Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 8 · 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, 18 like maths, 13 like science and 2 like neither. How many like both? (a) 9 (b) 7 (c) 2 (d) 22
2. 2.In a class of 37 children, 22 like maths, 14 like science and 8 like neither. How many like both? (a) 6 (b) 8 (c) 7 (d) 29
3. 3.In a class of 30 children, 17 like dance, 16 like music and 8 like neither. How many like both? (a) 22 (b) 8 (c) 11 (d) 3
4. 4.In a class of 50 children, 27 like tea, 26 like coffee and 5 like neither. How many like both? (a) 8 (b) 3 (c) 45 (d) 5
5. 5.In a class of 23 children, 17 like maths, 12 like science and 8 like both. How many like at least one of the two? (a) 13 (b) 21 (c) 29 (d) 23
6. 6.In a class of 19 children, 8 like maths, 10 like science and 5 like both. How many like at least one of the two? (a) 18 (b) 13 (c) 8 (d) 19
7. 7.In a class of 22 children, 10 like dance, 9 like music and 9 like neither. How many like both? (a) 6 (b) 7 (c) 9 (d) 13
8. 8.In a class of 43 children, 19 like tea, 32 like coffee and 4 like neither. How many like both? (a) 39 (b) 12 (c) 4 (d) 8
9. 9.In a class of 42 children, 17 like tea, 29 like coffee and 9 like both. How many like only tea? (a) 8 (b) 20 (c) 17 (d) 13
10. 10.In a class of 32 children, 11 like maths, 18 like science and 4 like both. How many like neither? (a) 11 (b) 4 (c) 3 (d) 7
11. 11.In a class of 29 children, 22 like dance, 8 like music and 2 like neither. How many like both? (a) 2 (b) 27 (c) 3 (d) 1
12. 12.In a class of 51 children, 25 like mangoes, 30 like bananas and 10 like both. How many like only mangoes? (a) 20 (b) 15 (c) 21 (d) 25
13. 13.In a class of 27 children, 16 like tea, 12 like coffee and 3 like neither. How many like both? (a) 4 (b) 24 (c) 3 (d) 1
14. 14.In a class of 33 children, 24 like tea, 13 like coffee and 7 like both. How many like neither? (a) 3 (b) 7 (c) 4 (d) 10
15. 15.In a class of 38 children, 9 like tea, 22 like coffee and 2 like both. How many like only tea? (a) 20 (b) 7 (c) 9 (d) 16
16. 16.In a class of 56 children, 30 like cricket, 29 like football and 11 like both. How many like at least one of the two? (a) 56 (b) 48 (c) 37 (d) 59
17. 17.In a class of 39 children, 21 like dance, 21 like music and 6 like both. How many like neither? (a) 6 (b) 4 (c) 9 (d) 3
18. 18.In a class of 45 children, 24 like cricket, 17 like football and 4 like both. How many like neither? (a) 8 (b) 12 (c) 4 (d) 9
19. 19.In a class of 33 children, 20 like tea, 14 like coffee and 10 like neither. How many like both? (a) 1 (b) 11 (c) 10 (d) 23
20. 20.In a class of 31 children, 9 like maths, 17 like science and 5 like both. How many like neither? (a) 10 (b) 5 (c) 15 (d) 11
21. 21.In a class of 28 children, 15 like maths, 21 like science and 12 like both. How many like neither? (a) 16 (b) 5 (c) 4 (d) 12
22. 22.In a class of 22 children, 11 like dance, 16 like music and 6 like both. How many like only dance? (a) 11 (b) 5 (c) 6 (d) 10
23. 23.In a class of 52 children, 25 like dance, 27 like music and 9 like both. How many like neither? (a) 10 (b) 9 (c) 0 (d) 18
24. 24.In a class of 42 children, 29 like tea, 19 like coffee and 12 like both. How many like at least one of the two? (a) 48 (b) 24 (c) 42 (d) 36
25. 25.In a class of 14 children, 8 like dance, 7 like music and 3 like both. How many like at least one of the two? (a) 12 (b) 14 (c) 15 (d) 9
26. 26.In a class of 49 children, 19 like maths, 25 like science and 5 like both. How many like at least one of the two? (a) 39 (b) 44 (c) 49 (d) 34
27. 27.In a class of 23 children, 16 like maths, 6 like science and 4 like neither. How many like both? (a) 4 (b) 3 (c) 2 (d) 19
28. 28.In a class of 57 children, 28 like maths, 27 like science and 8 like both. How many like only maths? (a) 30 (b) 19 (c) 28 (d) 20
29. 29.In a class of 44 children, 31 like mangoes, 15 like bananas and 11 like both. How many like neither? (a) 20 (b) 11 (c) 9 (d) 10
30. 30.In a class of 18 children, 7 like dance, 11 like music and 4 like both. How many like at least one of the two? (a) 15 (b) 14 (c) 10 (d) 18
31. 31.In a class of 27 children, 16 like mangoes, 15 like bananas and 8 like both. How many like neither? (a) 8 (b) 4 (c) 12 (d) 5
32. 32.In a class of 26 children, 12 like dance, 16 like music and 9 like both. How many like at least one of the two? (a) 10 (b) 19 (c) 28 (d) 26
33. 33.In a class of 35 children, 24 like dance, 10 like music and 7 like both. How many like only dance? (a) 24 (b) 25 (c) 3 (d) 17
34. 34.In a class of 38 children, 18 like tea, 20 like coffee and 8 like both. How many like neither? (a) 8 (b) 16 (c) 0 (d) 9
35. 35.In a class of 51 children, 27 like mangoes, 29 like bananas and 9 like both. How many like at least one of the two? (a) 47 (b) 38 (c) 56 (d) 51
36. 36.In a class of 27 children, 16 like cricket, 14 like football and 4 like both. How many like neither? (a) 5 (b) 2 (c) 1 (d) 4
37. 37.In a class of 54 children, 31 like maths, 31 like science and 11 like both. How many like at least one of the two? (a) 40 (b) 54 (c) 51 (d) 62
38. 38.In a class of 35 children, 24 like cricket, 9 like football and 4 like both. How many like at least one of the two? (a) 33 (b) 35 (c) 29 (d) 25
39. 39.In a class of 36 children, 21 like mangoes, 24 like bananas and 12 like both. How many like neither? (a) 3 (b) 15 (c) 12 (d) 4
40. 40.In a class of 35 children, 22 like mangoes, 15 like bananas and 4 like both. How many like neither? (a) 2 (b) 4 (c) 6 (d) 3

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