Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 790 · 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 23 children, 12 like maths, 14 like science and 5 like both. How many like only maths? (a) 7 (b) 5 (c) 9 (d) 12
2. 2.In a class of 49 children, 26 like cricket, 30 like football and 4 like neither. How many like both? (a) 45 (b) 7 (c) 4 (d) 11
3. 3.In a class of 44 children, 21 like dance, 18 like music and 5 like both. How many like neither? (a) 11 (b) 5 (c) 10 (d) 15
4. 4.In a class of 25 children, 10 like maths, 17 like science and 4 like both. How many like neither? (a) 4 (b) 6 (c) 2 (d) 3
5. 5.In a class of 29 children, 19 like maths, 9 like science and 2 like both. How many like neither? (a) 5 (b) 3 (c) 2 (d) 1
6. 6.In a class of 35 children, 23 like maths, 19 like science and 8 like both. How many like neither? (a) 2 (b) 8 (c) 1 (d) 9
7. 7.In a class of 19 children, 8 like cricket, 8 like football and 3 like both. How many like only cricket? (a) 8 (b) 5 (c) 11 (d) 3
8. 8.In a class of 32 children, 24 like maths, 19 like science and 12 like both. How many like neither? (a) 12 (b) 1 (c) 13 (d) 2
9. 9.In a class of 43 children, 15 like mangoes, 22 like bananas and 9 like neither. How many like both? (a) 34 (b) 9 (c) 3 (d) 4
10. 10.In a class of 33 children, 24 like dance, 15 like music and 11 like both. How many like neither? (a) 11 (b) 6 (c) 5 (d) 16
11. 11.In a class of 33 children, 15 like mangoes, 13 like bananas and 2 like both. How many like neither? (a) 5 (b) 2 (c) 7 (d) 9
12. 12.In a class of 32 children, 11 like tea, 24 like coffee and 8 like both. How many like only tea? (a) 8 (b) 16 (c) 3 (d) 11
13. 13.In a class of 26 children, 17 like dance, 20 like music and 1 like neither. How many like both? (a) 12 (b) 25 (c) 1 (d) 11
14. 14.In a class of 35 children, 19 like tea, 27 like coffee and 12 like both. How many like neither? (a) 2 (b) 13 (c) 12 (d) 1
15. 15.In a class of 39 children, 22 like tea, 12 like coffee and 3 like both. How many like only tea? (a) 9 (b) 22 (c) 19 (d) 27
16. 16.In a class of 34 children, 18 like cricket, 20 like football and 2 like neither. How many like both? (a) 6 (b) 32 (c) 4 (d) 2
17. 17.In a class of 47 children, 21 like cricket, 31 like football and 12 like both. How many like neither? (a) 8 (b) 12 (c) 7 (d) 19
18. 18.In a class of 33 children, 13 like tea, 25 like coffee and 8 like both. How many like only tea? (a) 17 (b) 5 (c) 8 (d) 13
19. 19.In a class of 41 children, 17 like dance, 23 like music and 6 like both. How many like at least one of the two? (a) 28 (b) 41 (c) 40 (d) 34
20. 20.In a class of 48 children, 22 like cricket, 21 like football and 2 like both. How many like neither? (a) 9 (b) 5 (c) 2 (d) 7
21. 21.In a class of 53 children, 24 like maths, 24 like science and 5 like both. How many like neither? (a) 10 (b) 5 (c) 15 (d) 11
22. 22.In a class of 28 children, 20 like maths, 8 like science and 4 like neither. How many like both? (a) 5 (b) 3 (c) 24 (d) 4
23. 23.In a class of 31 children, 25 like cricket, 11 like football and 8 like both. How many like neither? (a) 4 (b) 11 (c) 8 (d) 3
24. 24.In a class of 38 children, 9 like cricket, 22 like football and 10 like neither. How many like both? (a) 10 (b) 3 (c) 4 (d) 28
25. 25.In a class of 23 children, 15 like tea, 16 like coffee and 2 like neither. How many like both? (a) 21 (b) 10 (c) 2 (d) 8
26. 26.In a class of 31 children, 10 like dance, 16 like music and 3 like both. How many like only dance? (a) 15 (b) 10 (c) 13 (d) 7
27. 27.In a class of 46 children, 23 like cricket, 31 like football and 12 like both. How many like neither? (a) 16 (b) 12 (c) 4 (d) 5
28. 28.In a class of 48 children, 18 like maths, 26 like science and 10 like neither. How many like both? (a) 7 (b) 38 (c) 10 (d) 6
29. 29.In a class of 37 children, 25 like cricket, 14 like football and 3 like neither. How many like both? (a) 34 (b) 2 (c) 5 (d) 3
30. 30.In a class of 38 children, 15 like cricket, 24 like football and 5 like both. How many like at least one of the two? (a) 34 (b) 29 (c) 38 (d) 39
31. 31.In a class of 46 children, 32 like maths, 17 like science and 12 like both. How many like only maths? (a) 20 (b) 5 (c) 29 (d) 32
32. 32.In a class of 27 children, 20 like dance, 9 like music and 5 like both. How many like neither? (a) 5 (b) 8 (c) 4 (d) 3
33. 33.In a class of 25 children, 14 like cricket, 14 like football and 5 like both. How many like at least one of the two? (a) 25 (b) 18 (c) 28 (d) 23
34. 34.In a class of 26 children, 17 like tea, 16 like coffee and 11 like both. How many like only tea? (a) 6 (b) 17 (c) 5 (d) 10
35. 35.In a class of 29 children, 15 like dance, 15 like music and 4 like both. How many like only dance? (a) 14 (b) 4 (c) 15 (d) 11
36. 36.In a class of 30 children, 9 like cricket, 17 like football and 5 like both. How many like at least one of the two? (a) 30 (b) 21 (c) 16 (d) 26
37. 37.In a class of 50 children, 23 like mangoes, 26 like bananas and 7 like both. How many like neither? (a) 15 (b) 8 (c) 7 (d) 1
38. 38.In a class of 37 children, 21 like dance, 18 like music and 11 like both. How many like only dance? (a) 10 (b) 19 (c) 21 (d) 7
39. 39.In a class of 32 children, 13 like dance, 16 like music and 7 like neither. How many like both? (a) 7 (b) 25 (c) 4 (d) 5
40. 40.In a class of 46 children, 20 like tea, 23 like coffee and 6 like both. How many like neither? (a) 9 (b) 3 (c) 15 (d) 6

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