Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 624 · 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, 15 like dance, 21 like music and 4 like both. How many like neither? (a) 4 (b) 2 (c) 5 (d) 1
2. 2.In a class of 34 children, 19 like mangoes, 17 like bananas and 9 like both. How many like neither? (a) 16 (b) 8 (c) 9 (d) 7
3. 3.In a class of 41 children, 28 like tea, 12 like coffee and 9 like both. How many like only tea? (a) 3 (b) 29 (c) 28 (d) 19
4. 4.In a class of 21 children, 14 like maths, 12 like science and 4 like neither. How many like both? (a) 9 (b) 5 (c) 4 (d) 17
5. 5.In a class of 30 children, 16 like mangoes, 18 like bananas and 7 like both. How many like only mangoes? (a) 16 (b) 9 (c) 12 (d) 11
6. 6.In a class of 36 children, 24 like maths, 23 like science and 1 like neither. How many like both? (a) 1 (b) 11 (c) 12 (d) 35
7. 7.In a class of 32 children, 11 like maths, 22 like science and 2 like both. How many like only maths? (a) 20 (b) 10 (c) 11 (d) 9
8. 8.In a class of 36 children, 24 like maths, 15 like science and 1 like neither. How many like both? (a) 35 (b) 1 (c) 4 (d) 3
9. 9.In a class of 30 children, 16 like dance, 17 like music and 10 like both. How many like only dance? (a) 7 (b) 13 (c) 16 (d) 6
10. 10.In a class of 36 children, 19 like tea, 26 like coffee and 3 like neither. How many like both? (a) 9 (b) 3 (c) 33 (d) 12
11. 11.In a class of 56 children, 27 like mangoes, 31 like bananas and 11 like both. How many like only mangoes? (a) 16 (b) 20 (c) 27 (d) 25
12. 12.In a class of 31 children, 15 like mangoes, 16 like bananas and 4 like both. How many like neither? (a) 4 (b) 0 (c) 8 (d) 5
13. 13.In a class of 25 children, 13 like cricket, 19 like football and 8 like both. How many like only cricket? (a) 6 (b) 5 (c) 11 (d) 13
14. 14.In a class of 32 children, 17 like tea, 21 like coffee and 12 like both. How many like only tea? (a) 11 (b) 9 (c) 17 (d) 5
15. 15.In a class of 36 children, 20 like tea, 15 like coffee and 3 like both. How many like only tea? (a) 21 (b) 20 (c) 12 (d) 17
16. 16.In a class of 29 children, 15 like cricket, 19 like football and 11 like both. How many like neither? (a) 17 (b) 7 (c) 6 (d) 11
17. 17.In a class of 42 children, 29 like dance, 14 like music and 9 like both. How many like only dance? (a) 5 (b) 29 (c) 28 (d) 20
18. 18.In a class of 25 children, 12 like maths, 15 like science and 7 like both. How many like only maths? (a) 5 (b) 10 (c) 8 (d) 12
19. 19.In a class of 27 children, 11 like tea, 11 like coffee and 4 like both. How many like at least one of the two? (a) 14 (b) 27 (c) 22 (d) 18
20. 20.In a class of 23 children, 13 like mangoes, 13 like bananas and 10 like both. How many like only mangoes? (a) 13 (b) 10 (c) 3 (d) 4
21. 21.In a class of 44 children, 23 like mangoes, 21 like bananas and 9 like both. How many like at least one of the two? (a) 35 (b) 36 (c) 44 (d) 26
22. 22.In a class of 45 children, 21 like mangoes, 24 like bananas and 4 like both. How many like at least one of the two? (a) 37 (b) 41 (c) 45 (d) 42
23. 23.In a class of 46 children, 28 like mangoes, 21 like bananas and 8 like both. How many like at least one of the two? (a) 49 (b) 46 (c) 41 (d) 33
24. 24.In a class of 34 children, 12 like cricket, 23 like football and 6 like both. How many like neither? (a) 5 (b) 4 (c) 6 (d) 11
25. 25.In a class of 52 children, 27 like cricket, 26 like football and 8 like both. How many like at least one of the two? (a) 53 (b) 37 (c) 45 (d) 52
26. 26.In a class of 44 children, 22 like mangoes, 31 like bananas and 2 like neither. How many like both? (a) 2 (b) 9 (c) 11 (d) 42
27. 27.In a class of 41 children, 24 like tea, 21 like coffee and 5 like both. How many like at least one of the two? (a) 35 (b) 45 (c) 40 (d) 41
28. 28.In a class of 49 children, 25 like tea, 28 like coffee and 10 like both. How many like only tea? (a) 18 (b) 21 (c) 15 (d) 25
29. 29.In a class of 42 children, 28 like cricket, 22 like football and 11 like both. How many like neither? (a) 4 (b) 3 (c) 11 (d) 14
30. 30.In a class of 23 children, 10 like mangoes, 12 like bananas and 5 like both. How many like neither? (a) 6 (b) 5 (c) 11 (d) 1
31. 31.In a class of 41 children, 22 like tea, 16 like coffee and 7 like both. How many like at least one of the two? (a) 38 (b) 31 (c) 24 (d) 41
32. 32.In a class of 43 children, 25 like dance, 28 like music and 12 like both. How many like only dance? (a) 15 (b) 25 (c) 16 (d) 13
33. 33.In a class of 31 children, 17 like mangoes, 9 like bananas and 7 like neither. How many like both? (a) 7 (b) 3 (c) 24 (d) 2
34. 34.In a class of 35 children, 20 like tea, 24 like coffee and 1 like neither. How many like both? (a) 10 (b) 9 (c) 1 (d) 34
35. 35.In a class of 32 children, 10 like tea, 18 like coffee and 3 like both. How many like at least one of the two? (a) 32 (b) 28 (c) 25 (d) 22
36. 36.In a class of 20 children, 12 like tea, 16 like coffee and 1 like neither. How many like both? (a) 19 (b) 8 (c) 1 (d) 9
37. 37.In a class of 40 children, 20 like dance, 17 like music and 4 like both. How many like neither? (a) 3 (b) 4 (c) 11 (d) 7
38. 38.In a class of 31 children, 23 like maths, 7 like science and 3 like both. How many like at least one of the two? (a) 30 (b) 31 (c) 24 (d) 27
39. 39.In a class of 32 children, 19 like tea, 24 like coffee and 12 like both. How many like only tea? (a) 12 (b) 19 (c) 7 (d) 8
40. 40.In a class of 36 children, 17 like mangoes, 19 like bananas and 6 like both. How many like neither? (a) 0 (b) 6 (c) 12 (d) 7

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