Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 52 · 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 49 children, 23 like tea, 28 like coffee and 11 like both. How many like at least one of the two? (a) 40 (b) 29 (c) 51 (d) 49
2. 2.In a class of 38 children, 27 like cricket, 16 like football and 10 like both. How many like neither? (a) 6 (b) 10 (c) 5 (d) 15
3. 3.In a class of 24 children, 14 like cricket, 19 like football and 10 like both. How many like neither? (a) 2 (b) 10 (c) 1 (d) 11
4. 4.In a class of 29 children, 8 like mangoes, 17 like bananas and 8 like neither. How many like both? (a) 5 (b) 4 (c) 8 (d) 21
5. 5.In a class of 31 children, 11 like cricket, 25 like football and 8 like both. How many like at least one of the two? (a) 20 (b) 36 (c) 28 (d) 31
6. 6.In a class of 43 children, 16 like cricket, 25 like football and 5 like both. How many like at least one of the two? (a) 41 (b) 31 (c) 43 (d) 36
7. 7.In a class of 29 children, 11 like tea, 18 like coffee and 2 like both. How many like only tea? (a) 16 (b) 2 (c) 11 (d) 9
8. 8.In a class of 29 children, 14 like dance, 14 like music and 5 like both. How many like only dance? (a) 9 (b) 15 (c) 5 (d) 14
9. 9.In a class of 37 children, 18 like cricket, 29 like football and 12 like both. How many like only cricket? (a) 6 (b) 8 (c) 18 (d) 17
10. 10.In a class of 29 children, 16 like cricket, 11 like football and 5 like neither. How many like both? (a) 4 (b) 5 (c) 3 (d) 24
11. 11.In a class of 34 children, 21 like tea, 9 like coffee and 6 like neither. How many like both? (a) 6 (b) 28 (c) 2 (d) 3
12. 12.In a class of 48 children, 23 like dance, 24 like music and 5 like neither. How many like both? (a) 4 (b) 3 (c) 5 (d) 43
13. 13.In a class of 34 children, 24 like dance, 14 like music and 7 like both. How many like only dance? (a) 20 (b) 17 (c) 7 (d) 24
14. 14.In a class of 41 children, 21 like tea, 29 like coffee and 10 like both. How many like at least one of the two? (a) 41 (b) 40 (c) 50 (d) 30
15. 15.In a class of 46 children, 24 like dance, 27 like music and 8 like both. How many like at least one of the two? (a) 46 (b) 51 (c) 35 (d) 43
16. 16.In a class of 24 children, 12 like dance, 11 like music and 7 like neither. How many like both? (a) 7 (b) 17 (c) 5 (d) 6
17. 17.In a class of 44 children, 30 like maths, 16 like science and 9 like neither. How many like both? (a) 9 (b) 35 (c) 2 (d) 11
18. 18.In a class of 25 children, 9 like mangoes, 18 like bananas and 4 like both. How many like neither? (a) 6 (b) 4 (c) 3 (d) 2
19. 19.In a class of 43 children, 19 like mangoes, 21 like bananas and 7 like both. How many like neither? (a) 10 (b) 7 (c) 17 (d) 3
20. 20.In a class of 52 children, 27 like maths, 26 like science and 11 like both. How many like neither? (a) 21 (b) 9 (c) 11 (d) 10
21. 21.In a class of 21 children, 10 like dance, 10 like music and 6 like both. How many like at least one of the two? (a) 20 (b) 21 (c) 14 (d) 8
22. 22.In a class of 17 children, 9 like dance, 11 like music and 5 like both. How many like at least one of the two? (a) 15 (b) 20 (c) 17 (d) 10
23. 23.In a class of 47 children, 24 like mangoes, 26 like bananas and 9 like neither. How many like both? (a) 38 (b) 9 (c) 12 (d) 3
24. 24.In a class of 44 children, 31 like tea, 22 like coffee and 11 like both. How many like at least one of the two? (a) 42 (b) 31 (c) 53 (d) 44
25. 25.In a class of 22 children, 9 like cricket, 12 like football and 3 like both. How many like only cricket? (a) 9 (b) 6 (c) 3 (d) 10
26. 26.In a class of 38 children, 22 like tea, 17 like coffee and 9 like neither. How many like both? (a) 9 (b) 29 (c) 1 (d) 10
27. 27.In a class of 21 children, 12 like tea, 10 like coffee and 2 like both. How many like at least one of the two? (a) 20 (b) 18 (c) 22 (d) 21
28. 28.In a class of 28 children, 9 like tea, 15 like coffee and 10 like neither. How many like both? (a) 10 (b) 7 (c) 18 (d) 6
29. 29.In a class of 44 children, 29 like cricket, 23 like football and 11 like both. How many like neither? (a) 3 (b) 14 (c) 4 (d) 11
30. 30.In a class of 39 children, 21 like mangoes, 22 like bananas and 8 like both. How many like at least one of the two? (a) 43 (b) 27 (c) 35 (d) 39
31. 31.In a class of 49 children, 29 like maths, 29 like science and 10 like both. How many like neither? (a) 11 (b) 2 (c) 10 (d) 1
32. 32.In a class of 25 children, 11 like dance, 10 like music and 9 like neither. How many like both? (a) 9 (b) 16 (c) 5 (d) 6
33. 33.In a class of 31 children, 17 like cricket, 8 like football and 2 like both. How many like only cricket? (a) 17 (b) 6 (c) 23 (d) 15
34. 34.In a class of 25 children, 12 like cricket, 8 like football and 3 like both. How many like at least one of the two? (a) 20 (b) 25 (c) 14 (d) 17
35. 35.In a class of 39 children, 13 like dance, 28 like music and 9 like both. How many like only dance? (a) 11 (b) 4 (c) 19 (d) 13
36. 36.In a class of 42 children, 25 like cricket, 17 like football and 5 like both. How many like neither? (a) 10 (b) 6 (c) 5 (d) 0
37. 37.In a class of 39 children, 22 like dance, 14 like music and 7 like both. How many like at least one of the two? (a) 39 (b) 36 (c) 29 (d) 22
38. 38.In a class of 29 children, 14 like mangoes, 20 like bananas and 8 like both. How many like only mangoes? (a) 9 (b) 12 (c) 14 (d) 6
39. 39.In a class of 45 children, 22 like tea, 25 like coffee and 11 like both. How many like at least one of the two? (a) 47 (b) 36 (c) 25 (d) 45
40. 40.In a class of 33 children, 16 like tea, 14 like coffee and 4 like both. How many like neither? (a) 4 (b) 3 (c) 7 (d) 11

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