Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 11 · 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 20 children, 12 like mangoes, 12 like bananas and 8 like both. How many like at least one of the two? (a) 8 (b) 20 (c) 16 (d) 24
2. 2.In a class of 15 children, 7 like tea, 9 like coffee and 4 like both. How many like at least one of the two? (a) 16 (b) 12 (c) 15 (d) 8
3. 3.In a class of 22 children, 10 like mangoes, 15 like bananas and 1 like neither. How many like both? (a) 4 (b) 1 (c) 3 (d) 21
4. 4.In a class of 21 children, 7 like tea, 15 like coffee and 4 like both. How many like neither? (a) 4 (b) 7 (c) 2 (d) 3
5. 5.In a class of 42 children, 18 like tea, 27 like coffee and 8 like neither. How many like both? (a) 34 (b) 8 (c) 11 (d) 3
6. 6.In a class of 36 children, 14 like cricket, 25 like football and 6 like both. How many like at least one of the two? (a) 39 (b) 36 (c) 27 (d) 33
7. 7.In a class of 36 children, 22 like tea, 14 like coffee and 8 like neither. How many like both? (a) 7 (b) 28 (c) 8 (d) 9
8. 8.In a class of 25 children, 11 like tea, 7 like coffee and 3 like both. How many like at least one of the two? (a) 15 (b) 25 (c) 18 (d) 12
9. 9.In a class of 21 children, 10 like maths, 12 like science and 2 like neither. How many like both? (a) 1 (b) 19 (c) 2 (d) 3
10. 10.In a class of 25 children, 14 like mangoes, 18 like bananas and 8 like both. How many like neither? (a) 9 (b) 1 (c) 2 (d) 8
11. 11.In a class of 30 children, 18 like mangoes, 9 like bananas and 5 like neither. How many like both? (a) 2 (b) 3 (c) 25 (d) 5
12. 12.In a class of 25 children, 9 like tea, 16 like coffee and 4 like both. How many like only tea? (a) 9 (b) 12 (c) 4 (d) 5
13. 13.In a class of 28 children, 19 like cricket, 17 like football and 11 like both. How many like at least one of the two? (a) 25 (b) 36 (c) 28 (d) 14
14. 14.In a class of 36 children, 12 like dance, 21 like music and 6 like both. How many like at least one of the two? (a) 33 (b) 27 (c) 21 (d) 36
15. 15.In a class of 33 children, 17 like mangoes, 13 like bananas and 9 like neither. How many like both? (a) 24 (b) 7 (c) 6 (d) 9
16. 16.In a class of 34 children, 18 like maths, 14 like science and 8 like both. How many like only maths? (a) 20 (b) 6 (c) 10 (d) 18
17. 17.In a class of 21 children, 11 like cricket, 13 like football and 3 like neither. How many like both? (a) 6 (b) 18 (c) 3 (d) 7
18. 18.In a class of 39 children, 12 like tea, 25 like coffee and 10 like neither. How many like both? (a) 29 (b) 8 (c) 10 (d) 9
19. 19.In a class of 18 children, 11 like mangoes, 8 like bananas and 4 like both. How many like neither? (a) 7 (b) 3 (c) 2 (d) 4
20. 20.In a class of 50 children, 22 like cricket, 24 like football and 5 like both. How many like neither? (a) 14 (b) 5 (c) 4 (d) 9
21. 21.In a class of 38 children, 18 like mangoes, 15 like bananas and 2 like both. How many like at least one of the two? (a) 29 (b) 31 (c) 38 (d) 33
22. 22.In a class of 22 children, 12 like dance, 13 like music and 4 like both. How many like neither? (a) 4 (b) 1 (c) 2 (d) 5
23. 23.In a class of 33 children, 21 like mangoes, 13 like bananas and 3 like both. How many like only mangoes? (a) 21 (b) 20 (c) 18 (d) 10
24. 24.In a class of 30 children, 18 like tea, 16 like coffee and 6 like both. How many like at least one of the two? (a) 28 (b) 34 (c) 22 (d) 30
25. 25.In a class of 23 children, 12 like cricket, 12 like football and 2 like both. How many like at least one of the two? (a) 24 (b) 23 (c) 22 (d) 20
26. 26.In a class of 36 children, 14 like maths, 22 like science and 9 like neither. How many like both? (a) 27 (b) 10 (c) 8 (d) 9
27. 27.In a class of 34 children, 22 like mangoes, 17 like bananas and 7 like both. How many like neither? (a) 7 (b) 9 (c) 3 (d) 2
28. 28.In a class of 40 children, 22 like dance, 18 like music and 3 like both. How many like only dance? (a) 19 (b) 3 (c) 15 (d) 22
29. 29.In a class of 50 children, 21 like tea, 23 like coffee and 10 like neither. How many like both? (a) 40 (b) 4 (c) 10 (d) 5
30. 30.In a class of 36 children, 27 like cricket, 15 like football and 10 like both. How many like at least one of the two? (a) 22 (b) 32 (c) 42 (d) 36
31. 31.In a class of 51 children, 26 like cricket, 23 like football and 7 like both. How many like neither? (a) 9 (b) 16 (c) 2 (d) 7
32. 32.In a class of 38 children, 23 like cricket, 22 like football and 11 like both. How many like only cricket? (a) 11 (b) 23 (c) 16 (d) 12
33. 33.In a class of 25 children, 20 like cricket, 13 like football and 10 like both. How many like at least one of the two? (a) 33 (b) 25 (c) 23 (d) 13
34. 34.In a class of 45 children, 25 like tea, 24 like coffee and 3 like neither. How many like both? (a) 42 (b) 4 (c) 7 (d) 3
35. 35.In a class of 27 children, 10 like tea, 21 like coffee and 7 like both. How many like neither? (a) 10 (b) 4 (c) 7 (d) 3
36. 36.In a class of 41 children, 19 like mangoes, 24 like bananas and 6 like both. How many like at least one of the two? (a) 37 (b) 43 (c) 41 (d) 31
37. 37.In a class of 38 children, 18 like maths, 21 like science and 11 like both. How many like neither? (a) 11 (b) 21 (c) 9 (d) 10
38. 38.In a class of 32 children, 16 like cricket, 18 like football and 12 like both. How many like only cricket? (a) 16 (b) 6 (c) 14 (d) 4
39. 39.In a class of 37 children, 15 like dance, 28 like music and 3 like neither. How many like both? (a) 6 (b) 3 (c) 34 (d) 9
40. 40.In a class of 35 children, 24 like maths, 16 like science and 11 like both. How many like neither? (a) 17 (b) 11 (c) 7 (d) 6

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