Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 18 · 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 36 children, 16 like maths, 17 like science and 5 like both. How many like at least one of the two? (a) 36 (b) 33 (c) 28 (d) 23
2. 2.In a class of 41 children, 22 like dance, 17 like music and 3 like both. How many like at least one of the two? (a) 36 (b) 41 (c) 33 (d) 39
3. 3.In a class of 39 children, 15 like mangoes, 25 like bananas and 11 like both. How many like at least one of the two? (a) 40 (b) 39 (c) 29 (d) 18
4. 4.In a class of 47 children, 20 like cricket, 24 like football and 4 like both. How many like only cricket? (a) 16 (b) 4 (c) 20 (d) 23
5. 5.In a class of 27 children, 13 like dance, 20 like music and 7 like both. How many like only dance? (a) 7 (b) 13 (c) 5 (d) 6
6. 6.In a class of 25 children, 16 like cricket, 20 like football and 12 like both. How many like only cricket? (a) 5 (b) 4 (c) 16 (d) 8
7. 7.In a class of 39 children, 19 like tea, 26 like coffee and 12 like both. How many like neither? (a) 12 (b) 7 (c) 18 (d) 6
8. 8.In a class of 24 children, 13 like maths, 7 like science and 2 like both. How many like neither? (a) 6 (b) 8 (c) 2 (d) 4
9. 9.In a class of 32 children, 20 like mangoes, 14 like bananas and 8 like neither. How many like both? (a) 24 (b) 2 (c) 8 (d) 10
10. 10.In a class of 18 children, 12 like tea, 6 like coffee and 3 like both. How many like at least one of the two? (a) 15 (b) 16 (c) 12 (d) 18
11. 11.In a class of 35 children, 17 like mangoes, 15 like bananas and 10 like neither. How many like both? (a) 7 (b) 8 (c) 10 (d) 25
12. 12.In a class of 40 children, 13 like dance, 22 like music and 2 like both. How many like neither? (a) 9 (b) 7 (c) 2 (d) 5
13. 13.In a class of 51 children, 30 like tea, 22 like coffee and 11 like both. How many like neither? (a) 9 (b) 11 (c) 21 (d) 10
14. 14.In a class of 41 children, 11 like cricket, 24 like football and 10 like neither. How many like both? (a) 10 (b) 4 (c) 5 (d) 31
15. 15.In a class of 28 children, 11 like cricket, 17 like football and 7 like neither. How many like both? (a) 21 (b) 6 (c) 8 (d) 7
16. 16.In a class of 16 children, 7 like maths, 9 like science and 4 like both. How many like only maths? (a) 4 (b) 3 (c) 5 (d) 7
17. 17.In a class of 30 children, 10 like maths, 14 like science and 2 like both. How many like only maths? (a) 8 (b) 16 (c) 12 (d) 10
18. 18.In a class of 42 children, 18 like maths, 27 like science and 10 like both. How many like at least one of the two? (a) 35 (b) 45 (c) 42 (d) 25
19. 19.In a class of 49 children, 26 like maths, 26 like science and 9 like both. How many like neither? (a) 9 (b) 15 (c) 7 (d) 6
20. 20.In a class of 45 children, 28 like cricket, 28 like football and 12 like both. How many like neither? (a) 2 (b) 12 (c) 13 (d) 1
21. 21.In a class of 42 children, 27 like maths, 17 like science and 9 like neither. How many like both? (a) 9 (b) 11 (c) 2 (d) 33
22. 22.In a class of 35 children, 24 like maths, 13 like science and 5 like both. How many like at least one of the two? (a) 27 (b) 35 (c) 37 (d) 32
23. 23.In a class of 24 children, 17 like cricket, 14 like football and 10 like both. How many like only cricket? (a) 7 (b) 17 (c) 10 (d) 4
24. 24.In a class of 23 children, 17 like maths, 14 like science and 9 like both. How many like at least one of the two? (a) 13 (b) 22 (c) 23 (d) 31
25. 25.In a class of 31 children, 17 like mangoes, 18 like bananas and 8 like both. How many like neither? (a) 12 (b) 5 (c) 8 (d) 4
26. 26.In a class of 45 children, 24 like cricket, 24 like football and 10 like both. How many like at least one of the two? (a) 48 (b) 28 (c) 38 (d) 45
27. 27.In a class of 28 children, 11 like mangoes, 17 like bananas and 7 like both. How many like at least one of the two? (a) 14 (b) 21 (c) 28 (d) 22
28. 28.In a class of 44 children, 25 like cricket, 17 like football and 5 like both. How many like neither? (a) 2 (b) 5 (c) 7 (d) 12
29. 29.In a class of 28 children, 10 like mangoes, 18 like bananas and 4 like both. How many like at least one of the two? (a) 24 (b) 20 (c) 28 (d) 25
30. 30.In a class of 19 children, 13 like cricket, 13 like football and 9 like both. How many like only cricket? (a) 6 (b) 4 (c) 13 (d) 9
31. 31.In a class of 54 children, 29 like cricket, 26 like football and 9 like both. How many like neither? (a) 7 (b) 9 (c) 8 (d) 17
32. 32.In a class of 53 children, 32 like cricket, 30 like football and 12 like both. How many like only cricket? (a) 32 (b) 23 (c) 18 (d) 20
33. 33.In a class of 43 children, 13 like maths, 27 like science and 7 like both. How many like at least one of the two? (a) 43 (b) 40 (c) 33 (d) 26
34. 34.In a class of 31 children, 14 like cricket, 20 like football and 6 like both. How many like neither? (a) 6 (b) 4 (c) 3 (d) 9
35. 35.In a class of 38 children, 26 like cricket, 21 like football and 11 like both. How many like neither? (a) 13 (b) 3 (c) 11 (d) 2
36. 36.In a class of 34 children, 11 like cricket, 15 like football and 10 like neither. How many like both? (a) 10 (b) 3 (c) 2 (d) 24
37. 37.In a class of 25 children, 12 like tea, 7 like coffee and 8 like neither. How many like both? (a) 8 (b) 17 (c) 2 (d) 3
38. 38.In a class of 46 children, 28 like mangoes, 28 like bananas and 11 like both. How many like at least one of the two? (a) 34 (b) 45 (c) 46 (d) 56
39. 39.In a class of 11 children, 6 like tea, 7 like coffee and 3 like both. How many like only tea? (a) 3 (b) 6 (c) 2 (d) 4
40. 40.In a class of 49 children, 26 like maths, 26 like science and 6 like both. How many like at least one of the two? (a) 40 (b) 52 (c) 49 (d) 46

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