Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 731 · 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 51 children, 30 like maths, 24 like science and 7 like neither. How many like both? (a) 44 (b) 10 (c) 7 (d) 3
2. 2.In a class of 32 children, 19 like maths, 11 like science and 5 like both. How many like only maths? (a) 6 (b) 19 (c) 21 (d) 14
3. 3.In a class of 44 children, 19 like dance, 26 like music and 11 like both. How many like only dance? (a) 8 (b) 15 (c) 18 (d) 19
4. 4.In a class of 24 children, 13 like dance, 12 like music and 7 like both. How many like only dance? (a) 13 (b) 12 (c) 5 (d) 6
5. 5.In a class of 31 children, 15 like tea, 17 like coffee and 10 like neither. How many like both? (a) 10 (b) 21 (c) 11 (d) 1
6. 6.In a class of 30 children, 10 like maths, 19 like science and 3 like neither. How many like both? (a) 27 (b) 2 (c) 3 (d) 1
7. 7.In a class of 49 children, 21 like maths, 29 like science and 11 like both. How many like neither? (a) 9 (b) 10 (c) 11 (d) 21
8. 8.In a class of 43 children, 23 like tea, 29 like coffee and 12 like both. How many like neither? (a) 12 (b) 15 (c) 3 (d) 4
9. 9.In a class of 27 children, 12 like dance, 14 like music and 2 like both. How many like at least one of the two? (a) 27 (b) 22 (c) 24 (d) 26
10. 10.In a class of 27 children, 8 like cricket, 22 like football and 1 like neither. How many like both? (a) 26 (b) 3 (c) 1 (d) 4
11. 11.In a class of 44 children, 28 like maths, 21 like science and 11 like both. How many like only maths? (a) 23 (b) 17 (c) 10 (d) 28
12. 12.In a class of 21 children, 12 like cricket, 12 like football and 5 like both. How many like at least one of the two? (a) 21 (b) 14 (c) 24 (d) 19
13. 13.In a class of 37 children, 22 like mangoes, 9 like bananas and 3 like both. How many like at least one of the two? (a) 25 (b) 28 (c) 31 (d) 37
14. 14.In a class of 29 children, 13 like dance, 19 like music and 10 like both. How many like only dance? (a) 13 (b) 9 (c) 3 (d) 10
15. 15.In a class of 42 children, 21 like dance, 24 like music and 4 like both. How many like only dance? (a) 18 (b) 21 (c) 17 (d) 20
16. 16.In a class of 38 children, 24 like mangoes, 12 like bananas and 4 like both. How many like at least one of the two? (a) 36 (b) 38 (c) 32 (d) 28
17. 17.In a class of 50 children, 27 like dance, 24 like music and 10 like both. How many like neither? (a) 8 (b) 10 (c) 19 (d) 9
18. 18.In a class of 51 children, 26 like maths, 27 like science and 9 like both. How many like only maths? (a) 24 (b) 26 (c) 18 (d) 17
19. 19.In a class of 24 children, 16 like mangoes, 13 like bananas and 10 like both. How many like only mangoes? (a) 16 (b) 11 (c) 6 (d) 3
20. 20.In a class of 30 children, 26 like maths, 11 like science and 8 like both. How many like neither? (a) 8 (b) 2 (c) 1 (d) 9
21. 21.In a class of 37 children, 23 like mangoes, 18 like bananas and 9 like both. How many like neither? (a) 14 (b) 5 (c) 6 (d) 9
22. 22.In a class of 39 children, 16 like cricket, 24 like football and 5 like neither. How many like both? (a) 1 (b) 6 (c) 5 (d) 34
23. 23.In a class of 23 children, 12 like maths, 11 like science and 3 like both. How many like neither? (a) 0 (b) 6 (c) 4 (d) 3
24. 24.In a class of 26 children, 11 like mangoes, 13 like bananas and 7 like both. How many like neither? (a) 16 (b) 7 (c) 9 (d) 2
25. 25.In a class of 28 children, 8 like tea, 21 like coffee and 5 like both. How many like only tea? (a) 16 (b) 3 (c) 7 (d) 8
26. 26.In a class of 31 children, 22 like tea, 5 like coffee and 2 like both. How many like only tea? (a) 22 (b) 3 (c) 20 (d) 26
27. 27.In a class of 39 children, 26 like cricket, 20 like football and 1 like neither. How many like both? (a) 8 (b) 7 (c) 38 (d) 1
28. 28.In a class of 29 children, 19 like tea, 7 like coffee and 4 like both. How many like neither? (a) 7 (b) 11 (c) 3 (d) 4
29. 29.In a class of 32 children, 16 like maths, 11 like science and 5 like both. How many like at least one of the two? (a) 27 (b) 17 (c) 32 (d) 22
30. 30.In a class of 40 children, 22 like mangoes, 12 like bananas and 4 like both. How many like only mangoes? (a) 22 (b) 8 (c) 18 (d) 28
31. 31.In a class of 33 children, 12 like cricket, 22 like football and 4 like both. How many like only cricket? (a) 18 (b) 11 (c) 8 (d) 12
32. 32.In a class of 23 children, 9 like tea, 13 like coffee and 5 like both. How many like at least one of the two? (a) 22 (b) 17 (c) 23 (d) 12
33. 33.In a class of 27 children, 14 like cricket, 20 like football and 10 like both. How many like only cricket? (a) 7 (b) 10 (c) 4 (d) 14
34. 34.In a class of 22 children, 8 like cricket, 14 like football and 5 like both. How many like only cricket? (a) 8 (b) 9 (c) 3 (d) 5
35. 35.In a class of 34 children, 15 like tea, 18 like coffee and 8 like both. How many like at least one of the two? (a) 17 (b) 33 (c) 34 (d) 25
36. 36.In a class of 42 children, 22 like mangoes, 18 like bananas and 10 like neither. How many like both? (a) 32 (b) 9 (c) 8 (d) 10
37. 37.In a class of 32 children, 16 like tea, 18 like coffee and 7 like both. How many like neither? (a) 7 (b) 6 (c) 5 (d) 12
38. 38.In a class of 41 children, 23 like cricket, 29 like football and 12 like both. How many like only cricket? (a) 23 (b) 17 (c) 11 (d) 12
39. 39.In a class of 39 children, 14 like dance, 28 like music and 9 like both. How many like only dance? (a) 14 (b) 19 (c) 11 (d) 5
40. 40.In a class of 43 children, 15 like cricket, 31 like football and 11 like both. How many like only cricket? (a) 20 (b) 4 (c) 15 (d) 12

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