Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 68 · 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 24 children, 20 like tea, 12 like coffee and 9 like both. How many like at least one of the two? (a) 24 (b) 32 (c) 14 (d) 23
2. 2.In a class of 37 children, 16 like maths, 25 like science and 9 like both. How many like only maths? (a) 9 (b) 16 (c) 7 (d) 12
3. 3.In a class of 26 children, 11 like cricket, 14 like football and 2 like both. How many like neither? (a) 5 (b) 2 (c) 3 (d) 1
4. 4.In a class of 44 children, 28 like dance, 23 like music and 8 like both. How many like at least one of the two? (a) 43 (b) 44 (c) 51 (d) 35
5. 5.In a class of 29 children, 7 like dance, 24 like music and 4 like both. How many like at least one of the two? (a) 23 (b) 31 (c) 27 (d) 29
6. 6.In a class of 34 children, 14 like cricket, 22 like football and 7 like both. How many like only cricket? (a) 7 (b) 15 (c) 14 (d) 12
7. 7.In a class of 32 children, 18 like maths, 21 like science and 8 like both. How many like at least one of the two? (a) 39 (b) 23 (c) 31 (d) 32
8. 8.In a class of 41 children, 23 like cricket, 24 like football and 10 like both. How many like neither? (a) 4 (b) 10 (c) 5 (d) 14
9. 9.In a class of 21 children, 10 like maths, 13 like science and 4 like both. How many like neither? (a) 3 (b) 6 (c) 2 (d) 4
10. 10.In a class of 25 children, 12 like cricket, 11 like football and 7 like neither. How many like both? (a) 6 (b) 5 (c) 7 (d) 18
11. 11.In a class of 13 children, 6 like mangoes, 6 like bananas and 3 like neither. How many like both? (a) 3 (b) 1 (c) 10 (d) 2
12. 12.In a class of 36 children, 17 like tea, 19 like coffee and 2 like both. How many like at least one of the two? (a) 32 (b) 36 (c) 34 (d) 35
13. 13.In a class of 17 children, 7 like cricket, 6 like football and 7 like neither. How many like both? (a) 10 (b) 4 (c) 3 (d) 7
14. 14.In a class of 50 children, 26 like tea, 32 like coffee and 12 like both. How many like neither? (a) 5 (b) 12 (c) 4 (d) 16
15. 15.In a class of 40 children, 23 like cricket, 12 like football and 4 like both. How many like neither? (a) 13 (b) 5 (c) 4 (d) 9
16. 16.In a class of 34 children, 15 like mangoes, 12 like bananas and 3 like both. How many like neither? (a) 7 (b) 10 (c) 3 (d) 13
17. 17.In a class of 31 children, 10 like maths, 20 like science and 3 like both. How many like neither? (a) 3 (b) 1 (c) 7 (d) 4
18. 18.In a class of 18 children, 8 like mangoes, 8 like bananas and 4 like both. How many like only mangoes? (a) 5 (b) 10 (c) 8 (d) 4
19. 19.In a class of 35 children, 26 like maths, 16 like science and 8 like both. How many like at least one of the two? (a) 35 (b) 34 (c) 26 (d) 42
20. 20.In a class of 34 children, 11 like tea, 24 like coffee and 3 like neither. How many like both? (a) 1 (b) 3 (c) 4 (d) 31
21. 21.In a class of 29 children, 16 like maths, 17 like science and 6 like both. How many like at least one of the two? (a) 29 (b) 21 (c) 27 (d) 33
22. 22.In a class of 26 children, 15 like cricket, 18 like football and 9 like both. How many like neither? (a) 11 (b) 3 (c) 9 (d) 2
23. 23.In a class of 28 children, 13 like cricket, 23 like football and 1 like neither. How many like both? (a) 27 (b) 9 (c) 8 (d) 1
24. 24.In a class of 27 children, 14 like maths, 16 like science and 9 like both. How many like at least one of the two? (a) 27 (b) 12 (c) 21 (d) 30
25. 25.In a class of 44 children, 16 like mangoes, 27 like bananas and 9 like both. How many like at least one of the two? (a) 43 (b) 34 (c) 25 (d) 44
26. 26.In a class of 33 children, 16 like dance, 22 like music and 7 like both. How many like at least one of the two? (a) 31 (b) 24 (c) 38 (d) 33
27. 27.In a class of 29 children, 16 like cricket, 12 like football and 2 like both. How many like only cricket? (a) 17 (b) 16 (c) 10 (d) 14
28. 28.In a class of 42 children, 19 like dance, 26 like music and 9 like both. How many like neither? (a) 7 (b) 9 (c) 15 (d) 6
29. 29.In a class of 39 children, 22 like dance, 21 like music and 8 like both. How many like only dance? (a) 14 (b) 22 (c) 13 (d) 18
30. 30.In a class of 31 children, 17 like dance, 14 like music and 4 like neither. How many like both? (a) 27 (b) 3 (c) 5 (d) 4
31. 31.In a class of 27 children, 9 like dance, 13 like music and 4 like both. How many like only dance? (a) 4 (b) 14 (c) 5 (d) 9
32. 32.In a class of 37 children, 21 like tea, 11 like coffee and 5 like both. How many like at least one of the two? (a) 32 (b) 27 (c) 37 (d) 22
33. 33.In a class of 26 children, 6 like mangoes, 14 like bananas and 2 like both. How many like neither? (a) 10 (b) 8 (c) 2 (d) 6
34. 34.In a class of 30 children, 21 like mangoes, 10 like bananas and 4 like neither. How many like both? (a) 5 (b) 1 (c) 4 (d) 26
35. 35.In a class of 35 children, 18 like cricket, 18 like football and 9 like both. How many like only cricket? (a) 18 (b) 9 (c) 10 (d) 17
36. 36.In a class of 51 children, 23 like maths, 25 like science and 5 like both. How many like at least one of the two? (a) 43 (b) 51 (c) 38 (d) 48
37. 37.In a class of 37 children, 20 like tea, 15 like coffee and 4 like neither. How many like both? (a) 33 (b) 3 (c) 4 (d) 2
38. 38.In a class of 30 children, 24 like dance, 11 like music and 6 like both. How many like neither? (a) 1 (b) 7 (c) 2 (d) 6
39. 39.In a class of 17 children, 12 like mangoes, 9 like bananas and 5 like both. How many like only mangoes? (a) 12 (b) 8 (c) 7 (d) 4
40. 40.In a class of 24 children, 17 like cricket, 10 like football and 4 like both. How many like at least one of the two? (a) 24 (b) 27 (c) 23 (d) 19

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