Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 46 · 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 33 children, 13 like dance, 29 like music and 1 like neither. How many like both? (a) 32 (b) 10 (c) 9 (d) 1
2. 2.In a class of 42 children, 23 like dance, 19 like music and 10 like neither. How many like both? (a) 32 (b) 11 (c) 10 (d) 9
3. 3.In a class of 41 children, 22 like tea, 22 like coffee and 4 like both. How many like neither? (a) 2 (b) 5 (c) 1 (d) 4
4. 4.In a class of 36 children, 15 like maths, 20 like science and 2 like both. How many like only maths? (a) 13 (b) 16 (c) 15 (d) 18
5. 5.In a class of 39 children, 25 like cricket, 14 like football and 5 like neither. How many like both? (a) 34 (b) 4 (c) 5 (d) 6
6. 6.In a class of 37 children, 17 like maths, 29 like science and 11 like both. How many like at least one of the two? (a) 37 (b) 35 (c) 46 (d) 24
7. 7.In a class of 34 children, 20 like tea, 13 like coffee and 6 like both. How many like neither? (a) 1 (b) 6 (c) 7 (d) 13
8. 8.In a class of 32 children, 24 like maths, 12 like science and 8 like both. How many like at least one of the two? (a) 32 (b) 20 (c) 36 (d) 28
9. 9.In a class of 44 children, 31 like cricket, 18 like football and 11 like both. How many like neither? (a) 6 (b) 17 (c) 11 (d) 7
10. 10.In a class of 29 children, 15 like dance, 17 like music and 6 like both. How many like only dance? (a) 9 (b) 11 (c) 15 (d) 12
11. 11.In a class of 41 children, 20 like tea, 24 like coffee and 7 like both. How many like at least one of the two? (a) 30 (b) 37 (c) 41 (d) 44
12. 12.In a class of 45 children, 24 like tea, 19 like coffee and 6 like both. How many like neither? (a) 2 (b) 6 (c) 14 (d) 8
13. 13.In a class of 22 children, 10 like mangoes, 8 like bananas and 2 like both. How many like only mangoes? (a) 8 (b) 14 (c) 6 (d) 10
14. 14.In a class of 48 children, 26 like mangoes, 29 like bananas and 11 like both. How many like at least one of the two? (a) 55 (b) 33 (c) 44 (d) 48
15. 15.In a class of 35 children, 24 like mangoes, 19 like bananas and 12 like both. How many like neither? (a) 16 (b) 12 (c) 5 (d) 4
16. 16.In a class of 19 children, 10 like tea, 10 like coffee and 5 like both. How many like at least one of the two? (a) 19 (b) 10 (c) 20 (d) 15
17. 17.In a class of 40 children, 20 like cricket, 26 like football and 9 like both. How many like neither? (a) 9 (b) 3 (c) 12 (d) 4
18. 18.In a class of 26 children, 11 like maths, 17 like science and 6 like neither. How many like both? (a) 8 (b) 20 (c) 2 (d) 6
19. 19.In a class of 43 children, 18 like maths, 23 like science and 7 like neither. How many like both? (a) 7 (b) 6 (c) 5 (d) 36
20. 20.In a class of 30 children, 10 like maths, 14 like science and 3 like both. How many like at least one of the two? (a) 18 (b) 30 (c) 21 (d) 24
21. 21.In a class of 49 children, 27 like maths, 25 like science and 12 like both. How many like neither? (a) 21 (b) 10 (c) 12 (d) 9
22. 22.In a class of 43 children, 25 like cricket, 18 like football and 6 like neither. How many like both? (a) 7 (b) 6 (c) 5 (d) 37
23. 23.In a class of 35 children, 23 like maths, 9 like science and 4 like both. How many like at least one of the two? (a) 32 (b) 35 (c) 28 (d) 24
24. 24.In a class of 30 children, 13 like mangoes, 20 like bananas and 5 like both. How many like neither? (a) 2 (b) 7 (c) 5 (d) 3
25. 25.In a class of 24 children, 6 like maths, 17 like science and 2 like both. How many like neither? (a) 3 (b) 5 (c) 1 (d) 2
26. 26.In a class of 23 children, 13 like dance, 8 like music and 5 like both. How many like only dance? (a) 3 (b) 15 (c) 13 (d) 8
27. 27.In a class of 39 children, 17 like mangoes, 31 like bananas and 11 like both. How many like neither? (a) 2 (b) 11 (c) 13 (d) 3
28. 28.In a class of 33 children, 16 like mangoes, 19 like bananas and 10 like both. How many like at least one of the two? (a) 33 (b) 35 (c) 15 (d) 25
29. 29.In a class of 40 children, 25 like maths, 19 like science and 5 like both. How many like neither? (a) 5 (b) 2 (c) 1 (d) 6
30. 30.In a class of 26 children, 6 like dance, 20 like music and 2 like both. How many like only dance? (a) 4 (b) 6 (c) 2 (d) 18
31. 31.In a class of 30 children, 19 like cricket, 13 like football and 4 like both. How many like at least one of the two? (a) 24 (b) 28 (c) 32 (d) 30
32. 32.In a class of 24 children, 15 like maths, 15 like science and 12 like both. How many like neither? (a) 6 (b) 7 (c) 12 (d) 18
33. 33.In a class of 46 children, 27 like dance, 18 like music and 9 like both. How many like neither? (a) 1 (b) 9 (c) 10 (d) 19
34. 34.In a class of 39 children, 26 like maths, 18 like science and 10 like both. How many like only maths? (a) 21 (b) 8 (c) 26 (d) 16
35. 35.In a class of 37 children, 17 like cricket, 19 like football and 2 like both. How many like only cricket? (a) 2 (b) 15 (c) 18 (d) 17
36. 36.In a class of 29 children, 17 like tea, 20 like coffee and 9 like both. How many like at least one of the two? (a) 37 (b) 19 (c) 28 (d) 29
37. 37.In a class of 42 children, 20 like tea, 21 like coffee and 7 like both. How many like at least one of the two? (a) 27 (b) 41 (c) 34 (d) 42
38. 38.In a class of 46 children, 29 like maths, 25 like science and 12 like both. How many like at least one of the two? (a) 46 (b) 54 (c) 42 (d) 30
39. 39.In a class of 41 children, 21 like cricket, 21 like football and 2 like both. How many like neither? (a) 1 (b) 2 (c) 3 (d) 0
40. 40.In a class of 29 children, 10 like cricket, 14 like football and 8 like neither. How many like both? (a) 21 (b) 4 (c) 8 (d) 3

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