Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 106 · 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 13 children, 7 like mangoes, 5 like bananas and 2 like both. How many like only mangoes? (a) 8 (b) 7 (c) 5 (d) 3
2. 2.In a class of 46 children, 26 like dance, 29 like music and 11 like both. How many like neither? (a) 11 (b) 2 (c) 13 (d) 3
3. 3.In a class of 49 children, 29 like cricket, 31 like football and 12 like both. How many like at least one of the two? (a) 48 (b) 49 (c) 36 (d) 60
4. 4.In a class of 36 children, 20 like cricket, 15 like football and 3 like both. How many like only cricket? (a) 12 (b) 20 (c) 17 (d) 21
5. 5.In a class of 29 children, 14 like tea, 20 like coffee and 1 like neither. How many like both? (a) 1 (b) 28 (c) 5 (d) 6
6. 6.In a class of 30 children, 21 like mangoes, 8 like bananas and 2 like both. How many like at least one of the two? (a) 29 (b) 30 (c) 27 (d) 25
7. 7.In a class of 43 children, 20 like tea, 25 like coffee and 12 like both. How many like at least one of the two? (a) 45 (b) 43 (c) 21 (d) 33
8. 8.In a class of 23 children, 15 like mangoes, 14 like bananas and 10 like both. How many like at least one of the two? (a) 29 (b) 23 (c) 9 (d) 19
9. 9.In a class of 35 children, 26 like dance, 13 like music and 6 like both. How many like only dance? (a) 26 (b) 7 (c) 20 (d) 22
10. 10.In a class of 40 children, 30 like maths, 16 like science and 11 like both. How many like at least one of the two? (a) 24 (b) 40 (c) 46 (d) 35
11. 11.In a class of 31 children, 23 like cricket, 9 like football and 6 like both. How many like only cricket? (a) 23 (b) 3 (c) 22 (d) 17
12. 12.In a class of 23 children, 15 like maths, 15 like science and 10 like both. How many like at least one of the two? (a) 20 (b) 23 (c) 10 (d) 30
13. 13.In a class of 23 children, 10 like dance, 16 like music and 4 like neither. How many like both? (a) 19 (b) 4 (c) 3 (d) 7
14. 14.In a class of 34 children, 16 like dance, 19 like music and 4 like both. How many like neither? (a) 7 (b) 4 (c) 2 (d) 3
15. 15.In a class of 25 children, 13 like mangoes, 18 like bananas and 2 like neither. How many like both? (a) 6 (b) 2 (c) 23 (d) 8
16. 16.In a class of 23 children, 12 like maths, 14 like science and 4 like both. How many like at least one of the two? (a) 22 (b) 26 (c) 18 (d) 23
17. 17.In a class of 15 children, 6 like cricket, 5 like football and 2 like both. How many like only cricket? (a) 10 (b) 3 (c) 4 (d) 6
18. 18.In a class of 29 children, 22 like cricket, 15 like football and 3 like neither. How many like both? (a) 3 (b) 8 (c) 26 (d) 11
19. 19.In a class of 26 children, 15 like tea, 17 like coffee and 8 like both. How many like at least one of the two? (a) 26 (b) 16 (c) 24 (d) 32
20. 20.In a class of 36 children, 15 like maths, 22 like science and 9 like both. How many like at least one of the two? (a) 36 (b) 28 (c) 19 (d) 37
21. 21.In a class of 35 children, 14 like maths, 25 like science and 2 like neither. How many like both? (a) 33 (b) 6 (c) 4 (d) 2
22. 22.In a class of 31 children, 9 like dance, 22 like music and 6 like both. How many like neither? (a) 12 (b) 0 (c) 7 (d) 6
23. 23.In a class of 26 children, 9 like maths, 13 like science and 5 like both. How many like only maths? (a) 9 (b) 8 (c) 4 (d) 13
24. 24.In a class of 35 children, 7 like dance, 22 like music and 9 like neither. How many like both? (a) 9 (b) 3 (c) 26 (d) 4
25. 25.In a class of 39 children, 24 like dance, 22 like music and 10 like both. How many like at least one of the two? (a) 26 (b) 46 (c) 39 (d) 36
26. 26.In a class of 48 children, 24 like mangoes, 26 like bananas and 9 like both. How many like at least one of the two? (a) 50 (b) 32 (c) 48 (d) 41
27. 27.In a class of 46 children, 23 like maths, 26 like science and 8 like both. How many like at least one of the two? (a) 41 (b) 33 (c) 46 (d) 49
28. 28.In a class of 31 children, 18 like tea, 17 like coffee and 10 like both. How many like at least one of the two? (a) 25 (b) 35 (c) 31 (d) 15
29. 29.In a class of 43 children, 21 like tea, 23 like coffee and 8 like both. How many like at least one of the two? (a) 36 (b) 43 (c) 28 (d) 44
30. 30.In a class of 27 children, 16 like mangoes, 14 like bananas and 7 like both. How many like only mangoes? (a) 13 (b) 7 (c) 9 (d) 16
31. 31.In a class of 32 children, 20 like cricket, 15 like football and 5 like both. How many like only cricket? (a) 10 (b) 17 (c) 15 (d) 20
32. 32.In a class of 35 children, 12 like dance, 29 like music and 9 like both. How many like only dance? (a) 6 (b) 12 (c) 20 (d) 3
33. 33.In a class of 43 children, 25 like dance, 15 like music and 9 like neither. How many like both? (a) 34 (b) 7 (c) 6 (d) 9
34. 34.In a class of 56 children, 27 like maths, 29 like science and 9 like neither. How many like both? (a) 47 (b) 10 (c) 8 (d) 9
35. 35.In a class of 47 children, 26 like dance, 20 like music and 8 like both. How many like only dance? (a) 27 (b) 26 (c) 18 (d) 12
36. 36.In a class of 31 children, 18 like mangoes, 7 like bananas and 4 like both. How many like only mangoes? (a) 18 (b) 24 (c) 14 (d) 3
37. 37.In a class of 35 children, 17 like mangoes, 28 like bananas and 12 like both. How many like only mangoes? (a) 16 (b) 5 (c) 7 (d) 17
38. 38.In a class of 30 children, 19 like cricket, 9 like football and 4 like both. How many like at least one of the two? (a) 20 (b) 24 (c) 30 (d) 28
39. 39.In a class of 30 children, 13 like cricket, 15 like football and 7 like both. How many like at least one of the two? (a) 14 (b) 30 (c) 28 (d) 21
40. 40.In a class of 33 children, 12 like cricket, 20 like football and 5 like both. How many like neither? (a) 11 (b) 5 (c) 1 (d) 6

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