Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 25 · 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 43 children, 21 like tea, 18 like coffee and 9 like neither. How many like both? (a) 34 (b) 6 (c) 9 (d) 5
2. 2.In a class of 44 children, 17 like tea, 31 like coffee and 12 like both. How many like at least one of the two? (a) 24 (b) 44 (c) 36 (d) 48
3. 3.In a class of 26 children, 6 like maths, 22 like science and 1 like neither. How many like both? (a) 2 (b) 1 (c) 3 (d) 25
4. 4.In a class of 52 children, 29 like dance, 24 like music and 11 like both. How many like only dance? (a) 18 (b) 13 (c) 29 (d) 28
5. 5.In a class of 27 children, 20 like tea, 7 like coffee and 2 like both. How many like only tea? (a) 18 (b) 20 (c) 5 (d) 2
6. 6.In a class of 33 children, 19 like mangoes, 14 like bananas and 4 like both. How many like neither? (a) 8 (b) 5 (c) 4 (d) 0
7. 7.In a class of 29 children, 22 like maths, 8 like science and 4 like both. How many like only maths? (a) 18 (b) 21 (c) 22 (d) 4
8. 8.In a class of 37 children, 12 like mangoes, 20 like bananas and 2 like both. How many like neither? (a) 7 (b) 2 (c) 5 (d) 9
9. 9.In a class of 41 children, 20 like maths, 23 like science and 7 like both. How many like at least one of the two? (a) 43 (b) 36 (c) 41 (d) 29
10. 10.In a class of 40 children, 19 like maths, 18 like science and 7 like both. How many like neither? (a) 17 (b) 7 (c) 3 (d) 10
11. 11.In a class of 37 children, 12 like tea, 26 like coffee and 5 like neither. How many like both? (a) 1 (b) 6 (c) 32 (d) 5
12. 12.In a class of 33 children, 14 like mangoes, 23 like bananas and 1 like neither. How many like both? (a) 4 (b) 5 (c) 1 (d) 32
13. 13.In a class of 21 children, 15 like tea, 12 like coffee and 7 like both. How many like only tea? (a) 5 (b) 15 (c) 9 (d) 8
14. 14.In a class of 38 children, 15 like cricket, 32 like football and 12 like both. How many like only cricket? (a) 3 (b) 15 (c) 20 (d) 6
15. 15.In a class of 19 children, 14 like maths, 12 like science and 9 like both. How many like neither? (a) 3 (b) 2 (c) 11 (d) 9
16. 16.In a class of 29 children, 8 like tea, 20 like coffee and 2 like both. How many like neither? (a) 2 (b) 5 (c) 3 (d) 1
17. 17.In a class of 44 children, 25 like maths, 28 like science and 11 like both. How many like at least one of the two? (a) 53 (b) 31 (c) 44 (d) 42
18. 18.In a class of 32 children, 13 like mangoes, 17 like bananas and 7 like both. How many like neither? (a) 7 (b) 2 (c) 9 (d) 16
19. 19.In a class of 28 children, 13 like cricket, 17 like football and 8 like both. How many like at least one of the two? (a) 30 (b) 14 (c) 28 (d) 22
20. 20.In a class of 31 children, 18 like tea, 19 like coffee and 8 like both. How many like at least one of the two? (a) 21 (b) 37 (c) 29 (d) 31
21. 21.In a class of 30 children, 16 like maths, 10 like science and 3 like both. How many like at least one of the two? (a) 20 (b) 26 (c) 23 (d) 30
22. 22.In a class of 20 children, 11 like maths, 12 like science and 7 like both. How many like neither? (a) 7 (b) 5 (c) 11 (d) 4
23. 23.In a class of 38 children, 17 like cricket, 24 like football and 6 like neither. How many like both? (a) 9 (b) 32 (c) 3 (d) 6
24. 24.In a class of 44 children, 25 like cricket, 23 like football and 6 like both. How many like only cricket? (a) 21 (b) 17 (c) 19 (d) 25
25. 25.In a class of 27 children, 7 like maths, 13 like science and 9 like neither. How many like both? (a) 2 (b) 9 (c) 3 (d) 18
26. 26.In a class of 20 children, 12 like tea, 14 like coffee and 8 like both. How many like at least one of the two? (a) 26 (b) 20 (c) 10 (d) 18
27. 27.In a class of 22 children, 11 like tea, 10 like coffee and 6 like both. How many like neither? (a) 6 (b) 1 (c) 13 (d) 7
28. 28.In a class of 49 children, 24 like cricket, 21 like football and 5 like both. How many like neither? (a) 4 (b) 14 (c) 5 (d) 9
29. 29.In a class of 39 children, 14 like dance, 17 like music and 2 like both. How many like at least one of the two? (a) 31 (b) 27 (c) 39 (d) 29
30. 30.In a class of 36 children, 18 like dance, 19 like music and 11 like both. How many like at least one of the two? (a) 26 (b) 37 (c) 36 (d) 15
31. 31.In a class of 18 children, 9 like tea, 8 like coffee and 5 like both. How many like at least one of the two? (a) 17 (b) 12 (c) 18 (d) 7
32. 32.In a class of 42 children, 17 like mangoes, 29 like bananas and 11 like both. How many like at least one of the two? (a) 42 (b) 35 (c) 24 (d) 46
33. 33.In a class of 17 children, 13 like dance, 9 like music and 6 like both. How many like at least one of the two? (a) 17 (b) 16 (c) 10 (d) 22
34. 34.In a class of 26 children, 13 like maths, 16 like science and 5 like both. How many like neither? (a) 3 (b) 7 (c) 5 (d) 2
35. 35.In a class of 26 children, 8 like cricket, 12 like football and 8 like neither. How many like both? (a) 2 (b) 18 (c) 3 (d) 8
36. 36.In a class of 36 children, 12 like cricket, 20 like football and 10 like neither. How many like both? (a) 7 (b) 26 (c) 10 (d) 6
37. 37.In a class of 48 children, 27 like dance, 23 like music and 11 like both. How many like neither? (a) 10 (b) 9 (c) 11 (d) 20
38. 38.In a class of 18 children, 12 like dance, 11 like music and 6 like both. How many like at least one of the two? (a) 23 (b) 11 (c) 17 (d) 18
39. 39.In a class of 35 children, 19 like maths, 19 like science and 10 like both. How many like only maths? (a) 10 (b) 16 (c) 9 (d) 19
40. 40.In a class of 28 children, 18 like cricket, 17 like football and 10 like both. How many like at least one of the two? (a) 35 (b) 28 (c) 15 (d) 25

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