Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 13 · 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 28 children, 9 like dance, 21 like music and 3 like both. How many like only dance? (a) 6 (b) 9 (c) 7 (d) 18
2. 2.In a class of 23 children, 13 like tea, 9 like coffee and 3 like both. How many like neither? (a) 1 (b) 7 (c) 4 (d) 3
3. 3.In a class of 32 children, 17 like maths, 21 like science and 11 like both. How many like only maths? (a) 17 (b) 11 (c) 6 (d) 10
4. 4.In a class of 39 children, 18 like maths, 23 like science and 6 like neither. How many like both? (a) 8 (b) 33 (c) 6 (d) 2
5. 5.In a class of 14 children, 8 like maths, 8 like science and 4 like both. How many like at least one of the two? (a) 8 (b) 12 (c) 14 (d) 16
6. 6.In a class of 46 children, 22 like maths, 28 like science and 12 like both. How many like only maths? (a) 16 (b) 22 (c) 10 (d) 18
7. 7.In a class of 38 children, 17 like dance, 21 like music and 4 like both. How many like neither? (a) 8 (b) 0 (c) 4 (d) 5
8. 8.In a class of 41 children, 21 like mangoes, 23 like bananas and 5 like both. How many like only mangoes? (a) 16 (b) 5 (c) 21 (d) 18
9. 9.In a class of 49 children, 23 like mangoes, 25 like bananas and 8 like both. How many like neither? (a) 1 (b) 8 (c) 17 (d) 9
10. 10.In a class of 27 children, 6 like cricket, 18 like football and 2 like both. How many like at least one of the two? (a) 24 (b) 27 (c) 20 (d) 22
11. 11.In a class of 40 children, 12 like cricket, 21 like football and 3 like both. How many like only cricket? (a) 19 (b) 18 (c) 12 (d) 9
12. 12.In a class of 32 children, 17 like maths, 10 like science and 2 like both. How many like at least one of the two? (a) 23 (b) 25 (c) 27 (d) 32
13. 13.In a class of 19 children, 9 like cricket, 6 like football and 3 like both. How many like at least one of the two? (a) 9 (b) 15 (c) 19 (d) 12
14. 14.In a class of 19 children, 6 like tea, 15 like coffee and 3 like both. How many like neither? (a) 4 (b) 1 (c) 3 (d) 2
15. 15.In a class of 29 children, 8 like cricket, 24 like football and 2 like neither. How many like both? (a) 2 (b) 5 (c) 27 (d) 3
16. 16.In a class of 40 children, 28 like mangoes, 13 like bananas and 8 like both. How many like at least one of the two? (a) 41 (b) 25 (c) 33 (d) 40
17. 17.In a class of 32 children, 15 like mangoes, 19 like bananas and 8 like both. How many like neither? (a) 6 (b) 8 (c) 14 (d) 7
18. 18.In a class of 23 children, 13 like maths, 17 like science and 10 like both. How many like only maths? (a) 7 (b) 3 (c) 6 (d) 13
19. 19.In a class of 33 children, 21 like maths, 8 like science and 4 like both. How many like neither? (a) 8 (b) 9 (c) 4 (d) 12
20. 20.In a class of 32 children, 19 like mangoes, 10 like bananas and 7 like both. How many like only mangoes? (a) 22 (b) 3 (c) 12 (d) 19
21. 21.In a class of 47 children, 23 like maths, 31 like science and 12 like both. How many like at least one of the two? (a) 42 (b) 47 (c) 54 (d) 30
22. 22.In a class of 31 children, 8 like tea, 19 like coffee and 9 like neither. How many like both? (a) 9 (b) 6 (c) 5 (d) 22
23. 23.In a class of 44 children, 25 like maths, 20 like science and 10 like both. How many like only maths? (a) 24 (b) 25 (c) 10 (d) 15
24. 24.In a class of 43 children, 16 like tea, 30 like coffee and 12 like both. How many like neither? (a) 9 (b) 12 (c) 21 (d) 10
25. 25.In a class of 45 children, 19 like tea, 22 like coffee and 3 like both. How many like neither? (a) 3 (b) 7 (c) 10 (d) 4
26. 26.In a class of 36 children, 17 like cricket, 17 like football and 2 like both. How many like at least one of the two? (a) 30 (b) 34 (c) 32 (d) 36
27. 27.In a class of 34 children, 16 like maths, 26 like science and 11 like both. How many like only maths? (a) 16 (b) 5 (c) 15 (d) 8
28. 28.In a class of 29 children, 12 like dance, 18 like music and 4 like both. How many like at least one of the two? (a) 22 (b) 30 (c) 29 (d) 26
29. 29.In a class of 31 children, 18 like cricket, 20 like football and 9 like both. How many like at least one of the two? (a) 20 (b) 38 (c) 31 (d) 29
30. 30.In a class of 41 children, 16 like cricket, 26 like football and 7 like both. How many like only cricket? (a) 9 (b) 15 (c) 16 (d) 19
31. 31.In a class of 39 children, 19 like mangoes, 22 like bananas and 4 like both. How many like neither? (a) 2 (b) 3 (c) 6 (d) 4
32. 32.In a class of 51 children, 31 like cricket, 30 like football and 12 like both. How many like neither? (a) 14 (b) 3 (c) 2 (d) 12
33. 33.In a class of 41 children, 31 like tea, 21 like coffee and 1 like neither. How many like both? (a) 40 (b) 12 (c) 11 (d) 1
34. 34.In a class of 47 children, 23 like dance, 22 like music and 6 like neither. How many like both? (a) 5 (b) 41 (c) 6 (d) 4
35. 35.In a class of 35 children, 26 like cricket, 16 like football and 10 like both. How many like at least one of the two? (a) 42 (b) 32 (c) 35 (d) 22
36. 36.In a class of 37 children, 13 like dance, 21 like music and 7 like neither. How many like both? (a) 4 (b) 30 (c) 5 (d) 7
37. 37.In a class of 28 children, 14 like dance, 17 like music and 10 like both. How many like at least one of the two? (a) 11 (b) 21 (c) 31 (d) 28
38. 38.In a class of 39 children, 26 like dance, 21 like music and 11 like both. How many like at least one of the two? (a) 47 (b) 39 (c) 25 (d) 36
39. 39.In a class of 33 children, 22 like dance, 11 like music and 2 like both. How many like neither? (a) 4 (b) 0 (c) 2 (d) 3
40. 40.In a class of 32 children, 18 like cricket, 18 like football and 5 like neither. How many like both? (a) 9 (b) 5 (c) 27 (d) 4

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