Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 381 · 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 50 children, 27 like dance, 25 like music and 7 like both. How many like at least one of the two? (a) 52 (b) 38 (c) 45 (d) 50
2. 2.In a class of 37 children, 19 like tea, 25 like coffee and 8 like both. How many like neither? (a) 1 (b) 9 (c) 2 (d) 8
3. 3.In a class of 35 children, 11 like mangoes, 23 like bananas and 5 like both. How many like only mangoes? (a) 12 (b) 6 (c) 11 (d) 18
4. 4.In a class of 46 children, 21 like cricket, 26 like football and 6 like both. How many like only cricket? (a) 15 (b) 21 (c) 20 (d) 6
5. 5.In a class of 29 children, 15 like maths, 22 like science and 11 like both. How many like only maths? (a) 11 (b) 7 (c) 4 (d) 15
6. 6.In a class of 30 children, 20 like dance, 17 like music and 9 like both. How many like only dance? (a) 11 (b) 8 (c) 13 (d) 20
7. 7.In a class of 21 children, 9 like mangoes, 12 like bananas and 5 like neither. How many like both? (a) 16 (b) 5 (c) 4 (d) 6
8. 8.In a class of 57 children, 31 like dance, 27 like music and 11 like both. How many like only dance? (a) 20 (b) 30 (c) 31 (d) 16
9. 9.In a class of 37 children, 25 like mangoes, 14 like bananas and 6 like neither. How many like both? (a) 8 (b) 2 (c) 6 (d) 31
10. 10.In a class of 30 children, 21 like mangoes, 14 like bananas and 6 like both. How many like at least one of the two? (a) 23 (b) 35 (c) 29 (d) 30
11. 11.In a class of 35 children, 14 like maths, 25 like science and 11 like both. How many like at least one of the two? (a) 28 (b) 17 (c) 39 (d) 35
12. 12.In a class of 34 children, 22 like tea, 19 like coffee and 9 like both. How many like at least one of the two? (a) 41 (b) 32 (c) 23 (d) 34
13. 13.In a class of 48 children, 26 like maths, 25 like science and 6 like neither. How many like both? (a) 6 (b) 3 (c) 9 (d) 42
14. 14.In a class of 43 children, 17 like tea, 22 like coffee and 4 like both. How many like neither? (a) 12 (b) 4 (c) 8 (d) 9
15. 15.In a class of 22 children, 8 like cricket, 16 like football and 3 like both. How many like only cricket? (a) 8 (b) 6 (c) 13 (d) 5
16. 16.In a class of 32 children, 18 like maths, 15 like science and 10 like both. How many like neither? (a) 9 (b) 10 (c) 8 (d) 19
17. 17.In a class of 33 children, 22 like tea, 13 like coffee and 5 like both. How many like only tea? (a) 22 (b) 17 (c) 8 (d) 20
18. 18.In a class of 36 children, 16 like mangoes, 21 like bananas and 2 like both. How many like only mangoes? (a) 19 (b) 16 (c) 14 (d) 15
19. 19.In a class of 33 children, 18 like mangoes, 21 like bananas and 7 like both. How many like at least one of the two? (a) 33 (b) 32 (c) 25 (d) 39
20. 20.In a class of 22 children, 5 like maths, 18 like science and 2 like both. How many like at least one of the two? (a) 22 (b) 21 (c) 23 (d) 19
21. 21.In a class of 33 children, 25 like mangoes, 16 like bananas and 1 like neither. How many like both? (a) 8 (b) 1 (c) 32 (d) 9
22. 22.In a class of 32 children, 20 like cricket, 10 like football and 6 like both. How many like only cricket? (a) 22 (b) 14 (c) 4 (d) 20
23. 23.In a class of 50 children, 20 like tea, 28 like coffee and 8 like both. How many like only tea? (a) 12 (b) 8 (c) 20 (d) 22
24. 24.In a class of 24 children, 15 like dance, 19 like music and 11 like both. How many like at least one of the two? (a) 12 (b) 34 (c) 23 (d) 24
25. 25.In a class of 33 children, 21 like mangoes, 22 like bananas and 11 like both. How many like only mangoes? (a) 11 (b) 9 (c) 21 (d) 10
26. 26.In a class of 32 children, 10 like mangoes, 21 like bananas and 3 like both. How many like only mangoes? (a) 7 (b) 11 (c) 18 (d) 10
27. 27.In a class of 34 children, 10 like mangoes, 21 like bananas and 6 like neither. How many like both? (a) 6 (b) 4 (c) 28 (d) 3
28. 28.In a class of 33 children, 20 like maths, 9 like science and 6 like neither. How many like both? (a) 6 (b) 2 (c) 27 (d) 3
29. 29.In a class of 23 children, 13 like mangoes, 9 like bananas and 4 like both. How many like only mangoes? (a) 9 (b) 5 (c) 14 (d) 13
30. 30.In a class of 28 children, 11 like maths, 15 like science and 8 like both. How many like at least one of the two? (a) 26 (b) 28 (c) 10 (d) 18
31. 31.In a class of 35 children, 21 like cricket, 18 like football and 8 like both. How many like only cricket? (a) 21 (b) 10 (c) 13 (d) 17
32. 32.In a class of 35 children, 15 like tea, 19 like coffee and 4 like neither. How many like both? (a) 3 (b) 4 (c) 31 (d) 2
33. 33.In a class of 48 children, 29 like maths, 29 like science and 2 like neither. How many like both? (a) 2 (b) 10 (c) 12 (d) 46
34. 34.In a class of 27 children, 12 like mangoes, 11 like bananas and 6 like both. How many like at least one of the two? (a) 17 (b) 11 (c) 27 (d) 23
35. 35.In a class of 47 children, 25 like cricket, 25 like football and 6 like both. How many like at least one of the two? (a) 50 (b) 47 (c) 38 (d) 44
36. 36.In a class of 31 children, 22 like maths, 8 like science and 4 like neither. How many like both? (a) 27 (b) 4 (c) 3 (d) 2
37. 37.In a class of 43 children, 27 like mangoes, 18 like bananas and 7 like neither. How many like both? (a) 2 (b) 7 (c) 36 (d) 9
38. 38.In a class of 45 children, 28 like mangoes, 25 like bananas and 3 like neither. How many like both? (a) 8 (b) 3 (c) 11 (d) 42
39. 39.In a class of 27 children, 20 like cricket, 7 like football and 3 like both. How many like only cricket? (a) 17 (b) 4 (c) 20 (d) 3
40. 40.In a class of 29 children, 7 like mangoes, 15 like bananas and 9 like neither. How many like both? (a) 3 (b) 20 (c) 9 (d) 2

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