Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 360 · 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 41 children, 23 like mangoes, 15 like bananas and 9 like neither. How many like both? (a) 9 (b) 7 (c) 32 (d) 6
2. 2.In a class of 40 children, 23 like cricket, 13 like football and 6 like both. How many like neither? (a) 4 (b) 10 (c) 6 (d) 16
3. 3.In a class of 48 children, 26 like dance, 19 like music and 9 like neither. How many like both? (a) 9 (b) 39 (c) 7 (d) 6
4. 4.In a class of 22 children, 9 like maths, 15 like science and 4 like both. How many like neither? (a) 2 (b) 3 (c) 4 (d) 6
5. 5.In a class of 28 children, 14 like tea, 8 like coffee and 3 like both. How many like at least one of the two? (a) 16 (b) 19 (c) 28 (d) 22
6. 6.In a class of 32 children, 17 like dance, 22 like music and 8 like both. How many like only dance? (a) 9 (b) 14 (c) 17 (d) 10
7. 7.In a class of 41 children, 21 like maths, 21 like science and 9 like both. How many like neither? (a) 8 (b) 7 (c) 9 (d) 17
8. 8.In a class of 32 children, 25 like mangoes, 12 like bananas and 3 like neither. How many like both? (a) 5 (b) 3 (c) 8 (d) 29
9. 9.In a class of 24 children, 16 like dance, 16 like music and 3 like neither. How many like both? (a) 21 (b) 8 (c) 3 (d) 11
10. 10.In a class of 27 children, 17 like mangoes, 14 like bananas and 10 like both. How many like only mangoes? (a) 17 (b) 13 (c) 7 (d) 4
11. 11.In a class of 20 children, 10 like dance, 12 like music and 5 like both. How many like at least one of the two? (a) 12 (b) 22 (c) 17 (d) 20
12. 12.In a class of 32 children, 18 like mangoes, 7 like bananas and 3 like both. How many like at least one of the two? (a) 19 (b) 22 (c) 25 (d) 32
13. 13.In a class of 27 children, 20 like tea, 10 like coffee and 5 like both. How many like at least one of the two? (a) 30 (b) 20 (c) 25 (d) 27
14. 14.In a class of 38 children, 19 like dance, 19 like music and 2 like both. How many like at least one of the two? (a) 34 (b) 38 (c) 36 (d) 37
15. 15.In a class of 33 children, 14 like dance, 18 like music and 7 like both. How many like only dance? (a) 7 (b) 14 (c) 15 (d) 11
16. 16.In a class of 33 children, 21 like tea, 14 like coffee and 5 like both. How many like neither? (a) 8 (b) 3 (c) 4 (d) 5
17. 17.In a class of 36 children, 15 like dance, 19 like music and 8 like neither. How many like both? (a) 6 (b) 28 (c) 7 (d) 8
18. 18.In a class of 44 children, 25 like maths, 24 like science and 9 like both. How many like neither? (a) 5 (b) 9 (c) 13 (d) 4
19. 19.In a class of 24 children, 16 like mangoes, 10 like bananas and 4 like neither. How many like both? (a) 2 (b) 6 (c) 20 (d) 4
20. 20.In a class of 24 children, 11 like maths, 9 like science and 2 like both. How many like neither? (a) 2 (b) 8 (c) 4 (d) 6
21. 21.In a class of 32 children, 16 like maths, 26 like science and 11 like both. How many like neither? (a) 12 (b) 2 (c) 1 (d) 11
22. 22.In a class of 29 children, 18 like cricket, 12 like football and 2 like neither. How many like both? (a) 1 (b) 3 (c) 27 (d) 2
23. 23.In a class of 30 children, 21 like cricket, 8 like football and 3 like both. How many like neither? (a) 4 (b) 7 (c) 3 (d) 1
24. 24.In a class of 52 children, 25 like mangoes, 27 like bananas and 7 like both. How many like neither? (a) 14 (b) 0 (c) 8 (d) 7
25. 25.In a class of 20 children, 12 like mangoes, 8 like bananas and 3 like both. How many like at least one of the two? (a) 17 (b) 18 (c) 14 (d) 20
26. 26.In a class of 36 children, 15 like mangoes, 23 like bananas and 7 like both. How many like at least one of the two? (a) 38 (b) 36 (c) 31 (d) 24
27. 27.In a class of 22 children, 15 like mangoes, 13 like bananas and 8 like both. How many like neither? (a) 10 (b) 2 (c) 8 (d) 3
28. 28.In a class of 31 children, 17 like cricket, 15 like football and 1 like neither. How many like both? (a) 3 (b) 30 (c) 1 (d) 2
29. 29.In a class of 37 children, 27 like tea, 14 like coffee and 3 like neither. How many like both? (a) 34 (b) 7 (c) 3 (d) 4
30. 30.In a class of 24 children, 18 like dance, 10 like music and 7 like both. How many like only dance? (a) 11 (b) 3 (c) 14 (d) 18
31. 31.In a class of 33 children, 16 like dance, 13 like music and 6 like both. How many like at least one of the two? (a) 17 (b) 33 (c) 23 (d) 29
32. 32.In a class of 15 children, 10 like cricket, 7 like football and 3 like both. How many like only cricket? (a) 10 (b) 8 (c) 4 (d) 7
33. 33.In a class of 15 children, 9 like maths, 6 like science and 3 like neither. How many like both? (a) 3 (b) 2 (c) 12 (d) 4
34. 34.In a class of 32 children, 24 like dance, 10 like music and 5 like neither. How many like both? (a) 7 (b) 2 (c) 5 (d) 27
35. 35.In a class of 24 children, 17 like maths, 7 like science and 4 like both. How many like only maths? (a) 4 (b) 17 (c) 3 (d) 13
36. 36.In a class of 34 children, 13 like cricket, 28 like football and 9 like both. How many like neither? (a) 3 (b) 9 (c) 2 (d) 11
37. 37.In a class of 34 children, 18 like cricket, 17 like football and 11 like both. How many like neither? (a) 9 (b) 21 (c) 11 (d) 10
38. 38.In a class of 33 children, 14 like cricket, 17 like football and 8 like both. How many like neither? (a) 2 (b) 10 (c) 18 (d) 8
39. 39.In a class of 23 children, 7 like mangoes, 15 like bananas and 4 like both. How many like at least one of the two? (a) 23 (b) 22 (c) 18 (d) 14
40. 40.In a class of 30 children, 14 like maths, 24 like science and 1 like neither. How many like both? (a) 9 (b) 29 (c) 1 (d) 8

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