Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 827 · 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 23 children, 17 like maths, 7 like science and 4 like both. How many like neither? (a) 2 (b) 4 (c) 7 (d) 3
2. 2.In a class of 36 children, 28 like tea, 16 like coffee and 10 like both. How many like only tea? (a) 6 (b) 28 (c) 18 (d) 20
3. 3.In a class of 32 children, 15 like mangoes, 18 like bananas and 9 like both. How many like neither? (a) 17 (b) 7 (c) 8 (d) 9
4. 4.In a class of 50 children, 26 like dance, 27 like music and 11 like both. How many like neither? (a) 9 (b) 19 (c) 8 (d) 11
5. 5.In a class of 37 children, 16 like tea, 15 like coffee and 2 like both. How many like only tea? (a) 16 (b) 14 (c) 13 (d) 22
6. 6.In a class of 28 children, 15 like tea, 8 like coffee and 2 like both. How many like neither? (a) 2 (b) 5 (c) 9 (d) 7
7. 7.In a class of 26 children, 18 like cricket, 8 like football and 5 like both. How many like at least one of the two? (a) 21 (b) 26 (c) 16 (d) 22
8. 8.In a class of 38 children, 11 like cricket, 21 like football and 2 like both. How many like only cricket? (a) 11 (b) 19 (c) 9 (d) 17
9. 9.In a class of 21 children, 9 like cricket, 16 like football and 5 like both. How many like at least one of the two? (a) 21 (b) 25 (c) 20 (d) 15
10. 10.In a class of 37 children, 16 like cricket, 23 like football and 1 like neither. How many like both? (a) 2 (b) 36 (c) 3 (d) 1
11. 11.In a class of 25 children, 15 like cricket, 18 like football and 10 like both. How many like only cricket? (a) 8 (b) 7 (c) 15 (d) 5
12. 12.In a class of 41 children, 15 like dance, 22 like music and 7 like neither. How many like both? (a) 7 (b) 3 (c) 34 (d) 4
13. 13.In a class of 35 children, 14 like maths, 21 like science and 8 like neither. How many like both? (a) 7 (b) 8 (c) 27 (d) 9
14. 14.In a class of 19 children, 12 like dance, 9 like music and 3 like neither. How many like both? (a) 16 (b) 3 (c) 5 (d) 2
15. 15.In a class of 30 children, 11 like tea, 22 like coffee and 4 like both. How many like neither? (a) 5 (b) 1 (c) 2 (d) 4
16. 16.In a class of 21 children, 11 like maths, 10 like science and 3 like both. How many like only maths? (a) 11 (b) 7 (c) 8 (d) 3
17. 17.In a class of 16 children, 7 like tea, 6 like coffee and 6 like neither. How many like both? (a) 10 (b) 3 (c) 4 (d) 6
18. 18.In a class of 19 children, 8 like dance, 6 like music and 8 like neither. How many like both? (a) 4 (b) 11 (c) 8 (d) 3
19. 19.In a class of 36 children, 14 like maths, 29 like science and 10 like both. How many like neither? (a) 4 (b) 13 (c) 3 (d) 10
20. 20.In a class of 34 children, 7 like mangoes, 21 like bananas and 2 like both. How many like at least one of the two? (a) 24 (b) 26 (c) 28 (d) 34
21. 21.In a class of 31 children, 10 like maths, 18 like science and 9 like neither. How many like both? (a) 7 (b) 6 (c) 22 (d) 9
22. 22.In a class of 23 children, 9 like tea, 12 like coffee and 5 like both. How many like only tea? (a) 11 (b) 7 (c) 4 (d) 9
23. 23.In a class of 25 children, 11 like cricket, 8 like football and 2 like both. How many like neither? (a) 10 (b) 2 (c) 6 (d) 8
24. 24.In a class of 28 children, 11 like maths, 15 like science and 5 like both. How many like only maths? (a) 10 (b) 11 (c) 13 (d) 6
25. 25.In a class of 27 children, 12 like maths, 10 like science and 2 like both. How many like at least one of the two? (a) 22 (b) 27 (c) 18 (d) 20
26. 26.In a class of 44 children, 24 like cricket, 20 like football and 4 like both. How many like at least one of the two? (a) 44 (b) 41 (c) 40 (d) 36
27. 27.In a class of 36 children, 11 like dance, 24 like music and 6 like both. How many like only dance? (a) 11 (b) 18 (c) 5 (d) 12
28. 28.In a class of 25 children, 16 like mangoes, 9 like bananas and 5 like neither. How many like both? (a) 5 (b) 20 (c) 4 (d) 6
29. 29.In a class of 41 children, 13 like cricket, 24 like football and 9 like neither. How many like both? (a) 32 (b) 9 (c) 6 (d) 5
30. 30.In a class of 27 children, 16 like mangoes, 14 like bananas and 5 like both. How many like at least one of the two? (a) 27 (b) 20 (c) 30 (d) 25
31. 31.In a class of 25 children, 17 like maths, 10 like science and 4 like both. How many like at least one of the two? (a) 27 (b) 23 (c) 19 (d) 25
32. 32.In a class of 38 children, 26 like maths, 13 like science and 7 like both. How many like neither? (a) 6 (b) 13 (c) 7 (d) 5
33. 33.In a class of 32 children, 23 like cricket, 12 like football and 4 like both. How many like neither? (a) 4 (b) 2 (c) 5 (d) 1
34. 34.In a class of 38 children, 24 like cricket, 17 like football and 6 like both. How many like neither? (a) 3 (b) 6 (c) 4 (d) 9
35. 35.In a class of 27 children, 12 like cricket, 13 like football and 7 like neither. How many like both? (a) 20 (b) 6 (c) 5 (d) 7
36. 36.In a class of 33 children, 18 like maths, 17 like science and 7 like both. How many like neither? (a) 5 (b) 12 (c) 7 (d) 6
37. 37.In a class of 33 children, 18 like cricket, 8 like football and 2 like both. How many like only cricket? (a) 6 (b) 16 (c) 25 (d) 18
38. 38.In a class of 36 children, 19 like maths, 20 like science and 7 like both. How many like neither? (a) 7 (b) 11 (c) 5 (d) 4
39. 39.In a class of 45 children, 30 like maths, 15 like science and 10 like neither. How many like both? (a) 10 (b) 35 (c) 11 (d) 9
40. 40.In a class of 26 children, 20 like cricket, 16 like football and 11 like both. How many like only cricket? (a) 9 (b) 20 (c) 5 (d) 10

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