Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 880 · 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 37 children, 12 like dance, 25 like music and 9 like both. How many like at least one of the two? (a) 28 (b) 19 (c) 29 (d) 37
2. 2.In a class of 31 children, 24 like mangoes, 10 like bananas and 3 like neither. How many like both? (a) 6 (b) 3 (c) 7 (d) 28
3. 3.In a class of 44 children, 16 like cricket, 26 like football and 7 like both. How many like at least one of the two? (a) 28 (b) 44 (c) 35 (d) 42
4. 4.In a class of 31 children, 12 like dance, 19 like music and 2 like both. How many like neither? (a) 4 (b) 2 (c) 0 (d) 3
5. 5.In a class of 48 children, 19 like cricket, 22 like football and 9 like neither. How many like both? (a) 9 (b) 39 (c) 3 (d) 2
6. 6.In a class of 21 children, 8 like maths, 14 like science and 2 like neither. How many like both? (a) 3 (b) 19 (c) 1 (d) 2
7. 7.In a class of 39 children, 26 like maths, 19 like science and 9 like both. How many like only maths? (a) 10 (b) 20 (c) 17 (d) 26
8. 8.In a class of 38 children, 18 like tea, 16 like coffee and 5 like both. How many like only tea? (a) 11 (b) 13 (c) 22 (d) 18
9. 9.In a class of 32 children, 16 like tea, 21 like coffee and 6 like both. How many like only tea? (a) 16 (b) 10 (c) 11 (d) 15
10. 10.In a class of 44 children, 24 like dance, 22 like music and 7 like both. How many like only dance? (a) 17 (b) 24 (c) 22 (d) 15
11. 11.In a class of 28 children, 17 like maths, 15 like science and 11 like both. How many like neither? (a) 8 (b) 11 (c) 7 (d) 18
12. 12.In a class of 43 children, 17 like cricket, 24 like football and 7 like both. How many like neither? (a) 2 (b) 9 (c) 7 (d) 16
13. 13.In a class of 45 children, 23 like mangoes, 25 like bananas and 2 like neither. How many like both? (a) 2 (b) 3 (c) 5 (d) 43
14. 14.In a class of 36 children, 14 like maths, 21 like science and 2 like both. How many like only maths? (a) 19 (b) 12 (c) 14 (d) 15
15. 15.In a class of 28 children, 20 like mangoes, 19 like bananas and 1 like neither. How many like both? (a) 27 (b) 12 (c) 11 (d) 1
16. 16.In a class of 21 children, 8 like maths, 15 like science and 4 like both. How many like at least one of the two? (a) 23 (b) 19 (c) 15 (d) 21
17. 17.In a class of 31 children, 9 like tea, 22 like coffee and 4 like both. How many like neither? (a) 4 (b) 8 (c) 5 (d) 0
18. 18.In a class of 48 children, 30 like maths, 21 like science and 7 like neither. How many like both? (a) 7 (b) 41 (c) 10 (d) 3
19. 19.In a class of 32 children, 15 like cricket, 27 like football and 1 like neither. How many like both? (a) 11 (b) 10 (c) 1 (d) 31
20. 20.In a class of 26 children, 16 like tea, 11 like coffee and 3 like neither. How many like both? (a) 3 (b) 4 (c) 1 (d) 23
21. 21.In a class of 25 children, 21 like maths, 8 like science and 5 like both. How many like only maths? (a) 17 (b) 21 (c) 3 (d) 16
22. 22.In a class of 31 children, 19 like dance, 17 like music and 7 like both. How many like only dance? (a) 10 (b) 14 (c) 19 (d) 12
23. 23.In a class of 28 children, 17 like cricket, 8 like football and 7 like neither. How many like both? (a) 21 (b) 7 (c) 5 (d) 4
24. 24.In a class of 43 children, 21 like cricket, 21 like football and 2 like both. How many like neither? (a) 3 (b) 2 (c) 1 (d) 5
25. 25.In a class of 46 children, 21 like dance, 23 like music and 6 like both. How many like only dance? (a) 23 (b) 17 (c) 15 (d) 21
26. 26.In a class of 51 children, 25 like dance, 26 like music and 7 like both. How many like only dance? (a) 18 (b) 7 (c) 19 (d) 25
27. 27.In a class of 48 children, 18 like dance, 23 like music and 3 like both. How many like only dance? (a) 15 (b) 25 (c) 20 (d) 18
28. 28.In a class of 26 children, 13 like dance, 6 like music and 3 like both. How many like at least one of the two? (a) 13 (b) 26 (c) 19 (d) 16
29. 29.In a class of 36 children, 21 like cricket, 11 like football and 4 like both. How many like at least one of the two? (a) 36 (b) 32 (c) 24 (d) 28
30. 30.In a class of 45 children, 17 like mangoes, 24 like bananas and 4 like both. How many like only mangoes? (a) 13 (b) 20 (c) 21 (d) 17
31. 31.In a class of 36 children, 22 like maths, 7 like science and 3 like both. How many like neither? (a) 10 (b) 7 (c) 3 (d) 13
32. 32.In a class of 28 children, 15 like dance, 18 like music and 12 like both. How many like at least one of the two? (a) 28 (b) 9 (c) 33 (d) 21
33. 33.In a class of 21 children, 6 like dance, 13 like music and 3 like both. How many like only dance? (a) 6 (b) 10 (c) 8 (d) 3
34. 34.In a class of 31 children, 15 like dance, 13 like music and 6 like both. How many like at least one of the two? (a) 28 (b) 22 (c) 31 (d) 16
35. 35.In a class of 33 children, 13 like tea, 19 like coffee and 6 like neither. How many like both? (a) 5 (b) 6 (c) 4 (d) 27
36. 36.In a class of 52 children, 29 like tea, 25 like coffee and 10 like both. How many like neither? (a) 9 (b) 8 (c) 10 (d) 18
37. 37.In a class of 46 children, 19 like maths, 20 like science and 2 like both. How many like only maths? (a) 17 (b) 26 (c) 18 (d) 19
38. 38.In a class of 52 children, 26 like mangoes, 28 like bananas and 12 like both. How many like only mangoes? (a) 26 (b) 24 (c) 16 (d) 14
39. 39.In a class of 34 children, 12 like dance, 23 like music and 6 like both. How many like at least one of the two? (a) 35 (b) 34 (c) 29 (d) 23
40. 40.In a class of 24 children, 12 like mangoes, 15 like bananas and 9 like both. How many like at least one of the two? (a) 24 (b) 27 (c) 18 (d) 9

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