Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 327 · 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 44 children, 29 like dance, 18 like music and 9 like both. How many like only dance? (a) 9 (b) 29 (c) 20 (d) 26
2. 2.In a class of 29 children, 15 like maths, 14 like science and 2 like both. How many like at least one of the two? (a) 27 (b) 28 (c) 25 (d) 29
3. 3.In a class of 26 children, 13 like tea, 15 like coffee and 8 like both. How many like at least one of the two? (a) 26 (b) 28 (c) 12 (d) 20
4. 4.In a class of 27 children, 19 like mangoes, 11 like bananas and 6 like both. How many like only mangoes? (a) 19 (b) 16 (c) 5 (d) 13
5. 5.In a class of 33 children, 19 like dance, 17 like music and 5 like neither. How many like both? (a) 28 (b) 3 (c) 8 (d) 5
6. 6.In a class of 29 children, 20 like tea, 9 like coffee and 6 like both. How many like neither? (a) 0 (b) 12 (c) 6 (d) 7
7. 7.In a class of 15 children, 10 like cricket, 10 like football and 6 like both. How many like only cricket? (a) 4 (b) 5 (c) 10 (d) 6
8. 8.In a class of 45 children, 25 like maths, 26 like science and 6 like neither. How many like both? (a) 39 (b) 12 (c) 13 (d) 6
9. 9.In a class of 42 children, 23 like maths, 15 like science and 4 like both. How many like at least one of the two? (a) 42 (b) 30 (c) 38 (d) 34
10. 10.In a class of 26 children, 8 like mangoes, 14 like bananas and 5 like both. How many like only mangoes? (a) 3 (b) 8 (c) 9 (d) 12
11. 11.In a class of 47 children, 24 like tea, 23 like coffee and 6 like both. How many like at least one of the two? (a) 35 (b) 42 (c) 41 (d) 47
12. 12.In a class of 22 children, 6 like tea, 11 like coffee and 2 like both. How many like neither? (a) 7 (b) 9 (c) 2 (d) 5
13. 13.In a class of 50 children, 29 like tea, 28 like coffee and 9 like both. How many like at least one of the two? (a) 50 (b) 48 (c) 57 (d) 39
14. 14.In a class of 30 children, 15 like maths, 18 like science and 5 like both. How many like at least one of the two? (a) 28 (b) 23 (c) 33 (d) 30
15. 15.In a class of 30 children, 10 like mangoes, 16 like bananas and 6 like neither. How many like both? (a) 24 (b) 6 (c) 2 (d) 3
16. 16.In a class of 33 children, 22 like dance, 15 like music and 3 like neither. How many like both? (a) 4 (b) 3 (c) 7 (d) 30
17. 17.In a class of 31 children, 13 like tea, 21 like coffee and 3 like neither. How many like both? (a) 28 (b) 6 (c) 7 (d) 3
18. 18.In a class of 25 children, 12 like maths, 20 like science and 9 like both. How many like at least one of the two? (a) 23 (b) 25 (c) 14 (d) 32
19. 19.In a class of 34 children, 19 like tea, 17 like coffee and 5 like both. How many like at least one of the two? (a) 26 (b) 31 (c) 36 (d) 34
20. 20.In a class of 22 children, 9 like mangoes, 14 like bananas and 2 like both. How many like only mangoes? (a) 8 (b) 7 (c) 9 (d) 12
21. 21.In a class of 30 children, 18 like maths, 10 like science and 5 like both. How many like only maths? (a) 20 (b) 5 (c) 13 (d) 18
22. 22.In a class of 47 children, 25 like dance, 29 like music and 4 like neither. How many like both? (a) 11 (b) 43 (c) 7 (d) 4
23. 23.In a class of 42 children, 21 like cricket, 26 like football and 10 like both. How many like neither? (a) 15 (b) 6 (c) 10 (d) 5
24. 24.In a class of 36 children, 11 like dance, 25 like music and 8 like both. How many like only dance? (a) 8 (b) 11 (c) 3 (d) 17
25. 25.In a class of 32 children, 10 like maths, 22 like science and 4 like both. How many like only maths? (a) 4 (b) 6 (c) 10 (d) 18
26. 26.In a class of 51 children, 29 like mangoes, 28 like bananas and 3 like neither. How many like both? (a) 6 (b) 48 (c) 3 (d) 9
27. 27.In a class of 28 children, 22 like cricket, 10 like football and 7 like both. How many like at least one of the two? (a) 28 (b) 18 (c) 25 (d) 32
28. 28.In a class of 41 children, 23 like cricket, 20 like football and 3 like neither. How many like both? (a) 5 (b) 3 (c) 38 (d) 2
29. 29.In a class of 35 children, 24 like mangoes, 21 like bananas and 12 like both. How many like only mangoes? (a) 24 (b) 12 (c) 9 (d) 14
30. 30.In a class of 44 children, 31 like tea, 17 like coffee and 11 like both. How many like neither? (a) 8 (b) 7 (c) 18 (d) 11
31. 31.In a class of 35 children, 24 like maths, 13 like science and 6 like neither. How many like both? (a) 8 (b) 2 (c) 29 (d) 6
32. 32.In a class of 25 children, 12 like maths, 13 like science and 8 like neither. How many like both? (a) 9 (b) 8 (c) 7 (d) 17
33. 33.In a class of 32 children, 8 like tea, 22 like coffee and 2 like both. How many like only tea? (a) 20 (b) 10 (c) 8 (d) 6
34. 34.In a class of 32 children, 24 like dance, 12 like music and 5 like both. How many like only dance? (a) 20 (b) 7 (c) 24 (d) 19
35. 35.In a class of 43 children, 20 like cricket, 23 like football and 3 like both. How many like at least one of the two? (a) 43 (b) 37 (c) 41 (d) 40
36. 36.In a class of 19 children, 8 like maths, 9 like science and 5 like both. How many like at least one of the two? (a) 12 (b) 7 (c) 17 (d) 19
37. 37.In a class of 44 children, 22 like dance, 19 like music and 4 like both. How many like only dance? (a) 22 (b) 25 (c) 15 (d) 18
38. 38.In a class of 27 children, 13 like cricket, 20 like football and 4 like neither. How many like both? (a) 6 (b) 10 (c) 4 (d) 23
39. 39.In a class of 40 children, 16 like cricket, 19 like football and 2 like both. How many like neither? (a) 2 (b) 9 (c) 5 (d) 7
40. 40.In a class of 17 children, 6 like dance, 12 like music and 3 like both. How many like only dance? (a) 6 (b) 3 (c) 5 (d) 9

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