Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 585 · 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 33 children, 14 like mangoes, 12 like bananas and 2 like both. How many like only mangoes? (a) 14 (b) 10 (c) 21 (d) 12
2. 2.In a class of 35 children, 16 like maths, 19 like science and 3 like neither. How many like both? (a) 2 (b) 32 (c) 3 (d) 4
3. 3.In a class of 28 children, 9 like mangoes, 19 like bananas and 3 like neither. How many like both? (a) 4 (b) 25 (c) 3 (d) 2
4. 4.In a class of 45 children, 22 like cricket, 23 like football and 5 like both. How many like only cricket? (a) 5 (b) 17 (c) 22 (d) 18
5. 5.In a class of 37 children, 25 like mangoes, 16 like bananas and 9 like both. How many like at least one of the two? (a) 23 (b) 37 (c) 41 (d) 32
6. 6.In a class of 22 children, 15 like cricket, 11 like football and 5 like both. How many like neither? (a) 6 (b) 5 (c) 2 (d) 1
7. 7.In a class of 47 children, 23 like maths, 20 like science and 5 like both. How many like only maths? (a) 23 (b) 15 (c) 18 (d) 27
8. 8.In a class of 37 children, 22 like cricket, 16 like football and 4 like both. How many like neither? (a) 7 (b) 4 (c) 3 (d) 2
9. 9.In a class of 29 children, 8 like mangoes, 13 like bananas and 2 like both. How many like at least one of the two? (a) 19 (b) 21 (c) 17 (d) 29
10. 10.In a class of 20 children, 13 like cricket, 16 like football and 10 like both. How many like neither? (a) 2 (b) 1 (c) 11 (d) 10
11. 11.In a class of 30 children, 22 like mangoes, 13 like bananas and 6 like both. How many like neither? (a) 1 (b) 7 (c) 2 (d) 6
12. 12.In a class of 36 children, 28 like cricket, 15 like football and 11 like both. How many like only cricket? (a) 28 (b) 21 (c) 4 (d) 17
13. 13.In a class of 27 children, 11 like dance, 17 like music and 8 like both. How many like only dance? (a) 11 (b) 9 (c) 10 (d) 3
14. 14.In a class of 36 children, 22 like cricket, 13 like football and 6 like both. How many like only cricket? (a) 22 (b) 16 (c) 23 (d) 7
15. 15.In a class of 37 children, 28 like tea, 15 like coffee and 11 like both. How many like only tea? (a) 28 (b) 17 (c) 4 (d) 22
16. 16.In a class of 30 children, 9 like mangoes, 24 like bananas and 2 like neither. How many like both? (a) 28 (b) 3 (c) 5 (d) 2
17. 17.In a class of 35 children, 15 like maths, 13 like science and 2 like both. How many like at least one of the two? (a) 28 (b) 35 (c) 24 (d) 26
18. 18.In a class of 43 children, 21 like cricket, 19 like football and 6 like both. How many like only cricket? (a) 24 (b) 13 (c) 21 (d) 15
19. 19.In a class of 29 children, 18 like maths, 12 like science and 8 like neither. How many like both? (a) 8 (b) 1 (c) 21 (d) 9
20. 20.In a class of 44 children, 21 like mangoes, 20 like bananas and 2 like both. How many like neither? (a) 7 (b) 5 (c) 3 (d) 2
21. 21.In a class of 45 children, 16 like tea, 25 like coffee and 5 like both. How many like at least one of the two? (a) 45 (b) 41 (c) 31 (d) 36
22. 22.In a class of 38 children, 11 like mangoes, 25 like bananas and 5 like both. How many like neither? (a) 12 (b) 2 (c) 5 (d) 7
23. 23.In a class of 36 children, 12 like cricket, 22 like football and 3 like both. How many like neither? (a) 3 (b) 2 (c) 5 (d) 8
24. 24.In a class of 36 children, 13 like dance, 27 like music and 5 like neither. How many like both? (a) 31 (b) 5 (c) 9 (d) 4
25. 25.In a class of 27 children, 14 like cricket, 19 like football and 8 like both. How many like only cricket? (a) 11 (b) 8 (c) 6 (d) 14
26. 26.In a class of 37 children, 15 like mangoes, 17 like bananas and 2 like both. How many like neither? (a) 5 (b) 9 (c) 2 (d) 7
27. 27.In a class of 33 children, 10 like tea, 23 like coffee and 4 like both. How many like neither? (a) 8 (b) 5 (c) 4 (d) 0
28. 28.In a class of 43 children, 25 like maths, 21 like science and 5 like both. How many like at least one of the two? (a) 46 (b) 43 (c) 36 (d) 41
29. 29.In a class of 38 children, 18 like dance, 31 like music and 12 like both. How many like neither? (a) 2 (b) 13 (c) 1 (d) 12
30. 30.In a class of 40 children, 13 like maths, 27 like science and 7 like both. How many like only maths? (a) 13 (b) 20 (c) 7 (d) 6
31. 31.In a class of 43 children, 14 like maths, 26 like science and 7 like both. How many like at least one of the two? (a) 33 (b) 43 (c) 40 (d) 26
32. 32.In a class of 24 children, 12 like cricket, 15 like football and 4 like both. How many like at least one of the two? (a) 27 (b) 24 (c) 23 (d) 19
33. 33.In a class of 49 children, 23 like cricket, 23 like football and 4 like both. How many like neither? (a) 11 (b) 3 (c) 4 (d) 7
34. 34.In a class of 42 children, 19 like maths, 27 like science and 9 like both. How many like neither? (a) 9 (b) 6 (c) 5 (d) 14
35. 35.In a class of 21 children, 14 like tea, 13 like coffee and 1 like neither. How many like both? (a) 6 (b) 1 (c) 7 (d) 20
36. 36.In a class of 37 children, 17 like maths, 19 like science and 2 like both. How many like neither? (a) 2 (b) 1 (c) 5 (d) 3
37. 37.In a class of 22 children, 8 like tea, 9 like coffee and 2 like both. How many like at least one of the two? (a) 22 (b) 15 (c) 17 (d) 13
38. 38.In a class of 43 children, 17 like mangoes, 21 like bananas and 4 like both. How many like at least one of the two? (a) 43 (b) 30 (c) 34 (d) 38
39. 39.In a class of 41 children, 16 like mangoes, 20 like bananas and 4 like both. How many like at least one of the two? (a) 28 (b) 41 (c) 32 (d) 36
40. 40.In a class of 23 children, 7 like maths, 18 like science and 3 like both. How many like at least one of the two? (a) 23 (b) 25 (c) 19 (d) 22

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