Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 504 · 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 42 children, 24 like mangoes, 23 like bananas and 2 like neither. How many like both? (a) 40 (b) 7 (c) 2 (d) 5
2. 2.In a class of 28 children, 9 like tea, 19 like coffee and 4 like both. How many like only tea? (a) 15 (b) 5 (c) 4 (d) 9
3. 3.In a class of 22 children, 8 like mangoes, 16 like bananas and 5 like both. How many like neither? (a) 4 (b) 3 (c) 8 (d) 5
4. 4.In a class of 42 children, 14 like cricket, 26 like football and 6 like both. How many like at least one of the two? (a) 40 (b) 42 (c) 34 (d) 28
5. 5.In a class of 48 children, 24 like tea, 28 like coffee and 8 like both. How many like neither? (a) 8 (b) 12 (c) 4 (d) 5
6. 6.In a class of 50 children, 23 like tea, 30 like coffee and 10 like both. How many like neither? (a) 10 (b) 8 (c) 17 (d) 7
7. 7.In a class of 26 children, 12 like cricket, 10 like football and 6 like both. How many like at least one of the two? (a) 22 (b) 10 (c) 26 (d) 16
8. 8.In a class of 26 children, 9 like cricket, 19 like football and 4 like both. How many like neither? (a) 2 (b) 4 (c) 6 (d) 3
9. 9.In a class of 53 children, 30 like tea, 27 like coffee and 12 like both. How many like only tea? (a) 30 (b) 15 (c) 26 (d) 18
10. 10.In a class of 36 children, 21 like mangoes, 10 like bananas and 10 like neither. How many like both? (a) 6 (b) 26 (c) 5 (d) 10
11. 11.In a class of 54 children, 31 like maths, 25 like science and 11 like both. How many like neither? (a) 20 (b) 11 (c) 9 (d) 10
12. 12.In a class of 49 children, 21 like cricket, 28 like football and 9 like neither. How many like both? (a) 10 (b) 40 (c) 8 (d) 9
13. 13.In a class of 22 children, 11 like maths, 11 like science and 4 like both. How many like neither? (a) 4 (b) 0 (c) 8 (d) 5
14. 14.In a class of 47 children, 21 like maths, 24 like science and 4 like both. How many like neither? (a) 10 (b) 2 (c) 4 (d) 6
15. 15.In a class of 17 children, 8 like tea, 12 like coffee and 4 like both. How many like only tea? (a) 5 (b) 4 (c) 8 (d) 3
16. 16.In a class of 30 children, 13 like cricket, 19 like football and 3 like both. How many like only cricket? (a) 11 (b) 13 (c) 10 (d) 16
17. 17.In a class of 48 children, 23 like maths, 25 like science and 5 like both. How many like at least one of the two? (a) 48 (b) 44 (c) 43 (d) 38
18. 18.In a class of 33 children, 19 like maths, 15 like science and 10 like both. How many like neither? (a) 9 (b) 8 (c) 19 (d) 10
19. 19.In a class of 36 children, 23 like cricket, 18 like football and 7 like both. How many like neither? (a) 7 (b) 3 (c) 2 (d) 9
20. 20.In a class of 35 children, 15 like tea, 18 like coffee and 4 like both. How many like only tea? (a) 11 (b) 15 (c) 14 (d) 17
21. 21.In a class of 31 children, 14 like dance, 12 like music and 3 like both. How many like neither? (a) 5 (b) 11 (c) 8 (d) 3
22. 22.In a class of 41 children, 24 like dance, 21 like music and 6 like both. How many like at least one of the two? (a) 39 (b) 41 (c) 33 (d) 45
23. 23.In a class of 42 children, 15 like maths, 25 like science and 6 like both. How many like neither? (a) 8 (b) 2 (c) 6 (d) 14
24. 24.In a class of 19 children, 10 like maths, 12 like science and 6 like both. How many like only maths? (a) 7 (b) 4 (c) 6 (d) 10
25. 25.In a class of 31 children, 17 like mangoes, 17 like bananas and 10 like both. How many like neither? (a) 8 (b) 10 (c) 7 (d) 17
26. 26.In a class of 37 children, 20 like maths, 24 like science and 8 like both. How many like neither? (a) 1 (b) 8 (c) 9 (d) 2
27. 27.In a class of 37 children, 23 like dance, 20 like music and 1 like neither. How many like both? (a) 1 (b) 7 (c) 6 (d) 36
28. 28.In a class of 50 children, 24 like mangoes, 26 like bananas and 9 like both. How many like only mangoes? (a) 9 (b) 17 (c) 15 (d) 24
29. 29.In a class of 45 children, 25 like maths, 22 like science and 8 like both. How many like at least one of the two? (a) 47 (b) 39 (c) 31 (d) 45
30. 30.In a class of 38 children, 31 like mangoes, 18 like bananas and 1 like neither. How many like both? (a) 1 (b) 12 (c) 11 (d) 37
31. 31.In a class of 30 children, 11 like dance, 21 like music and 5 like both. How many like at least one of the two? (a) 27 (b) 30 (c) 32 (d) 22
32. 32.In a class of 43 children, 23 like maths, 17 like science and 7 like neither. How many like both? (a) 4 (b) 5 (c) 36 (d) 7
33. 33.In a class of 20 children, 10 like mangoes, 10 like bananas and 3 like both. How many like at least one of the two? (a) 20 (b) 17 (c) 18 (d) 14
34. 34.In a class of 30 children, 18 like dance, 7 like music and 9 like neither. How many like both? (a) 5 (b) 4 (c) 21 (d) 9
35. 35.In a class of 37 children, 21 like maths, 19 like science and 3 like neither. How many like both? (a) 34 (b) 6 (c) 7 (d) 3
36. 36.In a class of 33 children, 21 like mangoes, 8 like bananas and 3 like both. How many like only mangoes? (a) 5 (b) 18 (c) 25 (d) 21
37. 37.In a class of 27 children, 9 like dance, 21 like music and 6 like both. How many like at least one of the two? (a) 30 (b) 24 (c) 27 (d) 18
38. 38.In a class of 50 children, 22 like tea, 31 like coffee and 9 like neither. How many like both? (a) 12 (b) 9 (c) 41 (d) 3
39. 39.In a class of 40 children, 11 like maths, 24 like science and 4 like both. How many like at least one of the two? (a) 27 (b) 31 (c) 35 (d) 40
40. 40.In a class of 29 children, 14 like maths, 23 like science and 9 like both. How many like at least one of the two? (a) 37 (b) 19 (c) 29 (d) 28

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