Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 480 · 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 31 children, 26 like cricket, 13 like football and 9 like both. How many like neither? (a) 9 (b) 10 (c) 2 (d) 1
2. 2.In a class of 38 children, 20 like cricket, 19 like football and 4 like both. How many like neither? (a) 7 (b) 2 (c) 4 (d) 3
3. 3.In a class of 23 children, 11 like maths, 14 like science and 7 like both. How many like at least one of the two? (a) 11 (b) 25 (c) 23 (d) 18
4. 4.In a class of 49 children, 22 like dance, 23 like music and 10 like neither. How many like both? (a) 39 (b) 10 (c) 6 (d) 7
5. 5.In a class of 36 children, 27 like tea, 10 like coffee and 7 like both. How many like at least one of the two? (a) 36 (b) 23 (c) 30 (d) 37
6. 6.In a class of 31 children, 25 like cricket, 10 like football and 7 like both. How many like neither? (a) 10 (b) 7 (c) 4 (d) 3
7. 7.In a class of 14 children, 6 like cricket, 5 like football and 2 like both. How many like at least one of the two? (a) 11 (b) 14 (c) 7 (d) 9
8. 8.In a class of 39 children, 14 like mangoes, 27 like bananas and 7 like neither. How many like both? (a) 2 (b) 32 (c) 9 (d) 7
9. 9.In a class of 27 children, 7 like dance, 13 like music and 2 like both. How many like neither? (a) 2 (b) 7 (c) 11 (d) 9
10. 10.In a class of 27 children, 19 like maths, 9 like science and 2 like both. How many like only maths? (a) 18 (b) 7 (c) 17 (d) 19
11. 11.In a class of 53 children, 30 like cricket, 24 like football and 10 like both. How many like neither? (a) 19 (b) 9 (c) 8 (d) 10
12. 12.In a class of 23 children, 17 like maths, 9 like science and 2 like neither. How many like both? (a) 3 (b) 5 (c) 2 (d) 21
13. 13.In a class of 22 children, 5 like cricket, 9 like football and 2 like both. How many like neither? (a) 8 (b) 2 (c) 12 (d) 10
14. 14.In a class of 34 children, 17 like dance, 26 like music and 2 like neither. How many like both? (a) 2 (b) 9 (c) 32 (d) 11
15. 15.In a class of 38 children, 17 like cricket, 21 like football and 8 like both. How many like only cricket? (a) 8 (b) 13 (c) 17 (d) 9
16. 16.In a class of 36 children, 20 like mangoes, 17 like bananas and 8 like both. How many like only mangoes? (a) 9 (b) 20 (c) 12 (d) 19
17. 17.In a class of 39 children, 26 like tea, 16 like coffee and 8 like both. How many like neither? (a) 8 (b) 5 (c) 6 (d) 13
18. 18.In a class of 30 children, 15 like maths, 15 like science and 7 like both. How many like at least one of the two? (a) 23 (b) 16 (c) 30 (d) 24
19. 19.In a class of 33 children, 20 like cricket, 18 like football and 11 like both. How many like neither? (a) 7 (b) 11 (c) 6 (d) 17
20. 20.In a class of 25 children, 11 like cricket, 12 like football and 2 like both. How many like neither? (a) 2 (b) 4 (c) 6 (d) 5
21. 21.In a class of 24 children, 16 like cricket, 14 like football and 11 like both. How many like at least one of the two? (a) 8 (b) 19 (c) 24 (d) 30
22. 22.In a class of 37 children, 18 like mangoes, 19 like bananas and 6 like both. How many like neither? (a) 0 (b) 6 (c) 7 (d) 12
23. 23.In a class of 30 children, 22 like mangoes, 11 like bananas and 5 like both. How many like neither? (a) 5 (b) 3 (c) 2 (d) 7
24. 24.In a class of 48 children, 29 like cricket, 24 like football and 9 like both. How many like only cricket? (a) 15 (b) 29 (c) 24 (d) 20
25. 25.In a class of 32 children, 11 like mangoes, 22 like bananas and 7 like both. How many like at least one of the two? (a) 33 (b) 32 (c) 19 (d) 26
26. 26.In a class of 23 children, 15 like dance, 9 like music and 3 like both. How many like neither? (a) 3 (b) 1 (c) 5 (d) 2
27. 27.In a class of 40 children, 14 like maths, 23 like science and 3 like both. How many like at least one of the two? (a) 31 (b) 37 (c) 40 (d) 34
28. 28.In a class of 44 children, 29 like maths, 20 like science and 12 like both. How many like only maths? (a) 17 (b) 29 (c) 24 (d) 8
29. 29.In a class of 21 children, 12 like maths, 8 like science and 2 like both. How many like at least one of the two? (a) 20 (b) 18 (c) 16 (d) 21
30. 30.In a class of 18 children, 13 like tea, 11 like coffee and 8 like both. How many like only tea? (a) 3 (b) 13 (c) 5 (d) 7
31. 31.In a class of 41 children, 23 like maths, 15 like science and 10 like neither. How many like both? (a) 7 (b) 31 (c) 8 (d) 10
32. 32.In a class of 30 children, 13 like dance, 17 like music and 7 like neither. How many like both? (a) 23 (b) 6 (c) 8 (d) 7
33. 33.In a class of 36 children, 16 like mangoes, 20 like bananas and 3 like neither. How many like both? (a) 3 (b) 4 (c) 33 (d) 2
34. 34.In a class of 22 children, 9 like maths, 14 like science and 3 like neither. How many like both? (a) 3 (b) 4 (c) 1 (d) 19
35. 35.In a class of 36 children, 21 like dance, 8 like music and 3 like both. How many like at least one of the two? (a) 29 (b) 36 (c) 23 (d) 26
36. 36.In a class of 27 children, 15 like maths, 16 like science and 3 like neither. How many like both? (a) 24 (b) 4 (c) 3 (d) 7
37. 37.In a class of 34 children, 15 like tea, 15 like coffee and 5 like both. How many like at least one of the two? (a) 34 (b) 20 (c) 25 (d) 30
38. 38.In a class of 45 children, 15 like dance, 24 like music and 4 like both. How many like at least one of the two? (a) 31 (b) 45 (c) 35 (d) 39
39. 39.In a class of 41 children, 28 like mangoes, 22 like bananas and 3 like neither. How many like both? (a) 9 (b) 12 (c) 38 (d) 3
40. 40.In a class of 48 children, 28 like mangoes, 24 like bananas and 10 like both. How many like only mangoes? (a) 24 (b) 28 (c) 18 (d) 14

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