.In a class of 40 children, 23 like mangoes, 21 like bananas and 2 like neither. How many like both? (a) 6 (b) 38 (c) 4 (d) 2
13. 13.In a class of 33 children, 20 like dance, 8 like music and 2 like both. How many like at least one of the two? (a) 26 (b) 24 (c) 33 (d) 28
14. 14.In a class of 49 children, 22 like mangoes, 27 like bananas and 7 like neither. How many like both? (a) 8 (b) 42 (c) 6 (d) 7
15. 15.In a class of 24 children, 13 like maths, 13 like science and 7 like both. How many like neither? (a) 6 (b) 12 (c) 7 (d) 5
16. 16.In a class of 29 children, 20 like maths, 9 like science and 2 like both. How many like at least one of the two? (a) 29 (b) 28 (c) 25 (d) 27
17. 17.In a class of 32 children, 10 like maths, 19 like science and 3 like both. How many like at least one of the two? (a) 29 (b) 32 (c) 26 (d) 23
18. 18.In a class of 27 children, 7 like tea, 19 like coffee and 2 like both. How many like neither? (a) 5 (b) 3 (c) 2 (d) 1
19. 19.In a class of 28 children, 16 like tea, 18 like coffee and 11 like both. How many like only tea? (a) 10 (b) 16 (c) 7 (d) 5
20. 20.In a class of 48 children, 26 like cricket, 29 like football and 9 like both. How many like only cricket? (a) 20 (b) 17 (c) 19 (d) 26
21. 21.In a class of 42 children, 12 like dance, 22 like music and 10 like neither. How many like both? (a) 32 (b) 3 (c) 10 (d) 2
22. 22.In a class of 23 children, 10 like cricket, 12 like football and 7 like both. How many like neither? (a) 15 (b) 8 (c) 1 (d) 7
23. 23.In a class of 38 children, 9 like maths, 21 like science and 10 like neither. How many like both? (a) 2 (b) 10 (c) 3 (d) 28
24. 24.In a class of 23 children, 10 like tea, 10 like coffee and 7 like both. How many like at least one of the two? (a) 13 (b) 6 (c) 20 (d) 23
25. 25.In a class of 14 children, 8 like cricket, 6 like football and 3 like both. How many like neither? (a) 6 (b) 0 (c) 4 (d) 3
26. 26.In a class of 34 children, 26 like maths, 17 like science and 10 like both. How many like only maths? (a) 26 (b) 17 (c) 7 (d) 16
27. 27.In a class of 27 children, 15 like maths, 8 like science and 2 like both. How many like only maths? (a) 19 (b) 15 (c) 6 (d) 13
28. 28.In a class of 43 children, 31 like maths, 18 like science and 5 like neither. How many like both? (a) 11 (b) 6 (c) 5 (d) 38
29. 29.In a class of 34 children, 22 like tea, 11 like coffee and 7 like neither. How many like both? (a) 5 (b) 6 (c) 27 (d) 7
30. 30.In a class of 46 children, 30 like maths, 18 like science and 11 like both. How many like at least one of the two? (a) 48 (b) 26 (c) 46 (d) 37
31. 31.In a class of 32 children, 9 like maths, 25 like science and 6 like both. How many like neither? (a) 10 (b) 6 (c) 4 (d) 5
32. 32.In a class of 34 children, 21 like cricket, 13 like football and 2 like both. How many like only cricket? (a) 21 (b) 11 (c) 2 (d) 19
33. 33.In a class of 52 children, 30 like dance, 29 like music and 12 like both. How many like only dance? (a) 17 (b) 30 (c) 18 (d) 23
34. 34.In a class of 28 children, 15 like maths, 20 like science and 4 like neither. How many like both? (a) 7 (b) 4 (c) 24 (d) 11
35. 35.In a class of 36 children, 22 like cricket, 18 like football and 6 like both. How many like only cricket? (a) 18 (b) 22 (c) 16 (d) 12
36. 36.In a class of 39 children, 29 like maths, 19 like science and 10 like both. How many like neither? (a) 1 (b) 10 (c) 2 (d) 11
37. 37.In a class of 39 children, 21 like dance, 16 like music and 7 like both. How many like only dance? (a) 9 (b) 14 (c) 23 (d) 21
38. 38.In a class of 23 children, 13 like mangoes, 13 like bananas and 2 like neither. How many like both? (a) 21 (b) 5 (c) 2 (d) 3
39. 39.In a class of 36 children, 20 like mangoes, 10 like bananas and 4 like both. How many like at least one of the two? (a) 30 (b) 26 (c) 36 (d) 22
40. 40.In a class of 39 children, 24 like tea, 12 like coffee and 4 like both. How many like neither? (a) 7 (b) 4 (c) 11 (d) 3

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