Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 933 · 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 47 children, 25 like maths, 24 like science and 11 like both. How many like neither? (a) 11 (b) 9 (c) 10 (d) 20
2. 2.In a class of 27 children, 20 like maths, 12 like science and 7 like both. How many like neither? (a) 7 (b) 2 (c) 9 (d) 3
3. 3.In a class of 19 children, 7 like cricket, 6 like football and 3 like both. How many like neither? (a) 9 (b) 3 (c) 6 (d) 12
4. 4.In a class of 19 children, 9 like dance, 15 like music and 6 like both. How many like only dance? (a) 6 (b) 9 (c) 3 (d) 4
5. 5.In a class of 40 children, 28 like dance, 18 like music and 2 like neither. How many like both? (a) 8 (b) 38 (c) 6 (d) 2
6. 6.In a class of 36 children, 19 like tea, 20 like coffee and 5 like both. How many like neither? (a) 5 (b) 2 (c) 7 (d) 3
7. 7.In a class of 24 children, 16 like tea, 10 like coffee and 3 like both. How many like at least one of the two? (a) 23 (b) 24 (c) 20 (d) 26
8. 8.In a class of 51 children, 30 like dance, 28 like music and 5 like neither. How many like both? (a) 46 (b) 5 (c) 7 (d) 12
9. 9.In a class of 33 children, 17 like maths, 16 like science and 6 like both. How many like only maths? (a) 6 (b) 17 (c) 10 (d) 11
10. 10.In a class of 40 children, 16 like maths, 25 like science and 8 like neither. How many like both? (a) 32 (b) 1 (c) 8 (d) 9
11. 11.In a class of 35 children, 21 like maths, 8 like science and 3 like both. How many like at least one of the two? (a) 35 (b) 29 (c) 26 (d) 23
12. 12.In a class of 45 children, 26 like mangoes, 26 like bananas and 2 like neither. How many like both? (a) 43 (b) 7 (c) 2 (d) 9
13. 13.In a class of 45 children, 20 like mangoes, 25 like bananas and 8 like both. How many like at least one of the two? (a) 29 (b) 37 (c) 38 (d) 45
14. 14.In a class of 31 children, 13 like dance, 18 like music and 9 like both. How many like at least one of the two? (a) 13 (b) 31 (c) 23 (d) 22
15. 15.In a class of 37 children, 13 like mangoes, 21 like bananas and 5 like both. How many like at least one of the two? (a) 37 (b) 34 (c) 24 (d) 29
16. 16.In a class of 38 children, 14 like dance, 25 like music and 8 like neither. How many like both? (a) 8 (b) 9 (c) 30 (d) 1
17. 17.In a class of 34 children, 20 like maths, 17 like science and 12 like both. How many like only maths? (a) 17 (b) 20 (c) 5 (d) 8
18. 18.In a class of 30 children, 16 like cricket, 12 like football and 4 like both. How many like neither? (a) 4 (b) 10 (c) 6 (d) 2
19. 19.In a class of 36 children, 15 like tea, 22 like coffee and 2 like both. How many like only tea? (a) 20 (b) 14 (c) 15 (d) 13
20. 20.In a class of 33 children, 18 like cricket, 16 like football and 5 like both. How many like neither? (a) 4 (b) 3 (c) 9 (d) 5
21. 21.In a class of 43 children, 27 like tea, 17 like coffee and 10 like both. How many like neither? (a) 8 (b) 9 (c) 19 (d) 10
22. 22.In a class of 44 children, 31 like mangoes, 15 like bananas and 10 like neither. How many like both? (a) 34 (b) 2 (c) 10 (d) 12
23. 23.In a class of 30 children, 18 like cricket, 14 like football and 3 like both. How many like neither? (a) 4 (b) 2 (c) 3 (d) 1
24. 24.In a class of 23 children, 14 like cricket, 15 like football and 10 like both. How many like only cricket? (a) 5 (b) 14 (c) 8 (d) 4
25. 25.In a class of 39 children, 16 like maths, 22 like science and 2 like both. How many like only maths? (a) 17 (b) 20 (c) 14 (d) 16
26. 26.In a class of 31 children, 5 like dance, 22 like music and 2 like both. How many like neither? (a) 6 (b) 4 (c) 2 (d) 8
27. 27.In a class of 46 children, 23 like mangoes, 21 like bananas and 3 like both. How many like neither? (a) 5 (b) 2 (c) 8 (d) 3
28. 28.In a class of 45 children, 20 like maths, 21 like science and 2 like both. How many like neither? (a) 6 (b) 4 (c) 2 (d) 8
29. 29.In a class of 23 children, 11 like cricket, 11 like football and 5 like both. How many like at least one of the two? (a) 22 (b) 12 (c) 17 (d) 23
30. 30.In a class of 22 children, 16 like cricket, 10 like football and 1 like neither. How many like both? (a) 4 (b) 21 (c) 5 (d) 1
31. 31.In a class of 25 children, 14 like maths, 15 like science and 10 like both. How many like neither? (a) 10 (b) 7 (c) 16 (d) 6
32. 32.In a class of 43 children, 17 like cricket, 26 like football and 6 like both. How many like neither? (a) 0 (b) 6 (c) 7 (d) 12
33. 33.In a class of 34 children, 14 like maths, 28 like science and 9 like both. How many like neither? (a) 10 (b) 1 (c) 9 (d) 2
34. 34.In a class of 30 children, 22 like cricket, 13 like football and 7 like both. How many like only cricket? (a) 22 (b) 15 (c) 6 (d) 17
35. 35.In a class of 37 children, 24 like maths, 12 like science and 5 like both. How many like at least one of the two? (a) 37 (b) 31 (c) 26 (d) 36
36. 36.In a class of 28 children, 14 like tea, 11 like coffee and 9 like neither. How many like both? (a) 7 (b) 6 (c) 19 (d) 9
37. 37.In a class of 25 children, 15 like dance, 8 like music and 2 like both. How many like only dance? (a) 17 (b) 15 (c) 13 (d) 6
38. 38.In a class of 32 children, 9 like maths, 26 like science and 6 like both. How many like only maths? (a) 20 (b) 9 (c) 3 (d) 6
39. 39.In a class of 47 children, 20 like tea, 32 like coffee and 12 like both. How many like only tea? (a) 20 (b) 8 (c) 15 (d) 12
40. 40.In a class of 40 children, 22 like mangoes, 24 like bananas and 9 like both. How many like neither? (a) 9 (b) 12 (c) 4 (d) 3

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