Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 346 · 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 32 children, 15 like cricket, 13 like football and 9 like neither. How many like both? (a) 9 (b) 6 (c) 23 (d) 5
2. 2.In a class of 25 children, 17 like tea, 15 like coffee and 1 like neither. How many like both? (a) 8 (b) 7 (c) 24 (d) 1
3. 3.In a class of 35 children, 23 like cricket, 19 like football and 4 like neither. How many like both? (a) 11 (b) 7 (c) 4 (d) 31
4. 4.In a class of 20 children, 6 like cricket, 15 like football and 2 like both. How many like only cricket? (a) 13 (b) 4 (c) 6 (d) 5
5. 5.In a class of 53 children, 30 like maths, 25 like science and 12 like both. How many like only maths? (a) 13 (b) 28 (c) 18 (d) 30
6. 6.In a class of 21 children, 7 like mangoes, 13 like bananas and 3 like both. How many like at least one of the two? (a) 20 (b) 17 (c) 21 (d) 14
7. 7.In a class of 28 children, 16 like tea, 21 like coffee and 11 like both. How many like at least one of the two? (a) 15 (b) 37 (c) 28 (d) 26
8. 8.In a class of 33 children, 17 like tea, 17 like coffee and 4 like both. How many like neither? (a) 2 (b) 7 (c) 4 (d) 3
9. 9.In a class of 24 children, 10 like cricket, 17 like football and 4 like both. How many like at least one of the two? (a) 23 (b) 27 (c) 19 (d) 24
10. 10.In a class of 31 children, 17 like mangoes, 18 like bananas and 9 like both. How many like at least one of the two? (a) 35 (b) 26 (c) 31 (d) 17
11. 11.In a class of 34 children, 20 like maths, 11 like science and 5 like both. How many like neither? (a) 5 (b) 13 (c) 8 (d) 3
12. 12.In a class of 42 children, 19 like cricket, 27 like football and 5 like neither. How many like both? (a) 5 (b) 4 (c) 9 (d) 37
13. 13.In a class of 29 children, 22 like cricket, 14 like football and 9 like both. How many like only cricket? (a) 5 (b) 13 (c) 15 (d) 22
14. 14.In a class of 42 children, 28 like tea, 13 like coffee and 9 like both. How many like at least one of the two? (a) 41 (b) 32 (c) 42 (d) 23
15. 15.In a class of 34 children, 18 like cricket, 17 like football and 4 like both. How many like at least one of the two? (a) 27 (b) 35 (c) 31 (d) 34
16. 16.In a class of 33 children, 28 like cricket, 12 like football and 8 like both. How many like only cricket? (a) 21 (b) 28 (c) 20 (d) 4
17. 17.In a class of 23 children, 17 like maths, 7 like science and 4 like both. How many like only maths? (a) 17 (b) 16 (c) 3 (d) 13
18. 18.In a class of 39 children, 17 like mangoes, 30 like bananas and 10 like both. How many like at least one of the two? (a) 47 (b) 27 (c) 37 (d) 39
19. 19.In a class of 27 children, 16 like maths, 17 like science and 7 like both. How many like at least one of the two? (a) 19 (b) 33 (c) 26 (d) 27
20. 20.In a class of 34 children, 15 like tea, 18 like coffee and 3 like both. How many like neither? (a) 7 (b) 1 (c) 4 (d) 3
21. 21.In a class of 42 children, 24 like mangoes, 22 like bananas and 7 like neither. How many like both? (a) 4 (b) 35 (c) 7 (d) 11
22. 22.In a class of 40 children, 25 like tea, 13 like coffee and 8 like both. How many like neither? (a) 10 (b) 2 (c) 18 (d) 8
23. 23.In a class of 42 children, 29 like tea, 22 like coffee and 10 like both. How many like at least one of the two? (a) 31 (b) 42 (c) 41 (d) 51
24. 24.In a class of 26 children, 15 like mangoes, 15 like bananas and 9 like both. How many like at least one of the two? (a) 12 (b) 30 (c) 21 (d) 26
25. 25.In a class of 43 children, 21 like tea, 26 like coffee and 10 like both. How many like at least one of the two? (a) 47 (b) 43 (c) 37 (d) 27
26. 26.In a class of 29 children, 21 like mangoes, 6 like bananas and 3 like both. How many like neither? (a) 5 (b) 8 (c) 2 (d) 3
27. 27.In a class of 51 children, 23 like maths, 23 like science and 4 like both. How many like at least one of the two? (a) 51 (b) 42 (c) 38 (d) 46
28. 28.In a class of 42 children, 17 like dance, 21 like music and 4 like both. How many like at least one of the two? (a) 38 (b) 42 (c) 34 (d) 30
29. 29.In a class of 49 children, 29 like dance, 25 like music and 4 like neither. How many like both? (a) 9 (b) 5 (c) 45 (d) 4
30. 30.In a class of 45 children, 16 like mangoes, 27 like bananas and 10 like neither. How many like both? (a) 9 (b) 10 (c) 8 (d) 35
31. 31.In a class of 27 children, 14 like mangoes, 14 like bananas and 6 like both. How many like at least one of the two? (a) 28 (b) 27 (c) 22 (d) 16
32. 32.In a class of 23 children, 13 like maths, 13 like science and 7 like both. How many like only maths? (a) 10 (b) 7 (c) 6 (d) 13
33. 33.In a class of 12 children, 7 like dance, 5 like music and 2 like both. How many like at least one of the two? (a) 11 (b) 12 (c) 8 (d) 10
34. 34.In a class of 25 children, 6 like cricket, 21 like football and 3 like both. How many like at least one of the two? (a) 21 (b) 24 (c) 25 (d) 27
35. 35.In a class of 34 children, 8 like mangoes, 20 like bananas and 3 like both. How many like at least one of the two? (a) 22 (b) 34 (c) 28 (d) 25
36. 36.In a class of 40 children, 26 like tea, 14 like coffee and 8 like both. How many like neither? (a) 16 (b) 0 (c) 9 (d) 8
37. 37.In a class of 37 children, 16 like mangoes, 18 like bananas and 8 like neither. How many like both? (a) 29 (b) 8 (c) 6 (d) 5
38. 38.In a class of 45 children, 31 like maths, 22 like science and 11 like both. How many like at least one of the two? (a) 42 (b) 53 (c) 31 (d) 45
39. 39.In a class of 50 children, 27 like tea, 26 like coffee and 9 like both. How many like only tea? (a) 18 (b) 17 (c) 27 (d) 24
40. 40.In a class of 25 children, 14 like cricket, 13 like football and 7 like both. How many like at least one of the two? (a) 25 (b) 13 (c) 20 (d) 27

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