Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 94 · 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 54 children, 28 like maths, 28 like science and 9 like neither. How many like both? (a) 45 (b) 9 (c) 2 (d) 11
2. 2.In a class of 35 children, 23 like tea, 8 like coffee and 3 like both. How many like neither? (a) 4 (b) 7 (c) 10 (d) 3
3. 3.In a class of 25 children, 17 like dance, 12 like music and 9 like both. How many like at least one of the two? (a) 29 (b) 20 (c) 11 (d) 25
4. 4.In a class of 40 children, 18 like mangoes, 29 like bananas and 10 like both. How many like neither? (a) 3 (b) 10 (c) 13 (d) 4
5. 5.In a class of 36 children, 25 like tea, 15 like coffee and 11 like both. How many like neither? (a) 8 (b) 11 (c) 18 (d) 7
6. 6.In a class of 35 children, 11 like cricket, 18 like football and 9 like neither. How many like both? (a) 4 (b) 26 (c) 3 (d) 9
7. 7.In a class of 39 children, 15 like dance, 28 like music and 11 like both. How many like at least one of the two? (a) 43 (b) 21 (c) 32 (d) 39
8. 8.In a class of 27 children, 15 like mangoes, 21 like bananas and 11 like both. How many like at least one of the two? (a) 14 (b) 27 (c) 36 (d) 25
9. 9.In a class of 42 children, 20 like maths, 23 like science and 4 like both. How many like at least one of the two? (a) 43 (b) 39 (c) 35 (d) 42
10. 10.In a class of 36 children, 20 like tea, 11 like coffee and 10 like neither. How many like both? (a) 26 (b) 10 (c) 5 (d) 6
11. 11.In a class of 33 children, 23 like dance, 6 like music and 3 like both. How many like neither? (a) 3 (b) 7 (c) 10 (d) 4
12. 12.In a class of 46 children, 19 like maths, 20 like science and 2 like both. How many like at least one of the two? (a) 37 (b) 39 (c) 46 (d) 35
13. 13.In a class of 38 children, 19 like tea, 18 like coffee and 7 like neither. How many like both? (a) 31 (b) 7 (c) 5 (d) 6
14. 14.In a class of 35 children, 18 like maths, 26 like science and 11 like both. How many like only maths? (a) 18 (b) 15 (c) 7 (d) 9
15. 15.In a class of 31 children, 15 like dance, 17 like music and 9 like both. How many like at least one of the two? (a) 32 (b) 31 (c) 14 (d) 23
16. 16.In a class of 23 children, 12 like mangoes, 10 like bananas and 7 like neither. How many like both? (a) 5 (b) 6 (c) 16 (d) 7
17. 17.In a class of 29 children, 8 like maths, 22 like science and 2 like both. How many like neither? (a) 0 (b) 2 (c) 1 (d) 3
18. 18.In a class of 32 children, 27 like cricket, 15 like football and 11 like both. How many like at least one of the two? (a) 32 (b) 42 (c) 20 (d) 31
19. 19.In a class of 33 children, 10 like dance, 17 like music and 10 like neither. How many like both? (a) 4 (b) 5 (c) 10 (d) 23
20. 20.In a class of 32 children, 18 like tea, 14 like coffee and 8 like neither. How many like both? (a) 8 (b) 7 (c) 9 (d) 24
21. 21.In a class of 47 children, 24 like cricket, 24 like football and 4 like both. How many like at least one of the two? (a) 40 (b) 44 (c) 48 (d) 47
22. 22.In a class of 44 children, 16 like cricket, 24 like football and 5 like both. How many like neither? (a) 4 (b) 14 (c) 5 (d) 9
23. 23.In a class of 36 children, 24 like mangoes, 11 like bananas and 6 like both. How many like neither? (a) 7 (b) 1 (c) 13 (d) 6
24. 24.In a class of 29 children, 15 like tea, 13 like coffee and 2 like both. How many like neither? (a) 1 (b) 3 (c) 2 (d) 5
25. 25.In a class of 49 children, 26 like cricket, 24 like football and 7 like both. How many like only cricket? (a) 19 (b) 25 (c) 17 (d) 26
26. 26.In a class of 25 children, 10 like mangoes, 10 like bananas and 3 like both. How many like at least one of the two? (a) 17 (b) 14 (c) 25 (d) 20
27. 27.In a class of 26 children, 12 like tea, 13 like coffee and 4 like neither. How many like both? (a) 4 (b) 22 (c) 2 (d) 3
28. 28.In a class of 33 children, 18 like cricket, 24 like football and 12 like both. How many like at least one of the two? (a) 42 (b) 33 (c) 18 (d) 30
29. 29.In a class of 23 children, 12 like mangoes, 9 like bananas and 6 like neither. How many like both? (a) 5 (b) 4 (c) 17 (d) 6
30. 30.In a class of 42 children, 23 like maths, 13 like science and 4 like both. How many like only maths? (a) 29 (b) 23 (c) 19 (d) 9
31. 31.In a class of 33 children, 21 like dance, 18 like music and 9 like both. How many like at least one of the two? (a) 33 (b) 21 (c) 30 (d) 39
32. 32.In a class of 30 children, 18 like tea, 16 like coffee and 6 like both. How many like only tea? (a) 14 (b) 10 (c) 12 (d) 18
33. 33.In a class of 17 children, 9 like maths, 8 like science and 4 like both. How many like only maths? (a) 9 (b) 5 (c) 6 (d) 4
34. 34.In a class of 32 children, 20 like cricket, 10 like football and 4 like both. How many like neither? (a) 4 (b) 2 (c) 6 (d) 10
35. 35.In a class of 23 children, 10 like dance, 13 like music and 5 like neither. How many like both? (a) 4 (b) 18 (c) 6 (d) 5
36. 36.In a class of 49 children, 28 like maths, 23 like science and 12 like both. How many like neither? (a) 12 (b) 22 (c) 11 (d) 10
37. 37.In a class of 51 children, 24 like cricket, 24 like football and 7 like both. How many like at least one of the two? (a) 51 (b) 41 (c) 34 (d) 48
38. 38.In a class of 56 children, 31 like mangoes, 27 like bananas and 9 like neither. How many like both? (a) 2 (b) 11 (c) 47 (d) 9
39. 39.In a class of 35 children, 20 like tea, 13 like coffee and 6 like neither. How many like both? (a) 6 (b) 29 (c) 5 (d) 4
40. 40.In a class of 41 children, 19 like dance, 25 like music and 4 like neither. How many like both? (a) 7 (b) 37 (c) 4 (d) 3

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