Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 74 · 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 39 children, 27 like tea, 20 like coffee and 10 like both. How many like only tea? (a) 27 (b) 17 (c) 10 (d) 19
2. 2.In a class of 38 children, 21 like maths, 22 like science and 11 like both. How many like only maths? (a) 10 (b) 21 (c) 11 (d) 16
3. 3.In a class of 37 children, 16 like tea, 23 like coffee and 3 like both. How many like at least one of the two? (a) 39 (b) 37 (c) 36 (d) 33
4. 4.In a class of 44 children, 20 like dance, 24 like music and 7 like neither. How many like both? (a) 8 (b) 7 (c) 6 (d) 37
5. 5.In a class of 37 children, 15 like cricket, 18 like football and 6 like both. How many like only cricket? (a) 19 (b) 12 (c) 15 (d) 9
6. 6.In a class of 48 children, 28 like maths, 22 like science and 10 like neither. How many like both? (a) 38 (b) 2 (c) 10 (d) 12
7. 7.In a class of 38 children, 14 like cricket, 29 like football and 9 like both. How many like only cricket? (a) 20 (b) 14 (c) 9 (d) 5
8. 8.In a class of 42 children, 19 like cricket, 21 like football and 4 like both. How many like only cricket? (a) 21 (b) 15 (c) 17 (d) 19
9. 9.In a class of 35 children, 10 like tea, 23 like coffee and 5 like both. How many like at least one of the two? (a) 33 (b) 35 (c) 23 (d) 28
10. 10.In a class of 27 children, 17 like dance, 14 like music and 7 like both. How many like neither? (a) 4 (b) 7 (c) 3 (d) 10
11. 11.In a class of 24 children, 12 like cricket, 5 like football and 2 like both. How many like only cricket? (a) 12 (b) 3 (c) 19 (d) 10
12. 12.In a class of 32 children, 15 like mangoes, 20 like bananas and 4 like both. How many like neither? (a) 4 (b) 2 (c) 1 (d) 5
13. 13.In a class of 22 children, 7 like mangoes, 9 like bananas and 4 like both. How many like neither? (a) 14 (b) 6 (c) 4 (d) 10
14. 14.In a class of 30 children, 16 like cricket, 13 like football and 5 like both. How many like neither? (a) 11 (b) 1 (c) 6 (d) 5
15. 15.In a class of 35 children, 22 like cricket, 14 like football and 9 like both. How many like only cricket? (a) 22 (b) 21 (c) 5 (d) 13
16. 16.In a class of 35 children, 19 like dance, 17 like music and 7 like both. How many like only dance? (a) 10 (b) 19 (c) 18 (d) 12
17. 17.In a class of 44 children, 27 like mangoes, 21 like bananas and 11 like both. How many like at least one of the two? (a) 37 (b) 48 (c) 44 (d) 26
18. 18.In a class of 29 children, 10 like dance, 25 like music and 7 like both. How many like only dance? (a) 18 (b) 3 (c) 10 (d) 4
19. 19.In a class of 32 children, 17 like tea, 9 like coffee and 4 like both. How many like only tea? (a) 5 (b) 13 (c) 17 (d) 23
20. 20.In a class of 44 children, 31 like tea, 21 like coffee and 12 like both. How many like only tea? (a) 19 (b) 9 (c) 31 (d) 23
21. 21.In a class of 28 children, 18 like cricket, 15 like football and 9 like both. How many like only cricket? (a) 6 (b) 18 (c) 13 (d) 9
22. 22.In a class of 17 children, 8 like maths, 9 like science and 5 like neither. How many like both? (a) 12 (b) 5 (c) 4 (d) 6
23. 23.In a class of 43 children, 25 like dance, 16 like music and 5 like both. How many like only dance? (a) 11 (b) 20 (c) 27 (d) 25
24. 24.In a class of 22 children, 10 like tea, 13 like coffee and 5 like both. How many like at least one of the two? (a) 18 (b) 13 (c) 22 (d) 23
25. 25.In a class of 34 children, 26 like tea, 12 like coffee and 7 like both. How many like only tea? (a) 5 (b) 19 (c) 22 (d) 26
26. 26.In a class of 18 children, 9 like cricket, 12 like football and 2 like neither. How many like both? (a) 16 (b) 3 (c) 2 (d) 5
27. 27.In a class of 38 children, 16 like tea, 19 like coffee and 2 like both. How many like only tea? (a) 16 (b) 19 (c) 17 (d) 14
28. 28.In a class of 42 children, 27 like dance, 23 like music and 11 like both. How many like only dance? (a) 27 (b) 12 (c) 19 (d) 16
29. 29.In a class of 31 children, 15 like cricket, 14 like football and 4 like neither. How many like both? (a) 27 (b) 2 (c) 4 (d) 3
30. 30.In a class of 34 children, 16 like cricket, 21 like football and 6 like both. How many like only cricket? (a) 13 (b) 16 (c) 15 (d) 10
31. 31.In a class of 46 children, 23 like tea, 19 like coffee and 4 like both. How many like only tea? (a) 15 (b) 23 (c) 19 (d) 27
32. 32.In a class of 32 children, 26 like tea, 12 like coffee and 8 like both. How many like at least one of the two? (a) 32 (b) 22 (c) 30 (d) 38
33. 33.In a class of 33 children, 22 like tea, 15 like coffee and 6 like both. How many like neither? (a) 2 (b) 8 (c) 3 (d) 6
34. 34.In a class of 28 children, 18 like tea, 21 like coffee and 12 like both. How many like neither? (a) 12 (b) 13 (c) 2 (d) 1
35. 35.In a class of 44 children, 18 like maths, 20 like science and 4 like both. How many like only maths? (a) 16 (b) 18 (c) 14 (d) 24
36. 36.In a class of 41 children, 19 like dance, 27 like music and 10 like both. How many like at least one of the two? (a) 41 (b) 26 (c) 36 (d) 46
37. 37.In a class of 38 children, 15 like maths, 22 like science and 4 like both. How many like only maths? (a) 16 (b) 11 (c) 18 (d) 15
38. 38.In a class of 31 children, 17 like tea, 18 like coffee and 8 like neither. How many like both? (a) 23 (b) 8 (c) 4 (d) 12
39. 39.In a class of 34 children, 17 like tea, 23 like coffee and 10 like both. How many like only tea? (a) 11 (b) 17 (c) 13 (d) 7
40. 40.In a class of 51 children, 26 like dance, 26 like music and 10 like both. How many like only dance? (a) 26 (b) 25 (c) 10 (d) 16

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