Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 24 · 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, 16 like maths, 15 like science and 12 like both. How many like at least one of the two? (a) 31 (b) 19 (c) 7 (d) 20
2. 2.In a class of 36 children, 19 like tea, 23 like coffee and 3 like neither. How many like both? (a) 33 (b) 3 (c) 6 (d) 9
3. 3.In a class of 30 children, 7 like cricket, 19 like football and 3 like both. How many like at least one of the two? (a) 30 (b) 26 (c) 20 (d) 23
4. 4.In a class of 37 children, 18 like cricket, 18 like football and 4 like both. How many like only cricket? (a) 19 (b) 4 (c) 14 (d) 18
5. 5.In a class of 48 children, 23 like cricket, 23 like football and 8 like neither. How many like both? (a) 40 (b) 8 (c) 7 (d) 6
6. 6.In a class of 30 children, 15 like maths, 23 like science and 12 like both. How many like at least one of the two? (a) 26 (b) 38 (c) 14 (d) 30
7. 7.In a class of 33 children, 18 like maths, 11 like science and 4 like both. How many like only maths? (a) 7 (b) 14 (c) 18 (d) 22
8. 8.In a class of 47 children, 21 like maths, 24 like science and 5 like both. How many like at least one of the two? (a) 47 (b) 40 (c) 35 (d) 45
9. 9.In a class of 31 children, 14 like cricket, 26 like football and 10 like both. How many like only cricket? (a) 16 (b) 5 (c) 4 (d) 14
10. 10.In a class of 37 children, 10 like tea, 21 like coffee and 4 like both. How many like at least one of the two? (a) 23 (b) 37 (c) 31 (d) 27
11. 11.In a class of 47 children, 31 like mangoes, 24 like bananas and 12 like both. How many like only mangoes? (a) 23 (b) 31 (c) 12 (d) 19
12. 12.In a class of 23 children, 9 like mangoes, 12 like bananas and 3 like both. How many like at least one of the two? (a) 21 (b) 15 (c) 23 (d) 18
13. 13.In a class of 38 children, 25 like dance, 16 like music and 7 like neither. How many like both? (a) 10 (b) 31 (c) 7 (d) 3
14. 14.In a class of 33 children, 7 like maths, 20 like science and 2 like both. How many like only maths? (a) 7 (b) 18 (c) 5 (d) 13
15. 15.In a class of 38 children, 20 like cricket, 17 like football and 9 like both. How many like at least one of the two? (a) 37 (b) 28 (c) 38 (d) 19
16. 16.In a class of 43 children, 26 like tea, 16 like coffee and 8 like both. How many like neither? (a) 17 (b) 8 (c) 9 (d) 1
17. 17.In a class of 25 children, 8 like mangoes, 10 like bananas and 2 like both. How many like at least one of the two? (a) 18 (b) 25 (c) 16 (d) 14
18. 18.In a class of 18 children, 11 like maths, 7 like science and 3 like both. How many like at least one of the two? (a) 12 (b) 16 (c) 15 (d) 18
19. 19.In a class of 39 children, 31 like dance, 18 like music and 1 like neither. How many like both? (a) 1 (b) 38 (c) 11 (d) 10
20. 20.In a class of 41 children, 20 like maths, 20 like science and 5 like both. How many like neither? (a) 5 (b) 6 (c) 1 (d) 11
21. 21.In a class of 31 children, 11 like maths, 19 like science and 5 like both. How many like at least one of the two? (a) 31 (b) 25 (c) 30 (d) 20
22. 22.In a class of 37 children, 23 like tea, 17 like coffee and 5 like both. How many like at least one of the two? (a) 35 (b) 30 (c) 40 (d) 37
23. 23.In a class of 20 children, 12 like cricket, 9 like football and 2 like both. How many like at least one of the two? (a) 19 (b) 20 (c) 21 (d) 17
24. 24.In a class of 50 children, 30 like cricket, 21 like football and 11 like both. How many like only cricket? (a) 10 (b) 30 (c) 29 (d) 19
25. 25.In a class of 32 children, 19 like mangoes, 22 like bananas and 3 like neither. How many like both? (a) 29 (b) 3 (c) 12 (d) 9
26. 26.In a class of 42 children, 19 like cricket, 21 like football and 6 like both. How many like at least one of the two? (a) 34 (b) 42 (c) 28 (d) 40
27. 27.In a class of 40 children, 20 like mangoes, 13 like bananas and 9 like neither. How many like both? (a) 31 (b) 2 (c) 9 (d) 3
28. 28.In a class of 47 children, 25 like cricket, 26 like football and 9 like both. How many like at least one of the two? (a) 33 (b) 51 (c) 47 (d) 42
29. 29.In a class of 46 children, 27 like maths, 27 like science and 10 like both. How many like at least one of the two? (a) 54 (b) 44 (c) 34 (d) 46
30. 30.In a class of 22 children, 8 like cricket, 8 like football and 2 like both. How many like at least one of the two? (a) 14 (b) 22 (c) 12 (d) 16
31. 31.In a class of 35 children, 26 like dance, 14 like music and 6 like neither. How many like both? (a) 6 (b) 5 (c) 29 (d) 11
32. 32.In a class of 47 children, 23 like cricket, 25 like football and 9 like both. How many like only cricket? (a) 22 (b) 14 (c) 23 (d) 16
33. 33.In a class of 32 children, 17 like tea, 9 like coffee and 4 like both. How many like neither? (a) 4 (b) 14 (c) 10 (d) 6
34. 34.In a class of 20 children, 9 like tea, 12 like coffee and 5 like both. How many like neither? (a) 3 (b) 4 (c) 5 (d) 9
35. 35.In a class of 35 children, 15 like maths, 25 like science and 11 like both. How many like at least one of the two? (a) 35 (b) 18 (c) 40 (d) 29
36. 36.In a class of 33 children, 15 like maths, 20 like science and 5 like both. How many like at least one of the two? (a) 30 (b) 25 (c) 33 (d) 35
37. 37.In a class of 36 children, 19 like mangoes, 16 like bananas and 2 like both. How many like neither? (a) 1 (b) 5 (c) 2 (d) 3
38. 38.In a class of 26 children, 16 like mangoes, 10 like bananas and 2 like both. How many like neither? (a) 3 (b) 2 (c) 4 (d) 0
39. 39.In a class of 31 children, 14 like cricket, 20 like football and 8 like both. How many like neither? (a) 5 (b) 8 (c) 13 (d) 6
40. 40.In a class of 34 children, 17 like tea, 12 like coffee and 8 like neither. How many like both? (a) 8 (b) 26 (c) 3 (d) 4

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