Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 14 · 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 27 children, 18 like maths, 9 like science and 2 like neither. How many like both? (a) 2 (b) 3 (c) 25 (d) 1
2. 2.In a class of 34 children, 9 like mangoes, 21 like bananas and 2 like both. How many like neither? (a) 4 (b) 2 (c) 6 (d) 8
3. 3.In a class of 37 children, 17 like cricket, 31 like football and 1 like neither. How many like both? (a) 11 (b) 1 (c) 36 (d) 12
4. 4.In a class of 26 children, 21 like mangoes, 11 like bananas and 2 like neither. How many like both? (a) 6 (b) 24 (c) 2 (d) 8
5. 5.In a class of 40 children, 25 like tea, 19 like coffee and 7 like both. How many like only tea? (a) 21 (b) 18 (c) 25 (d) 12
6. 6.In a class of 32 children, 13 like tea, 27 like coffee and 10 like both. How many like at least one of the two? (a) 20 (b) 40 (c) 32 (d) 30
7. 7.In a class of 38 children, 23 like cricket, 20 like football and 6 like both. How many like only cricket? (a) 18 (b) 14 (c) 23 (d) 17
8. 8.In a class of 43 children, 32 like cricket, 20 like football and 3 like neither. How many like both? (a) 40 (b) 9 (c) 3 (d) 12
9. 9.In a class of 31 children, 23 like cricket, 19 like football and 12 like both. How many like neither? (a) 13 (b) 2 (c) 1 (d) 12
10. 10.In a class of 44 children, 22 like mangoes, 19 like bananas and 3 like both. How many like only mangoes? (a) 16 (b) 22 (c) 19 (d) 25
11. 11.In a class of 43 children, 15 like cricket, 21 like football and 10 like neither. How many like both? (a) 3 (b) 4 (c) 10 (d) 33
12. 12.In a class of 20 children, 7 like mangoes, 11 like bananas and 4 like both. How many like at least one of the two? (a) 20 (b) 18 (c) 14 (d) 10
13. 13.In a class of 55 children, 28 like mangoes, 29 like bananas and 11 like both. How many like only mangoes? (a) 17 (b) 18 (c) 28 (d) 26
14. 14.In a class of 42 children, 21 like dance, 28 like music and 8 like both. How many like only dance? (a) 20 (b) 21 (c) 14 (d) 13
15. 15.In a class of 43 children, 28 like mangoes, 19 like bananas and 10 like both. How many like only mangoes? (a) 24 (b) 9 (c) 28 (d) 18
16. 16.In a class of 40 children, 27 like maths, 16 like science and 11 like both. How many like at least one of the two? (a) 21 (b) 32 (c) 43 (d) 40
17. 17.In a class of 42 children, 24 like cricket, 19 like football and 4 like both. How many like neither? (a) 4 (b) 2 (c) 3 (d) 7
18. 18.In a class of 23 children, 14 like maths, 7 like science and 2 like both. How many like at least one of the two? (a) 21 (b) 23 (c) 19 (d) 17
19. 19.In a class of 32 children, 16 like tea, 16 like coffee and 9 like both. How many like at least one of the two? (a) 23 (b) 24 (c) 14 (d) 32
20. 20.In a class of 39 children, 24 like cricket, 24 like football and 12 like both. How many like neither? (a) 4 (b) 15 (c) 3 (d) 12
21. 21.In a class of 30 children, 21 like dance, 17 like music and 9 like both. How many like at least one of the two? (a) 29 (b) 20 (c) 38 (d) 30
22. 22.In a class of 32 children, 20 like mangoes, 13 like bananas and 6 like neither. How many like both? (a) 6 (b) 26 (c) 7 (d) 1
23. 23.In a class of 35 children, 17 like mangoes, 17 like bananas and 5 like neither. How many like both? (a) 3 (b) 30 (c) 4 (d) 5
24. 24.In a class of 22 children, 15 like tea, 7 like coffee and 3 like neither. How many like both? (a) 4 (b) 2 (c) 19 (d) 3
25. 25.In a class of 48 children, 25 like cricket, 25 like football and 5 like both. How many like only cricket? (a) 20 (b) 25 (c) 5 (d) 23
26. 26.In a class of 36 children, 17 like dance, 24 like music and 8 like both. How many like at least one of the two? (a) 25 (b) 36 (c) 33 (d) 41
27. 27.In a class of 34 children, 8 like tea, 20 like coffee and 4 like both. How many like only tea? (a) 14 (b) 4 (c) 8 (d) 16
28. 28.In a class of 47 children, 23 like tea, 18 like coffee and 4 like both. How many like neither? (a) 14 (b) 10 (c) 4 (d) 6
29. 29.In a class of 52 children, 30 like tea, 29 like coffee and 10 like both. How many like at least one of the two? (a) 59 (b) 52 (c) 49 (d) 39
30. 30.In a class of 19 children, 12 like dance, 15 like music and 9 like both. How many like neither? (a) 2 (b) 9 (c) 1 (d) 10
31. 31.In a class of 33 children, 14 like tea, 16 like coffee and 4 like both. How many like only tea? (a) 17 (b) 14 (c) 10 (d) 12
32. 32.In a class of 49 children, 22 like maths, 28 like science and 8 like both. How many like at least one of the two? (a) 42 (b) 50 (c) 34 (d) 49
33. 33.In a class of 39 children, 26 like tea, 18 like coffee and 9 like both. How many like only tea? (a) 17 (b) 21 (c) 26 (d) 9
34. 34.In a class of 36 children, 8 like cricket, 23 like football and 8 like neither. How many like both? (a) 8 (b) 4 (c) 28 (d) 3
35. 35.In a class of 35 children, 24 like cricket, 15 like football and 8 like both. How many like only cricket? (a) 16 (b) 7 (c) 24 (d) 20
36. 36.In a class of 37 children, 18 like tea, 18 like coffee and 3 like both. How many like at least one of the two? (a) 30 (b) 37 (c) 33 (d) 36
37. 37.In a class of 43 children, 13 like cricket, 23 like football and 10 like neither. How many like both? (a) 10 (b) 3 (c) 33 (d) 4
38. 38.In a class of 44 children, 22 like maths, 18 like science and 5 like both. How many like neither? (a) 14 (b) 5 (c) 4 (d) 9
39. 39.In a class of 27 children, 13 like dance, 9 like music and 2 like both. How many like neither? (a) 9 (b) 7 (c) 2 (d) 5
40. 40.In a class of 42 children, 25 like maths, 24 like science and 12 like both. How many like neither? (a) 12 (b) 17 (c) 6 (d) 5

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