Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 421 · 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 17 children, 7 like cricket, 10 like football and 3 like both. How many like only cricket? (a) 3 (b) 4 (c) 5 (d) 7
2. 2.In a class of 39 children, 20 like tea, 20 like coffee and 2 like both. How many like neither? (a) 2 (b) 0 (c) 3 (d) 1
3. 3.In a class of 41 children, 15 like tea, 21 like coffee and 3 like both. How many like only tea? (a) 18 (b) 12 (c) 15 (d) 20
4. 4.In a class of 38 children, 12 like maths, 22 like science and 5 like both. How many like only maths? (a) 7 (b) 17 (c) 16 (d) 12
5. 5.In a class of 52 children, 29 like tea, 25 like coffee and 9 like neither. How many like both? (a) 2 (b) 43 (c) 9 (d) 11
6. 6.In a class of 29 children, 16 like cricket, 6 like football and 3 like both. How many like only cricket? (a) 16 (b) 23 (c) 3 (d) 13
7. 7.In a class of 27 children, 20 like cricket, 7 like football and 2 like both. How many like at least one of the two? (a) 27 (b) 23 (c) 25 (d) 26
8. 8.In a class of 35 children, 24 like tea, 11 like coffee and 7 like both. How many like at least one of the two? (a) 21 (b) 29 (c) 28 (d) 35
9. 9.In a class of 30 children, 21 like cricket, 13 like football and 7 like both. How many like at least one of the two? (a) 30 (b) 27 (c) 34 (d) 20
10. 10.In a class of 38 children, 14 like dance, 19 like music and 7 like neither. How many like both? (a) 7 (b) 31 (c) 3 (d) 2
11. 11.In a class of 27 children, 13 like tea, 9 like coffee and 5 like both. How many like at least one of the two? (a) 17 (b) 12 (c) 22 (d) 27
12. 12.In a class of 31 children, 16 like maths, 9 like science and 8 like neither. How many like both? (a) 2 (b) 8 (c) 3 (d) 23
13. 13.In a class of 44 children, 18 like tea, 32 like coffee and 6 like neither. How many like both? (a) 38 (b) 13 (c) 12 (d) 6
14. 14.In a class of 19 children, 14 like maths, 13 like science and 2 like neither. How many like both? (a) 17 (b) 8 (c) 2 (d) 10
15. 15.In a class of 19 children, 11 like maths, 9 like science and 4 like both. How many like only maths? (a) 7 (b) 11 (c) 10 (d) 5
16. 16.In a class of 34 children, 22 like dance, 11 like music and 4 like both. How many like neither? (a) 1 (b) 9 (c) 5 (d) 4
17. 17.In a class of 22 children, 8 like mangoes, 9 like bananas and 3 like both. How many like neither? (a) 11 (b) 3 (c) 8 (d) 5
18. 18.In a class of 31 children, 21 like tea, 13 like coffee and 1 like neither. How many like both? (a) 4 (b) 30 (c) 3 (d) 1
19. 19.In a class of 23 children, 7 like maths, 9 like science and 3 like both. How many like neither? (a) 13 (b) 7 (c) 3 (d) 10
20. 20.In a class of 23 children, 15 like maths, 10 like science and 6 like both. How many like neither? (a) 6 (b) 4 (c) 5 (d) 10
21. 21.In a class of 45 children, 20 like tea, 21 like coffee and 9 like neither. How many like both? (a) 5 (b) 6 (c) 36 (d) 9
22. 22.In a class of 35 children, 22 like mangoes, 16 like bananas and 7 like neither. How many like both? (a) 28 (b) 3 (c) 10 (d) 7
23. 23.In a class of 38 children, 15 like dance, 27 like music and 8 like neither. How many like both? (a) 8 (b) 12 (c) 30 (d) 4
24. 24.In a class of 40 children, 18 like maths, 18 like science and 4 like both. How many like at least one of the two? (a) 28 (b) 32 (c) 40 (d) 36
25. 25.In a class of 31 children, 21 like dance, 13 like music and 6 like both. How many like only dance? (a) 21 (b) 15 (c) 18 (d) 7
26. 26.In a class of 22 children, 18 like cricket, 13 like football and 1 like neither. How many like both? (a) 1 (b) 21 (c) 10 (d) 9
27. 27.In a class of 32 children, 18 like mangoes, 18 like bananas and 9 like both. How many like only mangoes? (a) 14 (b) 10 (c) 18 (d) 9
28. 28.In a class of 46 children, 30 like tea, 24 like coffee and 11 like both. How many like only tea? (a) 19 (b) 22 (c) 30 (d) 13
29. 29.In a class of 45 children, 15 like dance, 28 like music and 8 like both. How many like at least one of the two? (a) 35 (b) 43 (c) 45 (d) 27
30. 30.In a class of 31 children, 22 like tea, 10 like coffee and 5 like both. How many like at least one of the two? (a) 32 (b) 31 (c) 22 (d) 27
31. 31.In a class of 24 children, 18 like mangoes, 16 like bananas and 11 like both. How many like only mangoes? (a) 5 (b) 7 (c) 18 (d) 8
32. 32.In a class of 34 children, 18 like cricket, 9 like football and 2 like both. How many like only cricket? (a) 18 (b) 25 (c) 7 (d) 16
33. 33.In a class of 25 children, 12 like maths, 11 like science and 4 like both. How many like neither? (a) 2 (b) 4 (c) 10 (d) 6
34. 34.In a class of 32 children, 20 like cricket, 12 like football and 8 like both. How many like only cricket? (a) 20 (b) 12 (c) 4 (d) 8
35. 35.In a class of 22 children, 7 like mangoes, 10 like bananas and 7 like neither. How many like both? (a) 15 (b) 2 (c) 3 (d) 7
36. 36.In a class of 26 children, 14 like tea, 11 like coffee and 5 like both. How many like at least one of the two? (a) 20 (b) 15 (c) 25 (d) 26
37. 37.In a class of 14 children, 8 like dance, 6 like music and 3 like both. How many like at least one of the two? (a) 12 (b) 8 (c) 14 (d) 11
38. 38.In a class of 31 children, 21 like cricket, 13 like football and 7 like both. How many like only cricket? (a) 21 (b) 18 (c) 14 (d) 6
39. 39.In a class of 35 children, 16 like dance, 19 like music and 3 like both. How many like only dance? (a) 3 (b) 14 (c) 16 (d) 13
40. 40.In a class of 34 children, 25 like mangoes, 10 like bananas and 4 like neither. How many like both? (a) 5 (b) 30 (c) 1 (d) 4

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