Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 471 · 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 33 children, 8 like tea, 20 like coffee and 2 like both. How many like neither? (a) 2 (b) 7 (c) 5 (d) 9
2. 2.In a class of 36 children, 25 like cricket, 13 like football and 6 like both. How many like at least one of the two? (a) 36 (b) 32 (c) 26 (d) 38
3. 3.In a class of 45 children, 25 like tea, 22 like coffee and 7 like both. How many like at least one of the two? (a) 45 (b) 47 (c) 33 (d) 40
4. 4.In a class of 23 children, 10 like dance, 14 like music and 7 like both. How many like at least one of the two? (a) 24 (b) 17 (c) 23 (d) 10
5. 5.In a class of 37 children, 15 like tea, 19 like coffee and 5 like both. How many like only tea? (a) 15 (b) 18 (c) 14 (d) 10
6. 6.In a class of 43 children, 25 like dance, 21 like music and 8 like both. How many like neither? (a) 6 (b) 13 (c) 8 (d) 5
7. 7.In a class of 35 children, 22 like cricket, 8 like football and 3 like both. How many like only cricket? (a) 22 (b) 19 (c) 27 (d) 5
8. 8.In a class of 20 children, 8 like mangoes, 15 like bananas and 4 like both. How many like at least one of the two? (a) 15 (b) 19 (c) 20 (d) 23
9. 9.In a class of 20 children, 6 like mangoes, 9 like bananas and 2 like both. How many like neither? (a) 5 (b) 9 (c) 2 (d) 7
10. 10.In a class of 38 children, 10 like mangoes, 21 like bananas and 3 like both. How many like only mangoes? (a) 18 (b) 17 (c) 10 (d) 7
11. 11.In a class of 26 children, 21 like maths, 13 like science and 9 like both. How many like neither? (a) 10 (b) 9 (c) 2 (d) 1
12. 12.In a class of 23 children, 8 like cricket, 13 like football and 3 like both. How many like only cricket? (a) 3 (b) 5 (c) 10 (d) 8
13. 13.In a class of 30 children, 15 like tea, 20 like coffee and 1 like neither. How many like both? (a) 29 (b) 1 (c) 5 (d) 6
14. 14.In a class of 22 children, 8 like maths, 11 like science and 5 like both. How many like at least one of the two? (a) 9 (b) 19 (c) 22 (d) 14
15. 15.In a class of 35 children, 23 like cricket, 18 like football and 9 like both. How many like at least one of the two? (a) 35 (b) 23 (c) 32 (d) 41
16. 16.In a class of 40 children, 17 like tea, 21 like coffee and 2 like both. How many like neither? (a) 6 (b) 5 (c) 2 (d) 4
17. 17.In a class of 31 children, 14 like mangoes, 20 like bananas and 7 like both. How many like neither? (a) 4 (b) 7 (c) 5 (d) 11
18. 18.In a class of 34 children, 23 like cricket, 16 like football and 8 like both. How many like only cricket? (a) 15 (b) 23 (c) 8 (d) 18
19. 19.In a class of 33 children, 7 like tea, 22 like coffee and 4 like both. How many like neither? (a) 4 (b) 8 (c) 9 (d) 12
20. 20.In a class of 36 children, 19 like maths, 14 like science and 5 like both. How many like only maths? (a) 19 (b) 22 (c) 9 (d) 14
21. 21.In a class of 30 children, 22 like dance, 15 like music and 8 like both. How many like neither? (a) 8 (b) 2 (c) 1 (d) 9
22. 22.In a class of 24 children, 11 like mangoes, 18 like bananas and 8 like both. How many like neither? (a) 8 (b) 3 (c) 4 (d) 11
23. 23.In a class of 28 children, 9 like cricket, 12 like football and 9 like neither. How many like both? (a) 19 (b) 2 (c) 9 (d) 3
24. 24.In a class of 20 children, 7 like dance, 15 like music and 3 like both. How many like neither? (a) 3 (b) 1 (c) 4 (d) 2
25. 25.In a class of 37 children, 20 like maths, 19 like science and 3 like both. How many like neither? (a) 3 (b) 4 (c) 1 (d) 2
26. 26.In a class of 37 children, 22 like dance, 21 like music and 6 like neither. How many like both? (a) 12 (b) 6 (c) 31 (d) 13
27. 27.In a class of 32 children, 15 like cricket, 14 like football and 5 like neither. How many like both? (a) 2 (b) 27 (c) 5 (d) 3
28. 28.In a class of 35 children, 11 like maths, 18 like science and 10 like neither. How many like both? (a) 10 (b) 4 (c) 5 (d) 25
29. 29.In a class of 28 children, 14 like cricket, 12 like football and 5 like both. How many like at least one of the two? (a) 16 (b) 26 (c) 28 (d) 21
30. 30.In a class of 45 children, 24 like cricket, 23 like football and 4 like both. How many like at least one of the two? (a) 45 (b) 47 (c) 43 (d) 39
31. 31.In a class of 35 children, 20 like mangoes, 9 like bananas and 2 like both. How many like at least one of the two? (a) 35 (b) 25 (c) 29 (d) 27
32. 32.In a class of 30 children, 13 like mangoes, 25 like bananas and 1 like neither. How many like both? (a) 29 (b) 8 (c) 1 (d) 9
33. 33.In a class of 38 children, 26 like tea, 13 like coffee and 6 like both. How many like at least one of the two? (a) 27 (b) 33 (c) 39 (d) 38
34. 34.In a class of 40 children, 25 like maths, 17 like science and 9 like both. How many like at least one of the two? (a) 40 (b) 33 (c) 24 (d) 42
35. 35.In a class of 40 children, 19 like maths, 26 like science and 2 like neither. How many like both? (a) 5 (b) 7 (c) 38 (d) 2
36. 36.In a class of 52 children, 22 like dance, 24 like music and 4 like both. How many like neither? (a) 4 (b) 10 (c) 14 (d) 6
37. 37.In a class of 29 children, 15 like maths, 11 like science and 7 like both. How many like neither? (a) 3 (b) 10 (c) 17 (d) 7
38. 38.In a class of 36 children, 24 like maths, 12 like science and 7 like neither. How many like both? (a) 6 (b) 29 (c) 7 (d) 8
39. 39.In a class of 35 children, 20 like cricket, 17 like football and 12 like both. How many like neither? (a) 12 (b) 11 (c) 10 (d) 22
40. 40.In a class of 40 children, 18 like maths, 30 like science and 11 like both. How many like only maths? (a) 10 (b) 18 (c) 7 (d) 19

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