Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 129 · 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 43 children, 24 like cricket, 24 like football and 7 like both. How many like at least one of the two? (a) 41 (b) 43 (c) 48 (d) 34
2. 2.In a class of 31 children, 18 like cricket, 5 like football and 2 like both. How many like neither? (a) 8 (b) 10 (c) 12 (d) 2
3. 3.In a class of 26 children, 12 like mangoes, 14 like bananas and 2 like neither. How many like both? (a) 3 (b) 24 (c) 2 (d) 1
4. 4.In a class of 39 children, 28 like dance, 21 like music and 2 like neither. How many like both? (a) 12 (b) 2 (c) 10 (d) 37
5. 5.In a class of 34 children, 22 like dance, 13 like music and 9 like both. How many like at least one of the two? (a) 26 (b) 34 (c) 17 (d) 35
6. 6.In a class of 33 children, 16 like maths, 17 like science and 3 like both. How many like only maths? (a) 3 (b) 14 (c) 16 (d) 13
7. 7.In a class of 41 children, 16 like cricket, 24 like football and 5 like both. How many like at least one of the two? (a) 40 (b) 35 (c) 30 (d) 41
8. 8.In a class of 31 children, 19 like mangoes, 14 like bananas and 10 like both. How many like only mangoes? (a) 19 (b) 4 (c) 9 (d) 17
9. 9.In a class of 43 children, 23 like cricket, 23 like football and 4 like both. How many like at least one of the two? (a) 43 (b) 46 (c) 42 (d) 38
10. 10.In a class of 41 children, 15 like maths, 24 like science and 9 like neither. How many like both? (a) 7 (b) 8 (c) 32 (d) 9
11. 11.In a class of 34 children, 20 like cricket, 12 like football and 2 like both. How many like at least one of the two? (a) 32 (b) 30 (c) 28 (d) 34
12. 12.In a class of 31 children, 18 like tea, 22 like coffee and 3 like neither. How many like both? (a) 28 (b) 9 (c) 3 (d) 12
13. 13.In a class of 21 children, 10 like cricket, 9 like football and 3 like both. How many like neither? (a) 2 (b) 5 (c) 3 (d) 8
14. 14.In a class of 31 children, 23 like mangoes, 16 like bananas and 9 like both. How many like neither? (a) 10 (b) 1 (c) 9 (d) 2
15. 15.In a class of 33 children, 27 like mangoes, 10 like bananas and 3 like neither. How many like both? (a) 30 (b) 3 (c) 4 (d) 7
16. 16.In a class of 34 children, 21 like maths, 16 like science and 8 like both. How many like only maths? (a) 18 (b) 21 (c) 8 (d) 13
17. 17.In a class of 44 children, 24 like cricket, 17 like football and 4 like both. How many like at least one of the two? (a) 37 (b) 41 (c) 44 (d) 33
18. 18.In a class of 51 children, 30 like mangoes, 30 like bananas and 12 like both. How many like neither? (a) 4 (b) 15 (c) 12 (d) 3
19. 19.In a class of 28 children, 11 like mangoes, 12 like bananas and 4 like both. How many like neither? (a) 13 (b) 5 (c) 4 (d) 9
20. 20.In a class of 33 children, 20 like mangoes, 19 like bananas and 9 like both. How many like only mangoes? (a) 20 (b) 14 (c) 10 (d) 11
21. 21.In a class of 27 children, 7 like tea, 21 like coffee and 4 like both. How many like neither? (a) 3 (b) 7 (c) 2 (d) 4
22. 22.In a class of 40 children, 19 like tea, 19 like coffee and 3 like both. How many like only tea? (a) 16 (b) 21 (c) 3 (d) 19
23. 23.In a class of 39 children, 21 like maths, 26 like science and 10 like both. How many like only maths? (a) 16 (b) 11 (c) 21 (d) 13
24. 24.In a class of 26 children, 13 like dance, 17 like music and 8 like both. How many like neither? (a) 12 (b) 5 (c) 4 (d) 8
25. 25.In a class of 34 children, 18 like tea, 15 like coffee and 5 like both. How many like neither? (a) 6 (b) 5 (c) 11 (d) 1
26. 26.In a class of 48 children, 26 like tea, 26 like coffee and 8 like both. How many like only tea? (a) 22 (b) 8 (c) 18 (d) 26
27. 27.In a class of 33 children, 14 like dance, 18 like music and 8 like neither. How many like both? (a) 25 (b) 8 (c) 7 (d) 6
28. 28.In a class of 22 children, 17 like maths, 14 like science and 10 like both. How many like only maths? (a) 17 (b) 4 (c) 7 (d) 8
29. 29.In a class of 30 children, 17 like tea, 14 like coffee and 6 like both. How many like neither? (a) 4 (b) 5 (c) 11 (d) 6
30. 30.In a class of 45 children, 27 like dance, 24 like music and 8 like both. How many like at least one of the two? (a) 45 (b) 35 (c) 51 (d) 43
31. 31.In a class of 24 children, 9 like maths, 10 like science and 2 like both. How many like at least one of the two? (a) 17 (b) 15 (c) 24 (d) 19
32. 32.In a class of 36 children, 24 like tea, 9 like coffee and 4 like both. How many like at least one of the two? (a) 25 (b) 33 (c) 29 (d) 36
33. 33.In a class of 20 children, 6 like tea, 15 like coffee and 1 like neither. How many like both? (a) 19 (b) 2 (c) 1 (d) 3
34. 34.In a class of 16 children, 8 like maths, 9 like science and 5 like both. How many like only maths? (a) 3 (b) 4 (c) 7 (d) 8
35. 35.In a class of 48 children, 24 like tea, 28 like coffee and 7 like neither. How many like both? (a) 7 (b) 41 (c) 11 (d) 4
36. 36.In a class of 33 children, 8 like mangoes, 25 like bananas and 5 like both. How many like only mangoes? (a) 20 (b) 3 (c) 5 (d) 8
37. 37.In a class of 32 children, 14 like maths, 20 like science and 1 like neither. How many like both? (a) 2 (b) 1 (c) 31 (d) 3
38. 38.In a class of 39 children, 21 like mangoes, 24 like bananas and 12 like both. How many like only mangoes? (a) 9 (b) 21 (c) 12 (d) 15
39. 39.In a class of 36 children, 14 like maths, 22 like science and 4 like both. How many like at least one of the two? (a) 33 (b) 36 (c) 32 (d) 28
40. 40.In a class of 34 children, 14 like dance, 20 like music and 7 like both. How many like only dance? (a) 7 (b) 13 (c) 8 (d) 14

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