Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 391 · 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 30 children, 14 like dance, 11 like music and 2 like both. How many like at least one of the two? (a) 25 (b) 30 (c) 23 (d) 21
2. 2.In a class of 28 children, 15 like mangoes, 20 like bananas and 11 like both. How many like only mangoes? (a) 15 (b) 8 (c) 9 (d) 4
3. 3.In a class of 33 children, 14 like tea, 23 like coffee and 8 like both. How many like at least one of the two? (a) 33 (b) 21 (c) 29 (d) 37
4. 4.In a class of 26 children, 11 like maths, 13 like science and 4 like both. How many like only maths? (a) 7 (b) 9 (c) 11 (d) 13
5. 5.In a class of 17 children, 7 like mangoes, 9 like bananas and 3 like both. How many like only mangoes? (a) 6 (b) 7 (c) 4 (d) 8
6. 6.In a class of 26 children, 10 like tea, 11 like coffee and 7 like neither. How many like both? (a) 19 (b) 7 (c) 3 (d) 2
7. 7.In a class of 35 children, 15 like dance, 28 like music and 3 like neither. How many like both? (a) 8 (b) 32 (c) 11 (d) 3
8. 8.In a class of 22 children, 9 like dance, 7 like music and 10 like neither. How many like both? (a) 10 (b) 12 (c) 5 (d) 4
9. 9.In a class of 41 children, 12 like cricket, 28 like football and 9 like neither. How many like both? (a) 8 (b) 32 (c) 7 (d) 9
10. 10.In a class of 52 children, 27 like cricket, 24 like football and 8 like both. How many like at least one of the two? (a) 52 (b) 43 (c) 51 (d) 35
11. 11.In a class of 33 children, 19 like cricket, 12 like football and 5 like both. How many like neither? (a) 12 (b) 7 (c) 5 (d) 2
12. 12.In a class of 41 children, 17 like mangoes, 26 like bananas and 6 like both. How many like only mangoes? (a) 15 (b) 17 (c) 11 (d) 20
13. 13.In a class of 25 children, 11 like dance, 16 like music and 2 like neither. How many like both? (a) 2 (b) 5 (c) 23 (d) 4
14. 14.In a class of 41 children, 12 like mangoes, 23 like bananas and 3 like both. How many like only mangoes? (a) 9 (b) 18 (c) 20 (d) 12
15. 15.In a class of 53 children, 26 like maths, 31 like science and 11 like both. How many like at least one of the two? (a) 53 (b) 46 (c) 35 (d) 57
16. 16.In a class of 31 children, 11 like maths, 26 like science and 2 like neither. How many like both? (a) 6 (b) 2 (c) 8 (d) 29
17. 17.In a class of 26 children, 19 like cricket, 18 like football and 1 like neither. How many like both? (a) 1 (b) 12 (c) 11 (d) 25
18. 18.In a class of 39 children, 22 like maths, 18 like science and 2 like both. How many like neither? (a) 2 (b) 3 (c) 0 (d) 1
19. 19.In a class of 29 children, 19 like maths, 11 like science and 4 like both. How many like neither? (a) 3 (b) 4 (c) 2 (d) 7
20. 20.In a class of 43 children, 21 like cricket, 21 like football and 7 like both. How many like neither? (a) 15 (b) 1 (c) 7 (d) 8
21. 21.In a class of 47 children, 24 like maths, 26 like science and 8 like both. How many like neither? (a) 13 (b) 5 (c) 8 (d) 6
22. 22.In a class of 38 children, 28 like cricket, 15 like football and 12 like both. How many like only cricket? (a) 3 (b) 16 (c) 28 (d) 23
23. 23.In a class of 33 children, 9 like maths, 20 like science and 10 like neither. How many like both? (a) 10 (b) 6 (c) 7 (d) 23
24. 24.In a class of 50 children, 26 like mangoes, 24 like bananas and 7 like both. How many like neither? (a) 14 (b) 0 (c) 8 (d) 7
25. 25.In a class of 26 children, 9 like tea, 14 like coffee and 9 like neither. How many like both? (a) 6 (b) 17 (c) 7 (d) 9
26. 26.In a class of 47 children, 23 like mangoes, 22 like bananas and 6 like both. How many like only mangoes? (a) 25 (b) 17 (c) 23 (d) 16
27. 27.In a class of 39 children, 21 like tea, 21 like coffee and 4 like both. How many like only tea? (a) 17 (b) 18 (c) 21 (d) 4
28. 28.In a class of 35 children, 20 like mangoes, 14 like bananas and 4 like both. How many like only mangoes? (a) 10 (b) 20 (c) 16 (d) 21
29. 29.In a class of 19 children, 11 like mangoes, 7 like bananas and 2 like both. How many like only mangoes? (a) 11 (b) 5 (c) 12 (d) 9
30. 30.In a class of 31 children, 20 like tea, 16 like coffee and 12 like both. How many like neither? (a) 19 (b) 7 (c) 8 (d) 12
31. 31.In a class of 41 children, 18 like tea, 25 like coffee and 6 like neither. How many like both? (a) 8 (b) 2 (c) 6 (d) 35
32. 32.In a class of 24 children, 16 like cricket, 17 like football and 2 like neither. How many like both? (a) 9 (b) 2 (c) 22 (d) 11
33. 33.In a class of 25 children, 10 like maths, 19 like science and 7 like both. How many like only maths? (a) 12 (b) 3 (c) 10 (d) 6
34. 34.In a class of 52 children, 25 like cricket, 30 like football and 8 like neither. How many like both? (a) 3 (b) 8 (c) 44 (d) 11
35. 35.In a class of 17 children, 9 like dance, 11 like music and 3 like neither. How many like both? (a) 7 (b) 3 (c) 6 (d) 14
36. 36.In a class of 26 children, 11 like maths, 14 like science and 4 like both. How many like neither? (a) 1 (b) 5 (c) 4 (d) 9
37. 37.In a class of 38 children, 20 like cricket, 11 like football and 9 like neither. How many like both? (a) 29 (b) 9 (c) 3 (d) 2
38. 38.In a class of 54 children, 30 like cricket, 31 like football and 11 like both. How many like neither? (a) 5 (b) 11 (c) 4 (d) 15
39. 39.In a class of 18 children, 13 like mangoes, 8 like bananas and 5 like both. How many like only mangoes? (a) 3 (b) 13 (c) 8 (d) 10
40. 40.In a class of 36 children, 18 like maths, 19 like science and 2 like neither. How many like both? (a) 3 (b) 34 (c) 1 (d) 2

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