Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 446 · 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 43 children, 24 like dance, 25 like music and 7 like both. How many like only dance? (a) 24 (b) 7 (c) 17 (d) 18
2. 2.In a class of 33 children, 22 like tea, 6 like coffee and 2 like both. How many like neither? (a) 2 (b) 5 (c) 7 (d) 9
3. 3.In a class of 41 children, 14 like dance, 24 like music and 4 like both. How many like neither? (a) 4 (b) 11 (c) 3 (d) 7
4. 4.In a class of 23 children, 10 like mangoes, 14 like bananas and 6 like both. How many like at least one of the two? (a) 23 (b) 24 (c) 12 (d) 18
5. 5.In a class of 22 children, 18 like dance, 5 like music and 2 like both. How many like only dance? (a) 16 (b) 18 (c) 17 (d) 3
6. 6.In a class of 42 children, 20 like cricket, 24 like football and 10 like neither. How many like both? (a) 10 (b) 12 (c) 32 (d) 2
7. 7.In a class of 30 children, 17 like mangoes, 8 like bananas and 3 like both. How many like only mangoes? (a) 5 (b) 17 (c) 22 (d) 14
8. 8.In a class of 31 children, 19 like maths, 6 like science and 2 like both. How many like only maths? (a) 25 (b) 4 (c) 17 (d) 19
9. 9.In a class of 29 children, 7 like dance, 17 like music and 3 like both. How many like only dance? (a) 4 (b) 7 (c) 14 (d) 12
10. 10.In a class of 48 children, 29 like maths, 25 like science and 4 like neither. How many like both? (a) 10 (b) 4 (c) 44 (d) 6
11. 11.In a class of 37 children, 15 like cricket, 28 like football and 3 like neither. How many like both? (a) 34 (b) 6 (c) 3 (d) 9
12. 12.In a class of 26 children, 10 like maths, 16 like science and 3 like both. How many like at least one of the two? (a) 23 (b) 20 (c) 24 (d) 26
13. 13.In a class of 22 children, 7 like maths, 10 like science and 9 like neither. How many like both? (a) 5 (b) 9 (c) 4 (d) 13
14. 14.In a class of 34 children, 21 like maths, 15 like science and 4 like both. How many like neither? (a) 3 (b) 6 (c) 2 (d) 4
15. 15.In a class of 49 children, 25 like cricket, 22 like football and 5 like both. How many like neither? (a) 12 (b) 2 (c) 7 (d) 5
16. 16.In a class of 29 children, 15 like dance, 15 like music and 4 like both. How many like only dance? (a) 14 (b) 15 (c) 11 (d) 4
17. 17.In a class of 49 children, 25 like maths, 24 like science and 8 like both. How many like neither? (a) 8 (b) 0 (c) 9 (d) 16
18. 18.In a class of 37 children, 19 like mangoes, 28 like bananas and 1 like neither. How many like both? (a) 10 (b) 11 (c) 1 (d) 36
19. 19.In a class of 39 children, 19 like maths, 21 like science and 4 like both. How many like only maths? (a) 19 (b) 17 (c) 18 (d) 15
20. 20.In a class of 32 children, 20 like maths, 9 like science and 3 like both. How many like at least one of the two? (a) 32 (b) 23 (c) 26 (d) 29
21. 21.In a class of 30 children, 20 like tea, 8 like coffee and 3 like both. How many like only tea? (a) 22 (b) 5 (c) 17 (d) 20
22. 22.In a class of 27 children, 16 like mangoes, 5 like bananas and 2 like both. How many like at least one of the two? (a) 21 (b) 27 (c) 19 (d) 17
23. 23.In a class of 31 children, 21 like mangoes, 11 like bananas and 6 like both. How many like at least one of the two? (a) 31 (b) 32 (c) 20 (d) 26
24. 24.In a class of 37 children, 24 like mangoes, 21 like bananas and 9 like both. How many like neither? (a) 9 (b) 10 (c) 2 (d) 1
25. 25.In a class of 23 children, 12 like tea, 10 like coffee and 4 like neither. How many like both? (a) 4 (b) 19 (c) 2 (d) 3
26. 26.In a class of 39 children, 24 like dance, 19 like music and 11 like both. How many like neither? (a) 18 (b) 11 (c) 8 (d) 7
27. 27.In a class of 29 children, 20 like tea, 17 like coffee and 10 like both. How many like only tea? (a) 10 (b) 20 (c) 7 (d) 12
28. 28.In a class of 33 children, 19 like mangoes, 7 like bananas and 2 like both. How many like at least one of the two? (a) 22 (b) 33 (c) 24 (d) 26
29. 29.In a class of 18 children, 10 like tea, 12 like coffee and 5 like both. How many like neither? (a) 5 (b) 6 (c) 1 (d) 2
30. 30.In a class of 42 children, 23 like mangoes, 20 like bananas and 5 like both. How many like only mangoes? (a) 22 (b) 15 (c) 23 (d) 18
31. 31.In a class of 19 children, 11 like cricket, 10 like football and 7 like both. How many like neither? (a) 6 (b) 5 (c) 7 (d) 12
32. 32.In a class of 36 children, 20 like maths, 8 like science and 2 like both. How many like at least one of the two? (a) 28 (b) 26 (c) 24 (d) 36
33. 33.In a class of 36 children, 22 like dance, 15 like music and 2 like neither. How many like both? (a) 3 (b) 34 (c) 1 (d) 2
34. 34.In a class of 39 children, 19 like tea, 17 like coffee and 3 like both. How many like only tea? (a) 19 (b) 22 (c) 14 (d) 16
35. 35.In a class of 26 children, 9 like tea, 13 like coffee and 6 like both. How many like neither? (a) 4 (b) 10 (c) 6 (d) 16
36. 36.In a class of 31 children, 12 like dance, 16 like music and 6 like both. How many like at least one of the two? (a) 16 (b) 22 (c) 28 (d) 31
37. 37.In a class of 32 children, 10 like cricket, 24 like football and 4 like both. How many like neither? (a) 6 (b) 3 (c) 4 (d) 2
38. 38.In a class of 21 children, 12 like maths, 9 like science and 3 like both. How many like neither? (a) 3 (b) 4 (c) 0 (d) 6
39. 39.In a class of 50 children, 30 like tea, 25 like coffee and 10 like both. How many like neither? (a) 5 (b) 15 (c) 6 (d) 10
40. 40.In a class of 31 children, 21 like tea, 13 like coffee and 7 like both. How many like neither? (a) 11 (b) 7 (c) 5 (d) 4

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