Venn Diagram Worksheet for Maths Olympiad

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

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