Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 180 · 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 39 children, 21 like mangoes, 21 like bananas and 8 like neither. How many like both? (a) 31 (b) 11 (c) 8 (d) 3
2. 2.In a class of 43 children, 21 like cricket, 25 like football and 5 like both. How many like at least one of the two? (a) 43 (b) 46 (c) 41 (d) 36
3. 3.In a class of 44 children, 18 like tea, 19 like coffee and 2 like both. How many like only tea? (a) 17 (b) 18 (c) 25 (d) 16
4. 4.In a class of 33 children, 15 like cricket, 22 like football and 4 like neither. How many like both? (a) 8 (b) 4 (c) 9 (d) 29
5. 5.In a class of 38 children, 28 like mangoes, 17 like bananas and 3 like neither. How many like both? (a) 35 (b) 7 (c) 3 (d) 10
6. 6.In a class of 38 children, 22 like cricket, 17 like football and 4 like both. How many like neither? (a) 7 (b) 4 (c) 2 (d) 3
7. 7.In a class of 37 children, 18 like cricket, 19 like football and 4 like both. How many like neither? (a) 0 (b) 5 (c) 8 (d) 4
8. 8.In a class of 38 children, 12 like cricket, 22 like football and 4 like both. How many like at least one of the two? (a) 38 (b) 30 (c) 34 (d) 26
9. 9.In a class of 26 children, 10 like tea, 8 like coffee and 2 like both. How many like at least one of the two? (a) 18 (b) 14 (c) 16 (d) 26
10. 10.In a class of 46 children, 19 like tea, 20 like coffee and 10 like neither. How many like both? (a) 10 (b) 4 (c) 3 (d) 36
11. 11.In a class of 35 children, 10 like maths, 20 like science and 7 like neither. How many like both? (a) 3 (b) 7 (c) 2 (d) 28
12. 12.In a class of 45 children, 23 like dance, 21 like music and 4 like neither. How many like both? (a) 2 (b) 41 (c) 4 (d) 3
13. 13.In a class of 35 children, 25 like dance, 10 like music and 6 like both. How many like only dance? (a) 25 (b) 19 (c) 4 (d) 6
14. 14.In a class of 29 children, 10 like cricket, 14 like football and 4 like both. How many like neither? (a) 4 (b) 5 (c) 13 (d) 9
15. 15.In a class of 29 children, 16 like maths, 16 like science and 12 like both. How many like neither? (a) 21 (b) 9 (c) 10 (d) 12
16. 16.In a class of 33 children, 22 like mangoes, 14 like bananas and 1 like neither. How many like both? (a) 1 (b) 3 (c) 32 (d) 4
17. 17.In a class of 39 children, 21 like dance, 17 like music and 6 like neither. How many like both? (a) 33 (b) 6 (c) 4 (d) 5
18. 18.In a class of 34 children, 16 like dance, 28 like music and 11 like both. How many like only dance? (a) 17 (b) 6 (c) 16 (d) 5
19. 19.In a class of 22 children, 9 like mangoes, 13 like bananas and 2 like both. How many like only mangoes? (a) 11 (b) 7 (c) 2 (d) 9
20. 20.In a class of 39 children, 24 like cricket, 12 like football and 4 like both. How many like at least one of the two? (a) 28 (b) 36 (c) 32 (d) 39
21. 21.In a class of 21 children, 17 like cricket, 13 like football and 1 like neither. How many like both? (a) 9 (b) 20 (c) 10 (d) 1
22. 22.In a class of 28 children, 18 like cricket, 12 like football and 1 like neither. How many like both? (a) 27 (b) 3 (c) 2 (d) 1
23. 23.In a class of 56 children, 28 like maths, 31 like science and 11 like both. How many like only maths? (a) 28 (b) 25 (c) 20 (d) 17
24. 24.In a class of 24 children, 10 like dance, 11 like music and 5 like both. How many like only dance? (a) 6 (b) 13 (c) 10 (d) 5
25. 25.In a class of 41 children, 23 like mangoes, 19 like bananas and 4 like both. How many like neither? (a) 7 (b) 2 (c) 4 (d) 3
26. 26.In a class of 39 children, 31 like maths, 16 like science and 4 like neither. How many like both? (a) 12 (b) 8 (c) 4 (d) 35
27. 27.In a class of 48 children, 25 like mangoes, 30 like bananas and 11 like both. How many like neither? (a) 11 (b) 4 (c) 5 (d) 15
28. 28.In a class of 27 children, 14 like cricket, 13 like football and 9 like both. How many like only cricket? (a) 9 (b) 5 (c) 4 (d) 14
29. 29.In a class of 27 children, 15 like mangoes, 15 like bananas and 6 like neither. How many like both? (a) 3 (b) 21 (c) 9 (d) 6
30. 30.In a class of 32 children, 11 like mangoes, 16 like bananas and 5 like both. How many like at least one of the two? (a) 17 (b) 32 (c) 22 (d) 27
31. 31.In a class of 38 children, 15 like mangoes, 25 like bananas and 12 like both. How many like only mangoes? (a) 15 (b) 13 (c) 12 (d) 3
32. 32.In a class of 36 children, 15 like mangoes, 32 like bananas and 1 like neither. How many like both? (a) 11 (b) 1 (c) 12 (d) 35
33. 33.In a class of 26 children, 10 like mangoes, 19 like bananas and 5 like both. How many like only mangoes? (a) 5 (b) 14 (c) 7 (d) 10
34. 34.In a class of 51 children, 25 like maths, 25 like science and 9 like neither. How many like both? (a) 8 (b) 42 (c) 7 (d) 9
35. 35.In a class of 37 children, 14 like dance, 23 like music and 4 like both. How many like at least one of the two? (a) 29 (b) 37 (c) 33 (d) 34
36. 36.In a class of 32 children, 22 like cricket, 8 like football and 5 like both. How many like at least one of the two? (a) 20 (b) 30 (c) 25 (d) 32
37. 37.In a class of 39 children, 18 like mangoes, 14 like bananas and 3 like both. How many like neither? (a) 7 (b) 3 (c) 10 (d) 13
38. 38.In a class of 45 children, 16 like tea, 27 like coffee and 8 like both. How many like at least one of the two? (a) 45 (b) 27 (c) 43 (d) 35
39. 39.In a class of 52 children, 27 like mangoes, 28 like bananas and 12 like both. How many like neither? (a) 12 (b) 9 (c) 10 (d) 21
40. 40.In a class of 40 children, 29 like tea, 16 like coffee and 12 like both. How many like only tea? (a) 17 (b) 29 (c) 4 (d) 24

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