Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 553 · 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, 13 like cricket, 19 like football and 8 like neither. How many like both? (a) 9 (b) 7 (c) 8 (d) 24
2. 2.In a class of 46 children, 16 like cricket, 27 like football and 7 like both. How many like neither? (a) 10 (b) 7 (c) 3 (d) 17
3. 3.In a class of 16 children, 9 like dance, 10 like music and 5 like both. How many like only dance? (a) 6 (b) 9 (c) 5 (d) 4
4. 4.In a class of 50 children, 22 like dance, 23 like music and 3 like both. How many like neither? (a) 8 (b) 11 (c) 3 (d) 5
5. 5.In a class of 39 children, 28 like tea, 20 like coffee and 2 like neither. How many like both? (a) 37 (b) 9 (c) 11 (d) 2
6. 6.In a class of 24 children, 12 like dance, 12 like music and 8 like neither. How many like both? (a) 9 (b) 7 (c) 16 (d) 8
7. 7.In a class of 36 children, 22 like cricket, 21 like football and 12 like both. How many like only cricket? (a) 9 (b) 15 (c) 10 (d) 22
8. 8.In a class of 38 children, 20 like dance, 18 like music and 7 like both. How many like at least one of the two? (a) 32 (b) 38 (c) 31 (d) 24
9. 9.In a class of 23 children, 12 like dance, 14 like music and 4 like both. How many like only dance? (a) 10 (b) 12 (c) 9 (d) 8
10. 10.In a class of 37 children, 24 like dance, 13 like music and 5 like both. How many like only dance? (a) 8 (b) 24 (c) 5 (d) 19
11. 11.In a class of 30 children, 16 like dance, 14 like music and 3 like both. How many like neither? (a) 3 (b) 6 (c) 4 (d) 0
12. 12.In a class of 26 children, 21 like mangoes, 5 like bananas and 2 like both. How many like at least one of the two? (a) 26 (b) 22 (c) 24 (d) 25
13. 13.In a class of 30 children, 15 like tea, 7 like coffee and 2 like both. How many like only tea? (a) 15 (b) 5 (c) 23 (d) 13
14. 14.In a class of 36 children, 22 like mangoes, 19 like bananas and 6 like neither. How many like both? (a) 30 (b) 5 (c) 6 (d) 11
15. 15.In a class of 37 children, 23 like maths, 18 like science and 7 like both. How many like at least one of the two? (a) 37 (b) 27 (c) 41 (d) 34
16. 16.In a class of 26 children, 15 like dance, 10 like music and 3 like neither. How many like both? (a) 3 (b) 23 (c) 1 (d) 2
17. 17.In a class of 36 children, 14 like mangoes, 25 like bananas and 6 like neither. How many like both? (a) 3 (b) 9 (c) 30 (d) 6
18. 18.In a class of 29 children, 13 like maths, 14 like science and 2 like both. How many like only maths? (a) 15 (b) 12 (c) 13 (d) 11
19. 19.In a class of 29 children, 7 like cricket, 18 like football and 6 like neither. How many like both? (a) 6 (b) 23 (c) 3 (d) 2
20. 20.In a class of 39 children, 27 like tea, 18 like coffee and 10 like both. How many like neither? (a) 14 (b) 10 (c) 4 (d) 5
21. 21.In a class of 30 children, 9 like maths, 21 like science and 2 like both. How many like neither? (a) 2 (b) 3 (c) 0 (d) 4
22. 22.In a class of 22 children, 15 like tea, 13 like coffee and 7 like both. How many like at least one of the two? (a) 22 (b) 21 (c) 28 (d) 14
23. 23.In a class of 18 children, 9 like mangoes, 9 like bananas and 4 like both. How many like at least one of the two? (a) 14 (b) 18 (c) 10 (d) 15
24. 24.In a class of 33 children, 16 like tea, 21 like coffee and 7 like both. How many like at least one of the two? (a) 23 (b) 37 (c) 30 (d) 33
25. 25.In a class of 27 children, 16 like dance, 14 like music and 8 like neither. How many like both? (a) 19 (b) 3 (c) 11 (d) 8
26. 26.In a class of 33 children, 14 like maths, 17 like science and 7 like both. How many like neither? (a) 16 (b) 9 (c) 7 (d) 2
27. 27.In a class of 33 children, 12 like tea, 22 like coffee and 3 like both. How many like at least one of the two? (a) 28 (b) 34 (c) 33 (d) 31
28. 28.In a class of 29 children, 16 like dance, 18 like music and 9 like both. How many like at least one of the two? (a) 16 (b) 34 (c) 25 (d) 29
29. 29.In a class of 37 children, 23 like cricket, 17 like football and 5 like both. How many like only cricket? (a) 18 (b) 12 (c) 23 (d) 20
30. 30.In a class of 28 children, 13 like maths, 14 like science and 2 like both. How many like at least one of the two? (a) 23 (b) 27 (c) 25 (d) 28
31. 31.In a class of 34 children, 17 like maths, 13 like science and 2 like both. How many like only maths? (a) 17 (b) 15 (c) 21 (d) 11
32. 32.In a class of 19 children, 9 like cricket, 13 like football and 4 like both. How many like neither? (a) 1 (b) 5 (c) 4 (d) 2
33. 33.In a class of 29 children, 14 like maths, 14 like science and 9 like neither. How many like both? (a) 7 (b) 8 (c) 9 (d) 20
34. 34.In a class of 35 children, 26 like dance, 17 like music and 10 like both. How many like neither? (a) 3 (b) 2 (c) 12 (d) 10
35. 35.In a class of 36 children, 7 like mangoes, 23 like bananas and 4 like both. How many like at least one of the two? (a) 26 (b) 22 (c) 30 (d) 36
36. 36.In a class of 23 children, 13 like maths, 11 like science and 2 like both. How many like at least one of the two? (a) 20 (b) 22 (c) 24 (d) 23
37. 37.In a class of 39 children, 26 like tea, 22 like coffee and 1 like neither. How many like both? (a) 1 (b) 9 (c) 38 (d) 10
38. 38.In a class of 26 children, 12 like cricket, 18 like football and 7 like both. How many like at least one of the two? (a) 30 (b) 16 (c) 23 (d) 26
39. 39.In a class of 31 children, 24 like mangoes, 12 like bananas and 9 like both. How many like only mangoes? (a) 15 (b) 3 (c) 24 (d) 19
40. 40.In a class of 33 children, 15 like tea, 13 like coffee and 4 like both. How many like only tea? (a) 15 (b) 11 (c) 9 (d) 20

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