Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 54 · 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 27 children, 11 like maths, 18 like science and 4 like both. How many like at least one of the two? (a) 27 (b) 25 (c) 29 (d) 21
2. 2.In a class of 28 children, 16 like maths, 8 like science and 2 like both. How many like neither? (a) 2 (b) 4 (c) 8 (d) 6
3. 3.In a class of 53 children, 31 like dance, 25 like music and 12 like both. How many like neither? (a) 12 (b) 9 (c) 21 (d) 10
4. 4.In a class of 31 children, 17 like cricket, 12 like football and 10 like neither. How many like both? (a) 10 (b) 21 (c) 8 (d) 9
5. 5.In a class of 33 children, 14 like cricket, 21 like football and 9 like both. How many like at least one of the two? (a) 17 (b) 33 (c) 35 (d) 26
6. 6.In a class of 33 children, 13 like mangoes, 15 like bananas and 9 like neither. How many like both? (a) 24 (b) 4 (c) 9 (d) 5
7. 7.In a class of 37 children, 20 like maths, 27 like science and 1 like neither. How many like both? (a) 1 (b) 36 (c) 10 (d) 11
8. 8.In a class of 48 children, 23 like cricket, 23 like football and 5 like both. How many like only cricket? (a) 18 (b) 25 (c) 23 (d) 5
9. 9.In a class of 36 children, 18 like cricket, 14 like football and 6 like neither. How many like both? (a) 2 (b) 30 (c) 3 (d) 6
10. 10.In a class of 34 children, 24 like cricket, 15 like football and 7 like both. How many like at least one of the two? (a) 39 (b) 34 (c) 32 (d) 25
11. 11.In a class of 30 children, 14 like tea, 18 like coffee and 3 like both. How many like at least one of the two? (a) 32 (b) 30 (c) 26 (d) 29
12. 12.In a class of 37 children, 15 like mangoes, 32 like bananas and 12 like both. How many like neither? (a) 2 (b) 14 (c) 12 (d) 3
13. 13.In a class of 36 children, 22 like tea, 14 like coffee and 5 like neither. How many like both? (a) 5 (b) 4 (c) 6 (d) 31
14. 14.In a class of 30 children, 17 like cricket, 22 like football and 11 like both. How many like neither? (a) 2 (b) 11 (c) 3 (d) 13
15. 15.In a class of 54 children, 27 like dance, 31 like music and 8 like neither. How many like both? (a) 4 (b) 12 (c) 46 (d) 8
16. 16.In a class of 34 children, 16 like cricket, 24 like football and 12 like both. How many like neither? (a) 18 (b) 12 (c) 7 (d) 6
17. 17.In a class of 36 children, 18 like dance, 23 like music and 7 like both. How many like at least one of the two? (a) 41 (b) 27 (c) 34 (d) 36
18. 18.In a class of 22 children, 14 like cricket, 15 like football and 9 like both. How many like at least one of the two? (a) 29 (b) 20 (c) 11 (d) 22
19. 19.In a class of 32 children, 7 like tea, 19 like coffee and 4 like both. How many like at least one of the two? (a) 18 (b) 22 (c) 26 (d) 32
20. 20.In a class of 19 children, 14 like tea, 5 like coffee and 2 like both. How many like neither? (a) 3 (b) 4 (c) 0 (d) 2
21. 21.In a class of 34 children, 24 like maths, 9 like science and 4 like both. How many like at least one of the two? (a) 25 (b) 33 (c) 34 (d) 29
22. 22.In a class of 30 children, 19 like dance, 13 like music and 3 like both. How many like at least one of the two? (a) 32 (b) 30 (c) 26 (d) 29
23. 23.In a class of 34 children, 17 like tea, 17 like coffee and 10 like both. How many like at least one of the two? (a) 25 (b) 34 (c) 14 (d) 24
24. 24.In a class of 43 children, 19 like mangoes, 27 like bananas and 11 like both. How many like neither? (a) 19 (b) 9 (c) 11 (d) 8
25. 25.In a class of 37 children, 14 like mangoes, 27 like bananas and 7 like both. How many like only mangoes? (a) 10 (b) 14 (c) 20 (d) 7
26. 26.In a class of 22 children, 17 like cricket, 6 like football and 2 like both. How many like at least one of the two? (a) 22 (b) 21 (c) 19 (d) 23
27. 27.In a class of 29 children, 15 like cricket, 15 like football and 3 like neither. How many like both? (a) 1 (b) 4 (c) 26 (d) 3
28. 28.In a class of 32 children, 20 like mangoes, 17 like bananas and 7 like both. How many like at least one of the two? (a) 32 (b) 37 (c) 23 (d) 30
29. 29.In a class of 32 children, 6 like maths, 19 like science and 3 like both. How many like at least one of the two? (a) 25 (b) 19 (c) 22 (d) 32
30. 30.In a class of 26 children, 21 like maths, 12 like science and 1 like neither. How many like both? (a) 7 (b) 25 (c) 8 (d) 1
31. 31.In a class of 33 children, 20 like dance, 16 like music and 5 like both. How many like only dance? (a) 17 (b) 20 (c) 15 (d) 11
32. 32.In a class of 32 children, 15 like cricket, 9 like football and 2 like both. How many like at least one of the two? (a) 22 (b) 24 (c) 32 (d) 20
33. 33.In a class of 39 children, 18 like mangoes, 23 like bananas and 3 like both. How many like neither? (a) 4 (b) 2 (c) 3 (d) 1
34. 34.In a class of 29 children, 16 like tea, 15 like coffee and 9 like both. How many like neither? (a) 7 (b) 9 (c) 8 (d) 16
35. 35.In a class of 35 children, 24 like cricket, 17 like football and 7 like both. How many like at least one of the two? (a) 41 (b) 34 (c) 27 (d) 35
36. 36.In a class of 33 children, 29 like tea, 12 like coffee and 9 like both. How many like only tea? (a) 3 (b) 21 (c) 20 (d) 29
37. 37.In a class of 48 children, 28 like tea, 23 like coffee and 9 like both. How many like only tea? (a) 14 (b) 25 (c) 28 (d) 19
38. 38.In a class of 36 children, 18 like mangoes, 21 like bananas and 11 like both. How many like at least one of the two? (a) 36 (b) 28 (c) 39 (d) 17
39. 39.In a class of 32 children, 14 like cricket, 25 like football and 10 like both. How many like only cricket? (a) 15 (b) 14 (c) 4 (d) 7
40. 40.In a class of 36 children, 25 like mangoes, 17 like bananas and 12 like both. How many like at least one of the two? (a) 30 (b) 36 (c) 18 (d) 42

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