Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 633 · 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, 28 like maths, 25 like science and 8 like both. How many like at least one of the two? (a) 54 (b) 45 (c) 53 (d) 37
2. 2.In a class of 33 children, 16 like tea, 15 like coffee and 6 like neither. How many like both? (a) 5 (b) 27 (c) 4 (d) 6
3. 3.In a class of 39 children, 21 like tea, 26 like coffee and 10 like both. How many like only tea? (a) 11 (b) 13 (c) 21 (d) 16
4. 4.In a class of 36 children, 24 like mangoes, 17 like bananas and 12 like both. How many like neither? (a) 12 (b) 7 (c) 8 (d) 19
5. 5.In a class of 40 children, 22 like mangoes, 25 like bananas and 9 like both. How many like only mangoes? (a) 15 (b) 13 (c) 16 (d) 22
6. 6.In a class of 40 children, 15 like tea, 24 like coffee and 6 like neither. How many like both? (a) 5 (b) 4 (c) 6 (d) 34
7. 7.In a class of 38 children, 13 like tea, 27 like coffee and 8 like both. How many like only tea? (a) 11 (b) 5 (c) 19 (d) 13
8. 8.In a class of 41 children, 23 like cricket, 27 like football and 10 like both. How many like only cricket? (a) 13 (b) 23 (c) 14 (d) 17
9. 9.In a class of 29 children, 14 like mangoes, 16 like bananas and 1 like neither. How many like both? (a) 1 (b) 2 (c) 28 (d) 3
10. 10.In a class of 38 children, 22 like mangoes, 14 like bananas and 5 like both. How many like at least one of the two? (a) 38 (b) 31 (c) 36 (d) 26
11. 11.In a class of 30 children, 21 like dance, 10 like music and 3 like both. How many like neither? (a) 1 (b) 2 (c) 3 (d) 5
12. 12.In a class of 31 children, 17 like cricket, 23 like football and 2 like neither. How many like both? (a) 2 (b) 29 (c) 11 (d) 9
13. 13.In a class of 32 children, 19 like tea, 8 like coffee and 10 like neither. How many like both? (a) 6 (b) 5 (c) 22 (d) 10
14. 14.In a class of 40 children, 13 like maths, 23 like science and 6 like both. How many like at least one of the two? (a) 36 (b) 40 (c) 24 (d) 30
15. 15.In a class of 49 children, 25 like cricket, 25 like football and 10 like both. How many like neither? (a) 9 (b) 19 (c) 8 (d) 10
16. 16.In a class of 51 children, 26 like tea, 26 like coffee and 6 like neither. How many like both? (a) 6 (b) 7 (c) 45 (d) 1
17. 17.In a class of 45 children, 28 like maths, 26 like science and 1 like neither. How many like both? (a) 44 (b) 10 (c) 1 (d) 9
18. 18.In a class of 44 children, 15 like maths, 23 like science and 9 like neither. How many like both? (a) 35 (b) 4 (c) 3 (d) 9
19. 19.In a class of 33 children, 14 like cricket, 20 like football and 4 like both. How many like at least one of the two? (a) 34 (b) 30 (c) 26 (d) 33
20. 20.In a class of 39 children, 29 like cricket, 18 like football and 9 like both. How many like only cricket? (a) 20 (b) 9 (c) 29 (d) 21
21. 21.In a class of 40 children, 22 like dance, 20 like music and 2 like neither. How many like both? (a) 4 (b) 2 (c) 38 (d) 5
22. 22.In a class of 26 children, 9 like cricket, 18 like football and 2 like both. How many like at least one of the two? (a) 25 (b) 26 (c) 23 (d) 27
23. 23.In a class of 22 children, 9 like tea, 9 like coffee and 4 like both. How many like neither? (a) 9 (b) 12 (c) 8 (d) 4
24. 24.In a class of 34 children, 24 like maths, 14 like science and 6 like both. How many like at least one of the two? (a) 38 (b) 32 (c) 26 (d) 34
25. 25.In a class of 28 children, 19 like tea, 17 like coffee and 2 like neither. How many like both? (a) 2 (b) 10 (c) 26 (d) 8
26. 26.In a class of 27 children, 19 like cricket, 13 like football and 7 like both. How many like only cricket? (a) 19 (b) 12 (c) 6 (d) 14
27. 27.In a class of 46 children, 23 like mangoes, 21 like bananas and 5 like both. How many like at least one of the two? (a) 46 (b) 34 (c) 39 (d) 44
28. 28.In a class of 38 children, 19 like dance, 14 like music and 3 like both. How many like at least one of the two? (a) 33 (b) 38 (c) 30 (d) 27
29. 29.In a class of 29 children, 6 like mangoes, 16 like bananas and 3 like both. How many like at least one of the two? (a) 19 (b) 29 (c) 16 (d) 22
30. 30.In a class of 23 children, 9 like tea, 15 like coffee and 5 like both. How many like neither? (a) 4 (b) 5 (c) 9 (d) 3
31. 31.In a class of 46 children, 30 like dance, 26 like music and 12 like both. How many like only dance? (a) 20 (b) 30 (c) 14 (d) 18
32. 32.In a class of 47 children, 23 like cricket, 20 like football and 4 like both. How many like at least one of the two? (a) 35 (b) 47 (c) 39 (d) 43
33. 33.In a class of 50 children, 29 like cricket, 27 like football and 12 like both. How many like neither? (a) 7 (b) 18 (c) 12 (d) 6
34. 34.In a class of 28 children, 16 like maths, 12 like science and 7 like both. How many like at least one of the two? (a) 22 (b) 21 (c) 14 (d) 28
35. 35.In a class of 34 children, 22 like tea, 13 like coffee and 9 like both. How many like neither? (a) 7 (b) 8 (c) 9 (d) 17
36. 36.In a class of 28 children, 21 like maths, 6 like science and 3 like both. How many like only maths? (a) 21 (b) 22 (c) 18 (d) 3
37. 37.In a class of 36 children, 28 like cricket, 16 like football and 2 like neither. How many like both? (a) 2 (b) 34 (c) 8 (d) 10
38. 38.In a class of 32 children, 18 like tea, 8 like coffee and 2 like both. How many like neither? (a) 2 (b) 10 (c) 8 (d) 6
39. 39.In a class of 42 children, 14 like tea, 20 like coffee and 2 like both. How many like only tea? (a) 14 (b) 18 (c) 22 (d) 12
40. 40.In a class of 33 children, 13 like tea, 20 like coffee and 3 like both. How many like only tea? (a) 10 (b) 17 (c) 13 (d) 3

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