Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 478 · 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 49 children, 27 like maths, 20 like science and 7 like both. How many like only maths? (a) 20 (b) 13 (c) 29 (d) 27
2. 2.In a class of 35 children, 22 like dance, 15 like music and 7 like both. How many like at least one of the two? (a) 37 (b) 30 (c) 35 (d) 23
3. 3.In a class of 38 children, 16 like maths, 18 like science and 6 like both. How many like neither? (a) 10 (b) 4 (c) 16 (d) 6
4. 4.In a class of 32 children, 18 like maths, 17 like science and 11 like both. How many like neither? (a) 11 (b) 8 (c) 9 (d) 19
5. 5.In a class of 21 children, 11 like mangoes, 15 like bananas and 2 like neither. How many like both? (a) 5 (b) 19 (c) 2 (d) 7
6. 6.In a class of 27 children, 11 like mangoes, 14 like bananas and 4 like both. How many like only mangoes? (a) 10 (b) 11 (c) 13 (d) 7
7. 7.In a class of 31 children, 17 like cricket, 17 like football and 9 like neither. How many like both? (a) 3 (b) 22 (c) 9 (d) 12
8. 8.In a class of 32 children, 19 like tea, 20 like coffee and 9 like both. How many like at least one of the two? (a) 21 (b) 32 (c) 30 (d) 39
9. 9.In a class of 48 children, 21 like cricket, 23 like football and 3 like both. How many like neither? (a) 3 (b) 7 (c) 4 (d) 10
10. 10.In a class of 29 children, 8 like cricket, 19 like football and 4 like both. How many like at least one of the two? (a) 29 (b) 27 (c) 23 (d) 19
11. 11.In a class of 18 children, 7 like maths, 14 like science and 4 like both. How many like neither? (a) 4 (b) 5 (c) 1 (d) 2
12. 12.In a class of 39 children, 19 like maths, 28 like science and 12 like both. How many like only maths? (a) 16 (b) 7 (c) 11 (d) 19
13. 13.In a class of 45 children, 26 like maths, 19 like science and 7 like both. How many like only maths? (a) 12 (b) 7 (c) 19 (d) 26
14. 14.In a class of 27 children, 5 like cricket, 16 like football and 2 like both. How many like at least one of the two? (a) 17 (b) 21 (c) 27 (d) 19
15. 15.In a class of 40 children, 19 like tea, 21 like coffee and 6 like neither. How many like both? (a) 34 (b) 7 (c) 5 (d) 6
16. 16.In a class of 28 children, 12 like maths, 11 like science and 9 like neither. How many like both? (a) 4 (b) 5 (c) 19 (d) 9
17. 17.In a class of 17 children, 10 like dance, 10 like music and 4 like both. How many like neither? (a) 2 (b) 5 (c) 4 (d) 1
18. 18.In a class of 48 children, 26 like maths, 21 like science and 9 like neither. How many like both? (a) 7 (b) 8 (c) 39 (d) 9
19. 19.In a class of 28 children, 11 like maths, 15 like science and 8 like both. How many like only maths? (a) 3 (b) 11 (c) 13 (d) 7
20. 20.In a class of 42 children, 22 like maths, 18 like science and 3 like both. How many like at least one of the two? (a) 42 (b) 34 (c) 40 (d) 37
21. 21.In a class of 19 children, 8 like dance, 7 like music and 4 like both. How many like only dance? (a) 8 (b) 4 (c) 12 (d) 3
22. 22.In a class of 30 children, 11 like cricket, 18 like football and 2 like both. How many like neither? (a) 5 (b) 2 (c) 1 (d) 3
23. 23.In a class of 40 children, 25 like mangoes, 15 like bananas and 9 like neither. How many like both? (a) 31 (b) 8 (c) 9 (d) 10
24. 24.In a class of 39 children, 26 like maths, 9 like science and 6 like both. How many like neither? (a) 10 (b) 16 (c) 4 (d) 6
25. 25.In a class of 35 children, 14 like dance, 22 like music and 6 like both. How many like at least one of the two? (a) 30 (b) 35 (c) 24 (d) 36
26. 26.In a class of 26 children, 20 like dance, 9 like music and 4 like both. How many like neither? (a) 4 (b) 1 (c) 2 (d) 5
27. 27.In a class of 42 children, 21 like maths, 22 like science and 6 like neither. How many like both? (a) 1 (b) 6 (c) 36 (d) 7
28. 28.In a class of 25 children, 11 like dance, 16 like music and 6 like both. How many like only dance? (a) 5 (b) 11 (c) 10 (d) 9
29. 29.In a class of 47 children, 22 like maths, 26 like science and 8 like both. How many like only maths? (a) 18 (b) 14 (c) 21 (d) 22
30. 30.In a class of 40 children, 24 like dance, 21 like music and 6 like both. How many like neither? (a) 6 (b) 2 (c) 1 (d) 7
31. 31.In a class of 46 children, 26 like tea, 26 like coffee and 10 like both. How many like only tea? (a) 20 (b) 26 (c) 16 (d) 10
32. 32.In a class of 19 children, 9 like mangoes, 9 like bananas and 3 like both. How many like at least one of the two? (a) 15 (b) 19 (c) 12 (d) 18
33. 33.In a class of 25 children, 20 like cricket, 9 like football and 2 like neither. How many like both? (a) 23 (b) 2 (c) 4 (d) 6
34. 34.In a class of 28 children, 18 like mangoes, 11 like bananas and 2 like both. How many like only mangoes? (a) 18 (b) 9 (c) 16 (d) 17
35. 35.In a class of 28 children, 7 like dance, 13 like music and 2 like both. How many like only dance? (a) 15 (b) 7 (c) 11 (d) 5
36. 36.In a class of 31 children, 11 like tea, 22 like coffee and 3 like both. How many like neither? (a) 3 (b) 1 (c) 2 (d) 4
37. 37.In a class of 30 children, 8 like dance, 20 like music and 4 like both. How many like only dance? (a) 10 (b) 4 (c) 8 (d) 16
38. 38.In a class of 33 children, 12 like mangoes, 17 like bananas and 5 like both. How many like at least one of the two? (a) 19 (b) 33 (c) 29 (d) 24
39. 39.In a class of 47 children, 25 like tea, 28 like coffee and 9 like both. How many like at least one of the two? (a) 53 (b) 44 (c) 47 (d) 35
40. 40.In a class of 25 children, 17 like cricket, 10 like football and 3 like both. How many like only cricket? (a) 15 (b) 17 (c) 14 (d) 7

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