Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 686 · 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 26 children, 11 like mangoes, 13 like bananas and 7 like both. How many like at least one of the two? (a) 17 (b) 24 (c) 10 (d) 26
2. 2.In a class of 49 children, 29 like dance, 29 like music and 10 like both. How many like neither? (a) 2 (b) 11 (c) 1 (d) 10
3. 3.In a class of 22 children, 15 like maths, 7 like science and 3 like both. How many like only maths? (a) 3 (b) 15 (c) 12 (d) 4
4. 4.In a class of 34 children, 12 like tea, 20 like coffee and 8 like both. How many like only tea? (a) 12 (b) 4 (c) 8 (d) 14
5. 5.In a class of 52 children, 29 like dance, 32 like music and 12 like both. How many like neither? (a) 12 (b) 3 (c) 4 (d) 15
6. 6.In a class of 39 children, 18 like cricket, 24 like football and 4 like neither. How many like both? (a) 7 (b) 4 (c) 3 (d) 35
7. 7.In a class of 33 children, 11 like dance, 16 like music and 3 like both. How many like only dance? (a) 17 (b) 11 (c) 13 (d) 8
8. 8.In a class of 42 children, 18 like dance, 24 like music and 9 like both. How many like only dance? (a) 15 (b) 18 (c) 9 (d) 10
9. 9.In a class of 45 children, 26 like maths, 27 like science and 9 like both. How many like only maths? (a) 18 (b) 9 (c) 26 (d) 17
10. 10.In a class of 26 children, 7 like dance, 18 like music and 2 like both. How many like only dance? (a) 8 (b) 7 (c) 16 (d) 5
11. 11.In a class of 16 children, 8 like mangoes, 11 like bananas and 4 like both. How many like neither? (a) 1 (b) 2 (c) 4 (d) 5
12. 12.In a class of 30 children, 12 like maths, 25 like science and 9 like both. How many like at least one of the two? (a) 28 (b) 37 (c) 30 (d) 19
13. 13.In a class of 29 children, 17 like maths, 14 like science and 1 like neither. How many like both? (a) 1 (b) 2 (c) 3 (d) 28
14. 14.In a class of 45 children, 19 like cricket, 23 like football and 9 like neither. How many like both? (a) 9 (b) 7 (c) 6 (d) 36
15. 15.In a class of 36 children, 14 like dance, 22 like music and 2 like neither. How many like both? (a) 2 (b) 1 (c) 3 (d) 34
16. 16.In a class of 42 children, 24 like cricket, 22 like football and 6 like neither. How many like both? (a) 4 (b) 10 (c) 6 (d) 36
17. 17.In a class of 46 children, 23 like cricket, 16 like football and 3 like both. How many like at least one of the two? (a) 46 (b) 33 (c) 39 (d) 36
18. 18.In a class of 47 children, 23 like tea, 17 like coffee and 3 like both. How many like at least one of the two? (a) 40 (b) 34 (c) 47 (d) 37
19. 19.In a class of 23 children, 14 like maths, 12 like science and 1 like neither. How many like both? (a) 1 (b) 3 (c) 4 (d) 22
20. 20.In a class of 25 children, 13 like mangoes, 14 like bananas and 9 like both. How many like only mangoes? (a) 11 (b) 4 (c) 5 (d) 13
21. 21.In a class of 45 children, 26 like maths, 24 like science and 9 like both. How many like neither? (a) 9 (b) 4 (c) 5 (d) 13
22. 22.In a class of 36 children, 20 like cricket, 17 like football and 4 like both. How many like neither? (a) 4 (b) 3 (c) 2 (d) 7
23. 23.In a class of 56 children, 27 like dance, 30 like music and 10 like neither. How many like both? (a) 10 (b) 46 (c) 11 (d) 1
24. 24.In a class of 29 children, 13 like mangoes, 19 like bananas and 5 like neither. How many like both? (a) 3 (b) 5 (c) 24 (d) 8
25. 25.In a class of 48 children, 28 like tea, 23 like coffee and 8 like neither. How many like both? (a) 40 (b) 11 (c) 8 (d) 3
26. 26.In a class of 43 children, 17 like mangoes, 21 like bananas and 3 like both. How many like at least one of the two? (a) 32 (b) 38 (c) 35 (d) 43
27. 27.In a class of 25 children, 17 like dance, 9 like music and 2 like both. How many like at least one of the two? (a) 25 (b) 24 (c) 26 (d) 22
28. 28.In a class of 39 children, 18 like dance, 22 like music and 3 like neither. How many like both? (a) 36 (b) 4 (c) 3 (d) 1
29. 29.In a class of 43 children, 20 like dance, 30 like music and 5 like neither. How many like both? (a) 12 (b) 38 (c) 5 (d) 7
30. 30.In a class of 21 children, 16 like maths, 8 like science and 5 like both. How many like neither? (a) 5 (b) 7 (c) 3 (d) 2
31. 31.In a class of 39 children, 16 like tea, 24 like coffee and 4 like both. How many like only tea? (a) 15 (b) 16 (c) 20 (d) 12
32. 32.In a class of 30 children, 12 like mangoes, 21 like bananas and 9 like both. How many like only mangoes? (a) 9 (b) 3 (c) 12 (d) 4
33. 33.In a class of 42 children, 24 like cricket, 25 like football and 10 like both. How many like neither? (a) 13 (b) 10 (c) 3 (d) 4
34. 34.In a class of 26 children, 15 like maths, 10 like science and 2 like both. How many like at least one of the two? (a) 25 (b) 26 (c) 21 (d) 23
35. 35.In a class of 36 children, 24 like maths, 12 like science and 9 like both. How many like only maths? (a) 9 (b) 24 (c) 15 (d) 3
36. 36.In a class of 47 children, 28 like dance, 19 like music and 8 like both. How many like at least one of the two? (a) 40 (b) 31 (c) 39 (d) 47
37. 37.In a class of 20 children, 9 like maths, 8 like science and 5 like neither. How many like both? (a) 3 (b) 5 (c) 15 (d) 2
38. 38.In a class of 37 children, 12 like mangoes, 24 like bananas and 7 like both. How many like neither? (a) 15 (b) 7 (c) 8 (d) 1
39. 39.In a class of 28 children, 10 like cricket, 20 like football and 3 like both. How many like only cricket? (a) 7 (b) 10 (c) 17 (d) 8
40. 40.In a class of 34 children, 13 like tea, 18 like coffee and 6 like both. How many like at least one of the two? (a) 19 (b) 25 (c) 31 (d) 34

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