Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 535 · 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 24 children, 12 like cricket, 13 like football and 5 like both. How many like neither? (a) 5 (b) 9 (c) 3 (d) 4
2. 2.In a class of 32 children, 16 like maths, 14 like science and 8 like both. How many like only maths? (a) 18 (b) 16 (c) 8 (d) 6
3. 3.In a class of 34 children, 20 like tea, 12 like coffee and 4 like neither. How many like both? (a) 30 (b) 4 (c) 2 (d) 3
4. 4.In a class of 19 children, 14 like maths, 5 like science and 2 like both. How many like only maths? (a) 2 (b) 14 (c) 3 (d) 12
5. 5.In a class of 10 children, 5 like dance, 5 like music and 2 like both. How many like at least one of the two? (a) 9 (b) 10 (c) 6 (d) 8
6. 6.In a class of 30 children, 16 like cricket, 15 like football and 2 like both. How many like only cricket? (a) 13 (b) 14 (c) 15 (d) 16
7. 7.In a class of 35 children, 13 like tea, 20 like coffee and 3 like both. How many like only tea? (a) 10 (b) 13 (c) 15 (d) 17
8. 8.In a class of 17 children, 12 like mangoes, 8 like bananas and 1 like neither. How many like both? (a) 16 (b) 4 (c) 1 (d) 3
9. 9.In a class of 24 children, 7 like tea, 19 like coffee and 3 like both. How many like only tea? (a) 16 (b) 4 (c) 7 (d) 5
10. 10.In a class of 34 children, 16 like mangoes, 18 like bananas and 9 like both. How many like at least one of the two? (a) 16 (b) 26 (c) 25 (d) 34
11. 11.In a class of 38 children, 11 like cricket, 24 like football and 4 like both. How many like at least one of the two? (a) 38 (b) 31 (c) 35 (d) 27
12. 12.In a class of 46 children, 28 like mangoes, 16 like bananas and 8 like both. How many like only mangoes? (a) 28 (b) 20 (c) 30 (d) 8
13. 13.In a class of 25 children, 12 like tea, 9 like coffee and 6 like both. How many like at least one of the two? (a) 9 (b) 15 (c) 21 (d) 25
14. 14.In a class of 45 children, 28 like cricket, 24 like football and 3 like neither. How many like both? (a) 42 (b) 7 (c) 3 (d) 10
15. 15.In a class of 44 children, 21 like dance, 18 like music and 2 like both. How many like only dance? (a) 16 (b) 21 (c) 26 (d) 19
16. 16.In a class of 38 children, 21 like tea, 11 like coffee and 3 like both. How many like neither? (a) 9 (b) 6 (c) 3 (d) 12
17. 17.In a class of 32 children, 19 like dance, 15 like music and 3 like both. How many like only dance? (a) 19 (b) 16 (c) 17 (d) 12
18. 18.In a class of 47 children, 18 like mangoes, 21 like bananas and 2 like both. How many like neither? (a) 10 (b) 2 (c) 8 (d) 12
19. 19.In a class of 38 children, 26 like dance, 16 like music and 9 like both. How many like at least one of the two? (a) 24 (b) 33 (c) 38 (d) 42
20. 20.In a class of 26 children, 19 like dance, 15 like music and 10 like both. How many like neither? (a) 12 (b) 3 (c) 2 (d) 10
21. 21.In a class of 29 children, 13 like dance, 11 like music and 5 like both. How many like neither? (a) 10 (b) 5 (c) 15 (d) 11
22. 22.In a class of 23 children, 13 like mangoes, 9 like bananas and 6 like both. How many like at least one of the two? (a) 23 (b) 10 (c) 22 (d) 16
23. 23.In a class of 43 children, 20 like cricket, 25 like football and 9 like both. How many like only cricket? (a) 16 (b) 20 (c) 18 (d) 11
24. 24.In a class of 22 children, 17 like cricket, 7 like football and 3 like both. How many like neither? (a) 3 (b) 4 (c) 1 (d) 2
25. 25.In a class of 47 children, 21 like tea, 22 like coffee and 2 like both. How many like at least one of the two? (a) 39 (b) 47 (c) 41 (d) 43
26. 26.In a class of 21 children, 14 like tea, 9 like coffee and 6 like both. How many like neither? (a) 6 (b) 5 (c) 10 (d) 4
27. 27.In a class of 46 children, 22 like cricket, 17 like football and 9 like neither. How many like both? (a) 37 (b) 9 (c) 2 (d) 3
28. 28.In a class of 40 children, 22 like maths, 14 like science and 6 like both. How many like only maths? (a) 26 (b) 8 (c) 22 (d) 16
29. 29.In a class of 41 children, 16 like mangoes, 20 like bananas and 5 like both. How many like neither? (a) 10 (b) 15 (c) 11 (d) 5
30. 30.In a class of 41 children, 16 like tea, 22 like coffee and 9 like neither. How many like both? (a) 32 (b) 9 (c) 7 (d) 6
31. 31.In a class of 13 children, 5 like maths, 6 like science and 2 like both. How many like only maths? (a) 3 (b) 4 (c) 7 (d) 5
32. 32.In a class of 35 children, 18 like dance, 21 like music and 8 like both. How many like neither? (a) 5 (b) 12 (c) 8 (d) 4
33. 33.In a class of 30 children, 11 like dance, 16 like music and 9 like neither. How many like both? (a) 6 (b) 7 (c) 21 (d) 9
34. 34.In a class of 41 children, 23 like dance, 16 like music and 8 like both. How many like neither? (a) 8 (b) 10 (c) 2 (d) 18
35. 35.In a class of 27 children, 16 like cricket, 12 like football and 3 like both. How many like at least one of the two? (a) 25 (b) 28 (c) 27 (d) 22
36. 36.In a class of 36 children, 19 like tea, 19 like coffee and 8 like both. How many like at least one of the two? (a) 38 (b) 36 (c) 30 (d) 22
37. 37.In a class of 41 children, 15 like tea, 30 like coffee and 12 like both. How many like neither? (a) 12 (b) 20 (c) 9 (d) 8
38. 38.In a class of 35 children, 12 like tea, 28 like coffee and 8 like both. How many like at least one of the two? (a) 40 (b) 32 (c) 24 (d) 35
39. 39.In a class of 41 children, 23 like dance, 24 like music and 11 like both. How many like only dance? (a) 17 (b) 13 (c) 12 (d) 23
40. 40.In a class of 40 children, 19 like tea, 18 like coffee and 2 like both. How many like only tea? (a) 19 (b) 16 (c) 17 (d) 22

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