Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 356 · 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 37 children, 21 like tea, 16 like coffee and 9 like neither. How many like both? (a) 28 (b) 10 (c) 8 (d) 9
2. 2.In a class of 31 children, 10 like maths, 21 like science and 2 like both. How many like at least one of the two? (a) 29 (b) 30 (c) 27 (d) 31
3. 3.In a class of 47 children, 19 like mangoes, 28 like bananas and 8 like both. How many like neither? (a) 9 (b) 0 (c) 16 (d) 8
4. 4.In a class of 48 children, 31 like dance, 28 like music and 12 like both. How many like at least one of the two? (a) 35 (b) 48 (c) 59 (d) 47
5. 5.In a class of 30 children, 12 like cricket, 21 like football and 6 like both. How many like only cricket? (a) 15 (b) 9 (c) 6 (d) 12
6. 6.In a class of 21 children, 10 like mangoes, 13 like bananas and 4 like both. How many like neither? (a) 2 (b) 4 (c) 6 (d) 3
7. 7.In a class of 41 children, 15 like dance, 29 like music and 10 like both. How many like at least one of the two? (a) 41 (b) 24 (c) 34 (d) 44
8. 8.In a class of 31 children, 18 like maths, 8 like science and 5 like both. How many like at least one of the two? (a) 26 (b) 16 (c) 31 (d) 21
9. 9.In a class of 41 children, 19 like dance, 25 like music and 10 like both. How many like neither? (a) 7 (b) 8 (c) 17 (d) 10
10. 10.In a class of 26 children, 6 like tea, 14 like coffee and 3 like both. How many like neither? (a) 3 (b) 6 (c) 12 (d) 9
11. 11.In a class of 24 children, 12 like maths, 14 like science and 9 like both. How many like only maths? (a) 12 (b) 5 (c) 3 (d) 10
12. 12.In a class of 30 children, 17 like tea, 14 like coffee and 9 like neither. How many like both? (a) 10 (b) 21 (c) 9 (d) 1
13. 13.In a class of 37 children, 23 like mangoes, 14 like bananas and 10 like both. How many like only mangoes? (a) 4 (b) 23 (c) 10 (d) 13
14. 14.In a class of 38 children, 18 like mangoes, 30 like bananas and 11 like both. How many like neither? (a) 2 (b) 12 (c) 1 (d) 11
15. 15.In a class of 42 children, 21 like tea, 23 like coffee and 12 like both. How many like neither? (a) 22 (b) 11 (c) 10 (d) 12
16. 16.In a class of 22 children, 15 like dance, 9 like music and 3 like both. How many like only dance? (a) 15 (b) 6 (c) 12 (d) 13
17. 17.In a class of 32 children, 10 like cricket, 18 like football and 4 like both. How many like at least one of the two? (a) 20 (b) 28 (c) 32 (d) 24
18. 18.In a class of 36 children, 17 like dance, 24 like music and 7 like both. How many like at least one of the two? (a) 41 (b) 36 (c) 27 (d) 34
19. 19.In a class of 23 children, 13 like cricket, 11 like football and 5 like both. How many like at least one of the two? (a) 19 (b) 24 (c) 23 (d) 14
20. 20.In a class of 31 children, 18 like tea, 12 like coffee and 5 like both. How many like neither? (a) 11 (b) 1 (c) 5 (d) 6
21. 21.In a class of 17 children, 13 like mangoes, 11 like bananas and 8 like both. How many like neither? (a) 1 (b) 2 (c) 9 (d) 8
22. 22.In a class of 23 children, 14 like mangoes, 10 like bananas and 3 like both. How many like neither? (a) 2 (b) 1 (c) 5 (d) 3
23. 23.In a class of 41 children, 27 like cricket, 13 like football and 7 like both. How many like neither? (a) 7 (b) 8 (c) 15 (d) 1
24. 24.In a class of 36 children, 15 like cricket, 26 like football and 8 like both. How many like only cricket? (a) 15 (b) 10 (c) 18 (d) 7
25. 25.In a class of 29 children, 21 like dance, 9 like music and 2 like both. How many like at least one of the two? (a) 26 (b) 29 (c) 30 (d) 28
26. 26.In a class of 37 children, 23 like maths, 21 like science and 10 like both. How many like only maths? (a) 23 (b) 16 (c) 13 (d) 11
27. 27.In a class of 21 children, 10 like mangoes, 14 like bananas and 4 like both. How many like at least one of the two? (a) 16 (b) 20 (c) 24 (d) 21
28. 28.In a class of 28 children, 20 like mangoes, 11 like bananas and 5 like both. How many like neither? (a) 2 (b) 5 (c) 3 (d) 7
29. 29.In a class of 21 children, 6 like tea, 13 like coffee and 2 like both. How many like at least one of the two? (a) 21 (b) 17 (c) 15 (d) 19
30. 30.In a class of 54 children, 27 like cricket, 26 like football and 8 like neither. How many like both? (a) 7 (b) 46 (c) 8 (d) 6
31. 31.In a class of 30 children, 13 like tea, 19 like coffee and 5 like neither. How many like both? (a) 5 (b) 2 (c) 25 (d) 7
32. 32.In a class of 37 children, 25 like dance, 11 like music and 7 like both. How many like neither? (a) 7 (b) 8 (c) 15 (d) 1
33. 33.In a class of 18 children, 10 like dance, 10 like music and 3 like both. How many like at least one of the two? (a) 17 (b) 20 (c) 14 (d) 18
34. 34.In a class of 21 children, 12 like tea, 12 like coffee and 7 like both. How many like at least one of the two? (a) 24 (b) 17 (c) 10 (d) 21
35. 35.In a class of 25 children, 21 like cricket, 6 like football and 3 like both. How many like at least one of the two? (a) 27 (b) 21 (c) 24 (d) 25
36. 36.In a class of 36 children, 17 like dance, 16 like music and 6 like both. How many like at least one of the two? (a) 36 (b) 33 (c) 21 (d) 27
37. 37.In a class of 26 children, 17 like dance, 12 like music and 5 like both. How many like neither? (a) 5 (b) 7 (c) 3 (d) 2
38. 38.In a class of 13 children, 7 like mangoes, 8 like bananas and 2 like neither. How many like both? (a) 11 (b) 5 (c) 2 (d) 4
39. 39.In a class of 35 children, 14 like cricket, 17 like football and 3 like both. How many like at least one of the two? (a) 25 (b) 28 (c) 31 (d) 35
40. 40.In a class of 37 children, 17 like maths, 21 like science and 2 like neither. How many like both? (a) 2 (b) 1 (c) 35 (d) 3

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