Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 66 · 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 38 children, 17 like cricket, 19 like football and 3 like both. How many like only cricket? (a) 17 (b) 16 (c) 19 (d) 14
2. 2.In a class of 31 children, 13 like cricket, 19 like football and 9 like neither. How many like both? (a) 9 (b) 1 (c) 22 (d) 10
3. 3.In a class of 16 children, 6 like cricket, 7 like football and 2 like both. How many like only cricket? (a) 6 (b) 9 (c) 4 (d) 5
4. 4.In a class of 29 children, 11 like mangoes, 16 like bananas and 8 like both. How many like neither? (a) 2 (b) 18 (c) 10 (d) 8
5. 5.In a class of 23 children, 13 like dance, 12 like music and 4 like both. How many like neither? (a) 2 (b) 4 (c) 3 (d) 6
6. 6.In a class of 25 children, 11 like cricket, 12 like football and 4 like neither. How many like both? (a) 2 (b) 4 (c) 3 (d) 21
7. 7.In a class of 34 children, 22 like mangoes, 12 like bananas and 2 like both. How many like at least one of the two? (a) 34 (b) 32 (c) 30 (d) 33
8. 8.In a class of 42 children, 16 like mangoes, 18 like bananas and 2 like both. How many like neither? (a) 10 (b) 8 (c) 12 (d) 2
9. 9.In a class of 30 children, 13 like tea, 20 like coffee and 1 like neither. How many like both? (a) 29 (b) 3 (c) 1 (d) 4
10. 10.In a class of 49 children, 29 like maths, 22 like science and 10 like both. How many like only maths? (a) 12 (b) 27 (c) 19 (d) 29
11. 11.In a class of 31 children, 13 like tea, 22 like coffee and 5 like both. How many like neither? (a) 2 (b) 1 (c) 6 (d) 5
12. 12.In a class of 32 children, 10 like cricket, 15 like football and 2 like both. How many like at least one of the two? (a) 23 (b) 32 (c) 21 (d) 25
13. 13.In a class of 52 children, 25 like mangoes, 24 like bananas and 5 like both. How many like neither? (a) 5 (b) 13 (c) 3 (d) 8
14. 14.In a class of 32 children, 14 like dance, 15 like music and 4 like both. How many like neither? (a) 11 (b) 7 (c) 3 (d) 4
15. 15.In a class of 39 children, 27 like dance, 21 like music and 3 like neither. How many like both? (a) 9 (b) 36 (c) 12 (d) 3
16. 16.In a class of 32 children, 19 like mangoes, 6 like bananas and 3 like both. How many like neither? (a) 10 (b) 13 (c) 7 (d) 3
17. 17.In a class of 32 children, 20 like mangoes, 14 like bananas and 4 like both. How many like neither? (a) 6 (b) 2 (c) 4 (d) 3
18. 18.In a class of 28 children, 9 like cricket, 19 like football and 2 like both. How many like neither? (a) 0 (b) 3 (c) 4 (d) 2
19. 19.In a class of 52 children, 30 like tea, 28 like coffee and 6 like neither. How many like both? (a) 13 (b) 6 (c) 12 (d) 46
20. 20.In a class of 38 children, 25 like maths, 11 like science and 8 like both. How many like at least one of the two? (a) 20 (b) 28 (c) 38 (d) 36
21. 21.In a class of 26 children, 14 like maths, 7 like science and 3 like both. How many like at least one of the two? (a) 26 (b) 18 (c) 15 (d) 21
22. 22.In a class of 30 children, 18 like cricket, 12 like football and 2 like both. How many like neither? (a) 4 (b) 2 (c) 0 (d) 3
23. 23.In a class of 47 children, 19 like dance, 26 like music and 8 like both. How many like only dance? (a) 21 (b) 18 (c) 11 (d) 19
24. 24.In a class of 21 children, 15 like dance, 13 like music and 8 like both. How many like only dance? (a) 5 (b) 8 (c) 15 (d) 7
25. 25.In a class of 41 children, 26 like tea, 13 like coffee and 6 like both. How many like only tea? (a) 26 (b) 20 (c) 7 (d) 28
26. 26.In a class of 14 children, 8 like cricket, 8 like football and 5 like both. How many like at least one of the two? (a) 16 (b) 11 (c) 6 (d) 14
27. 27.In a class of 40 children, 28 like cricket, 21 like football and 3 like neither. How many like both? (a) 9 (b) 3 (c) 37 (d) 12
28. 28.In a class of 35 children, 21 like mangoes, 15 like bananas and 7 like both. How many like neither? (a) 7 (b) 6 (c) 5 (d) 13
29. 29.In a class of 28 children, 19 like cricket, 20 like football and 12 like both. How many like neither? (a) 2 (b) 12 (c) 13 (d) 1
30. 30.In a class of 33 children, 19 like tea, 7 like coffee and 10 like neither. How many like both? (a) 10 (b) 4 (c) 3 (d) 23
31. 31.In a class of 27 children, 14 like cricket, 16 like football and 6 like both. How many like at least one of the two? (a) 24 (b) 30 (c) 27 (d) 18
32. 32.In a class of 46 children, 23 like mangoes, 21 like bananas and 3 like both. How many like at least one of the two? (a) 38 (b) 41 (c) 44 (d) 46
33. 33.In a class of 35 children, 25 like mangoes, 12 like bananas and 7 like neither. How many like both? (a) 28 (b) 2 (c) 9 (d) 7
34. 34.In a class of 29 children, 14 like dance, 15 like music and 3 like both. How many like at least one of the two? (a) 23 (b) 29 (c) 26 (d) 27
35. 35.In a class of 42 children, 20 like mangoes, 16 like bananas and 3 like both. How many like neither? (a) 6 (b) 9 (c) 12 (d) 3
36. 36.In a class of 49 children, 23 like dance, 25 like music and 6 like both. How many like neither? (a) 6 (b) 7 (c) 13 (d) 1
37. 37.In a class of 42 children, 28 like dance, 20 like music and 8 like both. How many like neither? (a) 8 (b) 10 (c) 2 (d) 3
38. 38.In a class of 32 children, 14 like maths, 21 like science and 7 like both. How many like at least one of the two? (a) 35 (b) 32 (c) 21 (d) 28
39. 39.In a class of 40 children, 26 like maths, 20 like science and 9 like both. How many like neither? (a) 4 (b) 12 (c) 3 (d) 9
40. 40.In a class of 37 children, 25 like tea, 19 like coffee and 11 like both. How many like only tea? (a) 25 (b) 18 (c) 8 (d) 14

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