Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 835 · 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 dance, 15 like music and 4 like neither. How many like both? (a) 10 (b) 6 (c) 4 (d) 23
2. 2.In a class of 45 children, 17 like cricket, 31 like football and 12 like both. How many like neither? (a) 21 (b) 10 (c) 12 (d) 9
3. 3.In a class of 37 children, 21 like cricket, 16 like football and 5 like both. How many like at least one of the two? (a) 37 (b) 33 (c) 27 (d) 32
4. 4.In a class of 44 children, 21 like tea, 27 like coffee and 7 like neither. How many like both? (a) 4 (b) 11 (c) 7 (d) 37
5. 5.In a class of 44 children, 16 like maths, 28 like science and 10 like both. How many like neither? (a) 10 (b) 0 (c) 20 (d) 11
6. 6.In a class of 30 children, 15 like mangoes, 13 like bananas and 6 like both. How many like at least one of the two? (a) 28 (b) 22 (c) 16 (d) 30
7. 7.In a class of 53 children, 29 like tea, 27 like coffee and 12 like both. How many like neither? (a) 10 (b) 12 (c) 9 (d) 21
8. 8.In a class of 25 children, 18 like dance, 10 like music and 5 like both. How many like only dance? (a) 5 (b) 15 (c) 13 (d) 18
9. 9.In a class of 26 children, 16 like mangoes, 11 like bananas and 5 like neither. How many like both? (a) 6 (b) 1 (c) 21 (d) 5
10. 10.In a class of 42 children, 30 like tea, 15 like coffee and 7 like neither. How many like both? (a) 10 (b) 7 (c) 35 (d) 3
11. 11.In a class of 32 children, 23 like mangoes, 14 like bananas and 6 like both. How many like only mangoes? (a) 18 (b) 8 (c) 17 (d) 23
12. 12.In a class of 36 children, 11 like dance, 20 like music and 9 like neither. How many like both? (a) 27 (b) 5 (c) 9 (d) 4
13. 13.In a class of 36 children, 20 like maths, 14 like science and 2 like both. How many like at least one of the two? (a) 34 (b) 30 (c) 36 (d) 32
14. 14.In a class of 32 children, 14 like tea, 19 like coffee and 8 like both. How many like neither? (a) 7 (b) 8 (c) 15 (d) 6
15. 15.In a class of 22 children, 17 like dance, 11 like music and 7 like both. How many like at least one of the two? (a) 14 (b) 22 (c) 21 (d) 28
16. 16.In a class of 25 children, 20 like cricket, 7 like football and 3 like both. How many like neither? (a) 3 (b) 4 (c) 1 (d) 2
17. 17.In a class of 34 children, 13 like cricket, 22 like football and 8 like both. How many like neither? (a) 6 (b) 7 (c) 8 (d) 15
18. 18.In a class of 35 children, 19 like cricket, 19 like football and 1 like neither. How many like both? (a) 34 (b) 3 (c) 4 (d) 1
19. 19.In a class of 48 children, 21 like maths, 27 like science and 10 like both. How many like only maths? (a) 17 (b) 11 (c) 21 (d) 10
20. 20.In a class of 33 children, 12 like maths, 27 like science and 9 like both. How many like at least one of the two? (a) 39 (b) 21 (c) 33 (d) 30
21. 21.In a class of 18 children, 12 like tea, 7 like coffee and 3 like both. How many like only tea? (a) 11 (b) 4 (c) 9 (d) 12
22. 22.In a class of 30 children, 19 like cricket, 17 like football and 6 like neither. How many like both? (a) 24 (b) 6 (c) 12 (d) 13
23. 23.In a class of 42 children, 30 like maths, 23 like science and 12 like both. How many like only maths? (a) 11 (b) 18 (c) 30 (d) 19
24. 24.In a class of 39 children, 18 like dance, 15 like music and 4 like both. How many like only dance? (a) 11 (b) 18 (c) 24 (d) 14
25. 25.In a class of 19 children, 12 like tea, 12 like coffee and 8 like both. How many like neither? (a) 11 (b) 4 (c) 3 (d) 8
26. 26.In a class of 30 children, 13 like tea, 22 like coffee and 10 like both. How many like neither? (a) 6 (b) 15 (c) 10 (d) 5
27. 27.In a class of 41 children, 23 like dance, 23 like music and 11 like both. How many like neither? (a) 7 (b) 11 (c) 6 (d) 17
28. 28.In a class of 41 children, 17 like maths, 29 like science and 12 like both. How many like only maths? (a) 5 (b) 12 (c) 17 (d) 6
29. 29.In a class of 36 children, 17 like tea, 20 like coffee and 5 like neither. How many like both? (a) 6 (b) 5 (c) 1 (d) 31
30. 30.In a class of 44 children, 18 like maths, 28 like science and 12 like both. How many like only maths? (a) 18 (b) 12 (c) 16 (d) 6
31. 31.In a class of 35 children, 13 like cricket, 20 like football and 5 like both. How many like only cricket? (a) 5 (b) 13 (c) 15 (d) 8
32. 32.In a class of 49 children, 28 like mangoes, 26 like bananas and 10 like both. How many like only mangoes? (a) 28 (b) 16 (c) 23 (d) 18
33. 33.In a class of 21 children, 13 like tea, 12 like coffee and 8 like both. How many like only tea? (a) 9 (b) 5 (c) 4 (d) 13
34. 34.In a class of 32 children, 23 like tea, 11 like coffee and 2 like neither. How many like both? (a) 30 (b) 2 (c) 4 (d) 5
35. 35.In a class of 42 children, 27 like cricket, 18 like football and 8 like both. How many like only cricket? (a) 27 (b) 24 (c) 10 (d) 19
36. 36.In a class of 43 children, 28 like cricket, 21 like football and 11 like both. How many like only cricket? (a) 10 (b) 28 (c) 22 (d) 17
37. 37.In a class of 36 children, 20 like cricket, 17 like football and 4 like both. How many like only cricket? (a) 19 (b) 20 (c) 16 (d) 13
38. 38.In a class of 40 children, 26 like tea, 21 like coffee and 3 like neither. How many like both? (a) 3 (b) 7 (c) 37 (d) 10
39. 39.In a class of 37 children, 14 like cricket, 21 like football and 5 like both. How many like neither? (a) 12 (b) 2 (c) 5 (d) 7
40. 40.In a class of 25 children, 20 like mangoes, 10 like bananas and 1 like neither. How many like both? (a) 24 (b) 1 (c) 5 (d) 6

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