Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 361 · 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 35 children, 20 like cricket, 18 like football and 3 like neither. How many like both? (a) 3 (b) 7 (c) 32 (d) 6
2. 2.In a class of 25 children, 12 like cricket, 21 like football and 9 like both. How many like only cricket? (a) 12 (b) 9 (c) 4 (d) 3
3. 3.In a class of 25 children, 11 like cricket, 14 like football and 7 like neither. How many like both? (a) 7 (b) 18 (c) 8 (d) 6
4. 4.In a class of 45 children, 19 like tea, 21 like coffee and 4 like both. How many like neither? (a) 4 (b) 9 (c) 5 (d) 13
5. 5.In a class of 34 children, 19 like tea, 16 like coffee and 7 like both. How many like only tea? (a) 18 (b) 12 (c) 19 (d) 9
6. 6.In a class of 38 children, 14 like tea, 26 like coffee and 10 like both. How many like neither? (a) 18 (b) 10 (c) 8 (d) 9
7. 7.In a class of 35 children, 9 like dance, 24 like music and 5 like both. How many like at least one of the two? (a) 35 (b) 28 (c) 33 (d) 23
8. 8.In a class of 23 children, 8 like mangoes, 8 like bananas and 2 like both. How many like neither? (a) 7 (b) 9 (c) 2 (d) 11
9. 9.In a class of 17 children, 10 like maths, 11 like science and 5 like both. How many like at least one of the two? (a) 11 (b) 16 (c) 17 (d) 21
10. 10.In a class of 41 children, 22 like cricket, 26 like football and 9 like both. How many like only cricket? (a) 22 (b) 15 (c) 17 (d) 13
11. 11.In a class of 44 children, 18 like maths, 28 like science and 10 like both. How many like only maths? (a) 10 (b) 16 (c) 8 (d) 18
12. 12.In a class of 22 children, 7 like mangoes, 10 like bananas and 3 like both. How many like at least one of the two? (a) 22 (b) 17 (c) 14 (d) 11
13. 13.In a class of 39 children, 16 like cricket, 26 like football and 7 like both. How many like neither? (a) 5 (b) 4 (c) 7 (d) 11
14. 14.In a class of 40 children, 15 like maths, 23 like science and 5 like both. How many like at least one of the two? (a) 33 (b) 28 (c) 38 (d) 40
15. 15.In a class of 29 children, 16 like mangoes, 11 like bananas and 4 like neither. How many like both? (a) 3 (b) 4 (c) 25 (d) 2
16. 16.In a class of 28 children, 15 like tea, 12 like coffee and 10 like neither. How many like both? (a) 9 (b) 8 (c) 18 (d) 10
17. 17.In a class of 24 children, 8 like tea, 11 like coffee and 3 like both. How many like neither? (a) 5 (b) 8 (c) 3 (d) 11
18. 18.In a class of 29 children, 12 like dance, 20 like music and 3 like neither. How many like both? (a) 3 (b) 26 (c) 6 (d) 7
19. 19.In a class of 25 children, 21 like dance, 9 like music and 1 like neither. How many like both? (a) 24 (b) 1 (c) 5 (d) 6
20. 20.In a class of 32 children, 14 like tea, 14 like coffee and 3 like both. How many like only tea? (a) 3 (b) 18 (c) 11 (d) 14
21. 21.In a class of 37 children, 9 like dance, 22 like music and 4 like both. How many like neither? (a) 6 (b) 14 (c) 4 (d) 10
22. 22.In a class of 35 children, 26 like cricket, 14 like football and 7 like both. How many like neither? (a) 3 (b) 9 (c) 2 (d) 7
23. 23.In a class of 43 children, 26 like maths, 17 like science and 10 like both. How many like only maths? (a) 7 (b) 10 (c) 16 (d) 26
24. 24.In a class of 37 children, 26 like maths, 20 like science and 12 like both. How many like only maths? (a) 26 (b) 8 (c) 17 (d) 14
25. 25.In a class of 36 children, 25 like dance, 11 like music and 6 like both. How many like only dance? (a) 19 (b) 25 (c) 6 (d) 5
26. 26.In a class of 38 children, 15 like cricket, 25 like football and 7 like neither. How many like both? (a) 31 (b) 7 (c) 2 (d) 9
27. 27.In a class of 30 children, 10 like mangoes, 21 like bananas and 2 like both. How many like only mangoes? (a) 10 (b) 19 (c) 8 (d) 9
28. 28.In a class of 35 children, 17 like maths, 25 like science and 5 like neither. How many like both? (a) 12 (b) 30 (c) 7 (d) 5
29. 29.In a class of 33 children, 15 like cricket, 11 like football and 10 like neither. How many like both? (a) 10 (b) 23 (c) 4 (d) 3
30. 30.In a class of 47 children, 17 like tea, 26 like coffee and 6 like both. How many like only tea? (a) 17 (b) 21 (c) 11 (d) 20
31. 31.In a class of 37 children, 17 like dance, 16 like music and 6 like both. How many like neither? (a) 4 (b) 16 (c) 6 (d) 10
32. 32.In a class of 33 children, 24 like dance, 17 like music and 9 like both. How many like only dance? (a) 24 (b) 16 (c) 15 (d) 8
33. 33.In a class of 42 children, 26 like mangoes, 24 like bananas and 10 like both. How many like only mangoes? (a) 16 (b) 18 (c) 14 (d) 26
34. 34.In a class of 37 children, 20 like cricket, 11 like football and 4 like both. How many like only cricket? (a) 26 (b) 20 (c) 16 (d) 7
35. 35.In a class of 33 children, 16 like dance, 18 like music and 2 like both. How many like at least one of the two? (a) 34 (b) 33 (c) 32 (d) 30
36. 36.In a class of 39 children, 18 like tea, 24 like coffee and 9 like both. How many like neither? (a) 7 (b) 6 (c) 9 (d) 15
37. 37.In a class of 46 children, 25 like cricket, 24 like football and 3 like neither. How many like both? (a) 43 (b) 6 (c) 3 (d) 7
38. 38.In a class of 36 children, 10 like mangoes, 26 like bananas and 6 like both. How many like only mangoes? (a) 10 (b) 6 (c) 20 (d) 4
39. 39.In a class of 28 children, 9 like maths, 15 like science and 9 like neither. How many like both? (a) 19 (b) 9 (c) 5 (d) 6
40. 40.In a class of 29 children, 10 like dance, 21 like music and 1 like neither. How many like both? (a) 3 (b) 28 (c) 2 (d) 1

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