Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 39 · 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, 21 like cricket, 12 like football and 6 like both. How many like neither? (a) 8 (b) 14 (c) 6 (d) 2
2. 2.In a class of 19 children, 10 like tea, 11 like coffee and 2 like neither. How many like both? (a) 17 (b) 2 (c) 5 (d) 4
3. 3.In a class of 38 children, 25 like maths, 20 like science and 10 like both. How many like neither? (a) 13 (b) 10 (c) 3 (d) 4
4. 4.In a class of 31 children, 11 like tea, 24 like coffee and 5 like both. How many like at least one of the two? (a) 35 (b) 25 (c) 31 (d) 30
5. 5.In a class of 39 children, 22 like mangoes, 20 like bananas and 5 like neither. How many like both? (a) 34 (b) 3 (c) 5 (d) 8
6. 6.In a class of 15 children, 5 like maths, 6 like science and 2 like both. How many like at least one of the two? (a) 15 (b) 9 (c) 11 (d) 7
7. 7.In a class of 37 children, 13 like tea, 24 like coffee and 5 like both. How many like neither? (a) 0 (b) 5 (c) 6 (d) 10
8. 8.In a class of 18 children, 9 like mangoes, 7 like bananas and 3 like both. How many like only mangoes? (a) 9 (b) 4 (c) 11 (d) 6
9. 9.In a class of 35 children, 28 like tea, 13 like coffee and 10 like both. How many like only tea? (a) 18 (b) 3 (c) 22 (d) 28
10. 10.In a class of 35 children, 20 like maths, 12 like science and 10 like neither. How many like both? (a) 25 (b) 8 (c) 10 (d) 7
11. 11.In a class of 40 children, 10 like cricket, 27 like football and 7 like both. How many like only cricket? (a) 3 (b) 10 (c) 13 (d) 20
12. 12.In a class of 13 children, 7 like dance, 7 like music and 3 like neither. How many like both? (a) 10 (b) 3 (c) 1 (d) 4
13. 13.In a class of 28 children, 15 like maths, 16 like science and 5 like both. How many like neither? (a) 5 (b) 3 (c) 7 (d) 2
14. 14.In a class of 38 children, 28 like dance, 15 like music and 3 like neither. How many like both? (a) 3 (b) 5 (c) 35 (d) 8
15. 15.In a class of 25 children, 15 like mangoes, 13 like bananas and 6 like both. How many like at least one of the two? (a) 22 (b) 25 (c) 16 (d) 28
16. 16.In a class of 39 children, 23 like tea, 17 like coffee and 6 like both. How many like at least one of the two? (a) 40 (b) 39 (c) 34 (d) 28
17. 17.In a class of 38 children, 13 like dance, 25 like music and 6 like both. How many like at least one of the two? (a) 38 (b) 33 (c) 26 (d) 32
18. 18.In a class of 46 children, 26 like dance, 25 like music and 11 like both. How many like only dance? (a) 14 (b) 21 (c) 26 (d) 15
19. 19.In a class of 42 children, 19 like tea, 26 like coffee and 9 like both. How many like only tea? (a) 19 (b) 16 (c) 10 (d) 17
20. 20.In a class of 25 children, 9 like tea, 16 like coffee and 3 like both. How many like at least one of the two? (a) 23 (b) 19 (c) 25 (d) 22
21. 21.In a class of 44 children, 19 like maths, 26 like science and 5 like neither. How many like both? (a) 39 (b) 6 (c) 1 (d) 5
22. 22.In a class of 19 children, 7 like mangoes, 7 like bananas and 2 like both. How many like at least one of the two? (a) 12 (b) 10 (c) 19 (d) 14
23. 23.In a class of 22 children, 9 like cricket, 9 like football and 5 like both. How many like neither? (a) 14 (b) 5 (c) 9 (d) 4
24. 24.In a class of 17 children, 7 like mangoes, 13 like bananas and 4 like both. How many like only mangoes? (a) 7 (b) 4 (c) 3 (d) 9
25. 25.In a class of 33 children, 17 like tea, 16 like coffee and 3 like neither. How many like both? (a) 2 (b) 30 (c) 3 (d) 4
26. 26.In a class of 33 children, 18 like dance, 21 like music and 6 like neither. How many like both? (a) 27 (b) 13 (c) 12 (d) 6
27. 27.In a class of 31 children, 22 like dance, 14 like music and 11 like both. How many like only dance? (a) 17 (b) 11 (c) 22 (d) 3
28. 28.In a class of 28 children, 22 like tea, 9 like coffee and 4 like both. How many like neither? (a) 2 (b) 4 (c) 5 (d) 1
29. 29.In a class of 16 children, 11 like tea, 8 like coffee and 4 like both. How many like only tea? (a) 8 (b) 4 (c) 11 (d) 7
30. 30.In a class of 40 children, 17 like cricket, 21 like football and 4 like both. How many like neither? (a) 2 (b) 4 (c) 10 (d) 6
31. 31.In a class of 37 children, 24 like cricket, 15 like football and 4 like both. How many like only cricket? (a) 24 (b) 22 (c) 11 (d) 20
32. 32.In a class of 41 children, 16 like maths, 25 like science and 10 like both. How many like at least one of the two? (a) 41 (b) 21 (c) 32 (d) 31
33. 33.In a class of 26 children, 14 like cricket, 15 like football and 9 like both. How many like at least one of the two? (a) 26 (b) 29 (c) 11 (d) 20
34. 34.In a class of 31 children, 16 like maths, 14 like science and 8 like both. How many like at least one of the two? (a) 30 (b) 22 (c) 31 (d) 14
35. 35.In a class of 15 children, 6 like cricket, 11 like football and 3 like both. How many like only cricket? (a) 4 (b) 6 (c) 8 (d) 3
36. 36.In a class of 19 children, 9 like cricket, 13 like football and 6 like both. How many like only cricket? (a) 7 (b) 3 (c) 6 (d) 9
37. 37.In a class of 41 children, 26 like tea, 16 like coffee and 10 like both. How many like at least one of the two? (a) 42 (b) 32 (c) 22 (d) 41
38. 38.In a class of 15 children, 8 like cricket, 6 like football and 4 like neither. How many like both? (a) 2 (b) 3 (c) 11 (d) 4
39. 39.In a class of 31 children, 17 like tea, 6 like coffee and 10 like neither. How many like both? (a) 2 (b) 21 (c) 3 (d) 10
40. 40.In a class of 40 children, 17 like mangoes, 26 like bananas and 7 like both. How many like neither? (a) 7 (b) 11 (c) 5 (d) 4

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