Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 759 · 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 40 children, 17 like cricket, 18 like football and 4 like both. How many like at least one of the two? (a) 40 (b) 35 (c) 31 (d) 27
2. 2.In a class of 44 children, 29 like tea, 23 like coffee and 11 like both. How many like neither? (a) 11 (b) 14 (c) 3 (d) 4
3. 3.In a class of 32 children, 14 like cricket, 13 like football and 9 like neither. How many like both? (a) 9 (b) 4 (c) 23 (d) 5
4. 4.In a class of 25 children, 11 like tea, 14 like coffee and 7 like neither. How many like both? (a) 18 (b) 6 (c) 7 (d) 8
5. 5.In a class of 35 children, 20 like maths, 16 like science and 2 like neither. How many like both? (a) 2 (b) 33 (c) 3 (d) 1
6. 6.In a class of 45 children, 21 like dance, 24 like music and 7 like both. How many like only dance? (a) 7 (b) 17 (c) 21 (d) 14
7. 7.In a class of 24 children, 12 like maths, 9 like science and 5 like neither. How many like both? (a) 3 (b) 19 (c) 5 (d) 2
8. 8.In a class of 37 children, 19 like tea, 21 like coffee and 8 like both. How many like at least one of the two? (a) 37 (b) 24 (c) 32 (d) 40
9. 9.In a class of 21 children, 8 like mangoes, 13 like bananas and 5 like both. How many like neither? (a) 5 (b) 10 (c) 6 (d) 0
10. 10.In a class of 36 children, 8 like cricket, 24 like football and 5 like both. How many like at least one of the two? (a) 27 (b) 36 (c) 32 (d) 22
11. 11.In a class of 29 children, 17 like cricket, 12 like football and 3 like both. How many like only cricket? (a) 17 (b) 14 (c) 9 (d) 3
12. 12.In a class of 38 children, 23 like dance, 9 like music and 4 like both. How many like only dance? (a) 23 (b) 19 (c) 5 (d) 29
13. 13.In a class of 41 children, 21 like cricket, 23 like football and 12 like both. How many like neither? (a) 21 (b) 9 (c) 12 (d) 10
14. 14.In a class of 39 children, 21 like mangoes, 17 like bananas and 4 like neither. How many like both? (a) 2 (b) 4 (c) 35 (d) 3
15. 15.In a class of 30 children, 7 like tea, 18 like coffee and 3 like both. How many like at least one of the two? (a) 19 (b) 30 (c) 25 (d) 22
16. 16.In a class of 22 children, 13 like tea, 14 like coffee and 7 like both. How many like neither? (a) 3 (b) 9 (c) 2 (d) 7
17. 17.In a class of 49 children, 19 like cricket, 22 like football and 2 like both. How many like neither? (a) 8 (b) 10 (c) 12 (d) 2
18. 18.In a class of 38 children, 26 like tea, 18 like coffee and 8 like both. How many like neither? (a) 10 (b) 8 (c) 3 (d) 2
19. 19.In a class of 20 children, 11 like maths, 10 like science and 5 like both. How many like at least one of the two? (a) 16 (b) 11 (c) 20 (d) 21
20. 20.In a class of 34 children, 21 like maths, 10 like science and 5 like both. How many like at least one of the two? (a) 34 (b) 21 (c) 31 (d) 26
21. 21.In a class of 36 children, 18 like maths, 15 like science and 2 like both. How many like neither? (a) 7 (b) 3 (c) 2 (d) 5
22. 22.In a class of 35 children, 16 like cricket, 22 like football and 8 like both. How many like neither? (a) 8 (b) 5 (c) 6 (d) 13
23. 23.In a class of 54 children, 29 like mangoes, 27 like bananas and 9 like both. How many like neither? (a) 16 (b) 8 (c) 7 (d) 9
24. 24.In a class of 29 children, 13 like cricket, 10 like football and 3 like both. How many like neither? (a) 3 (b) 6 (c) 12 (d) 9
25. 25.In a class of 19 children, 11 like mangoes, 7 like bananas and 5 like neither. How many like both? (a) 14 (b) 3 (c) 5 (d) 4
26. 26.In a class of 33 children, 12 like maths, 15 like science and 3 like both. How many like only maths? (a) 3 (b) 9 (c) 18 (d) 12
27. 27.In a class of 33 children, 26 like cricket, 14 like football and 8 like both. How many like at least one of the two? (a) 24 (b) 32 (c) 33 (d) 40
28. 28.In a class of 37 children, 16 like maths, 22 like science and 8 like both. How many like only maths? (a) 14 (b) 15 (c) 16 (d) 8
29. 29.In a class of 39 children, 22 like cricket, 10 like football and 3 like both. How many like only cricket? (a) 29 (b) 7 (c) 19 (d) 22
30. 30.In a class of 21 children, 9 like cricket, 10 like football and 2 like both. How many like at least one of the two? (a) 21 (b) 17 (c) 15 (d) 19
31. 31.In a class of 29 children, 15 like maths, 16 like science and 7 like both. How many like neither? (a) 12 (b) 7 (c) 5 (d) 6
32. 32.In a class of 38 children, 16 like dance, 19 like music and 5 like both. How many like neither? (a) 13 (b) 8 (c) 3 (d) 5
33. 33.In a class of 23 children, 12 like dance, 10 like music and 3 like both. How many like at least one of the two? (a) 23 (b) 16 (c) 19 (d) 22
34. 34.In a class of 30 children, 16 like tea, 20 like coffee and 1 like neither. How many like both? (a) 7 (b) 29 (c) 1 (d) 6
35. 35.In a class of 43 children, 23 like mangoes, 17 like bananas and 5 like both. How many like at least one of the two? (a) 30 (b) 35 (c) 40 (d) 43
36. 36.In a class of 42 children, 30 like dance, 21 like music and 11 like both. How many like neither? (a) 11 (b) 3 (c) 13 (d) 2
37. 37.In a class of 27 children, 16 like dance, 11 like music and 7 like both. How many like neither? (a) 7 (b) 0 (c) 8 (d) 14
38. 38.In a class of 47 children, 21 like cricket, 28 like football and 10 like both. How many like neither? (a) 10 (b) 9 (c) 8 (d) 18
39. 39.In a class of 29 children, 23 like dance, 12 like music and 9 like both. How many like only dance? (a) 3 (b) 17 (c) 23 (d) 14
40. 40.In a class of 38 children, 15 like cricket, 27 like football and 11 like both. How many like neither? (a) 18 (b) 7 (c) 8 (d) 11

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