Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 93 · 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 36 children, 21 like maths, 12 like science and 10 like neither. How many like both? (a) 8 (b) 26 (c) 7 (d) 10
2. 2.In a class of 33 children, 26 like dance, 16 like music and 12 like both. How many like at least one of the two? (a) 42 (b) 18 (c) 30 (d) 33
3. 3.In a class of 34 children, 25 like tea, 14 like coffee and 10 like both. How many like only tea? (a) 4 (b) 20 (c) 25 (d) 15
4. 4.In a class of 29 children, 9 like cricket, 15 like football and 2 like both. How many like only cricket? (a) 7 (b) 13 (c) 14 (d) 9
5. 5.In a class of 29 children, 23 like tea, 10 like coffee and 7 like both. How many like only tea? (a) 3 (b) 19 (c) 16 (d) 23
6. 6.In a class of 36 children, 19 like tea, 21 like coffee and 10 like both. How many like only tea? (a) 19 (b) 11 (c) 15 (d) 9
7. 7.In a class of 34 children, 7 like tea, 22 like coffee and 2 like both. How many like neither? (a) 9 (b) 7 (c) 5 (d) 2
8. 8.In a class of 43 children, 28 like maths, 24 like science and 1 like neither. How many like both? (a) 1 (b) 42 (c) 10 (d) 9
9. 9.In a class of 44 children, 17 like mangoes, 24 like bananas and 4 like both. How many like at least one of the two? (a) 44 (b) 33 (c) 37 (d) 41
10. 10.In a class of 37 children, 12 like mangoes, 22 like bananas and 7 like both. How many like neither? (a) 17 (b) 3 (c) 10 (d) 7
11. 11.In a class of 37 children, 22 like mangoes, 14 like bananas and 7 like both. How many like neither? (a) 7 (b) 8 (c) 1 (d) 15
12. 12.In a class of 38 children, 24 like cricket, 17 like football and 12 like both. How many like only cricket? (a) 12 (b) 5 (c) 24 (d) 21
13. 13.In a class of 43 children, 25 like maths, 27 like science and 2 like neither. How many like both? (a) 11 (b) 9 (c) 41 (d) 2
14. 14.In a class of 34 children, 23 like dance, 18 like music and 10 like both. How many like neither? (a) 13 (b) 4 (c) 3 (d) 10
15. 15.In a class of 31 children, 25 like dance, 10 like music and 6 like both. How many like at least one of the two? (a) 31 (b) 29 (c) 23 (d) 35
16. 16.In a class of 25 children, 10 like tea, 10 like coffee and 5 like both. How many like neither? (a) 5 (b) 11 (c) 15 (d) 10
17. 17.In a class of 26 children, 21 like cricket, 11 like football and 2 like neither. How many like both? (a) 8 (b) 6 (c) 24 (d) 2
18. 18.In a class of 37 children, 20 like cricket, 13 like football and 9 like neither. How many like both? (a) 28 (b) 6 (c) 9 (d) 5
19. 19.In a class of 18 children, 7 like maths, 9 like science and 4 like neither. How many like both? (a) 14 (b) 3 (c) 2 (d) 4
20. 20.In a class of 24 children, 5 like dance, 13 like music and 2 like both. How many like only dance? (a) 5 (b) 3 (c) 11 (d) 2
21. 21.In a class of 22 children, 6 like dance, 18 like music and 3 like both. How many like at least one of the two? (a) 24 (b) 22 (c) 18 (d) 21
22. 22.In a class of 19 children, 10 like maths, 13 like science and 7 like both. How many like at least one of the two? (a) 9 (b) 19 (c) 23 (d) 16
23. 23.In a class of 34 children, 14 like mangoes, 28 like bananas and 10 like both. How many like only mangoes? (a) 14 (b) 6 (c) 18 (d) 4
24. 24.In a class of 27 children, 16 like tea, 18 like coffee and 11 like both. How many like neither? (a) 11 (b) 4 (c) 15 (d) 5
25. 25.In a class of 36 children, 24 like dance, 16 like music and 5 like both. How many like at least one of the two? (a) 35 (b) 30 (c) 40 (d) 36
26. 26.In a class of 32 children, 16 like dance, 16 like music and 5 like both. How many like only dance? (a) 5 (b) 16 (c) 11 (d) 12
27. 27.In a class of 38 children, 27 like tea, 17 like coffee and 9 like both. How many like only tea? (a) 27 (b) 8 (c) 18 (d) 21
28. 28.In a class of 31 children, 16 like cricket, 17 like football and 10 like both. How many like only cricket? (a) 7 (b) 14 (c) 6 (d) 16
29. 29.In a class of 35 children, 20 like mangoes, 24 like bananas and 1 like neither. How many like both? (a) 34 (b) 10 (c) 9 (d) 1
30. 30.In a class of 36 children, 15 like tea, 25 like coffee and 9 like both. How many like at least one of the two? (a) 22 (b) 36 (c) 31 (d) 40
31. 31.In a class of 37 children, 23 like mangoes, 23 like bananas and 10 like both. How many like only mangoes? (a) 10 (b) 23 (c) 14 (d) 13
32. 32.In a class of 34 children, 18 like tea, 25 like coffee and 10 like both. How many like at least one of the two? (a) 34 (b) 33 (c) 43 (d) 23
33. 33.In a class of 24 children, 19 like dance, 15 like music and 12 like both. How many like neither? (a) 14 (b) 2 (c) 3 (d) 12
34. 34.In a class of 16 children, 11 like maths, 6 like science and 2 like neither. How many like both? (a) 14 (b) 3 (c) 1 (d) 2
35. 35.In a class of 21 children, 12 like tea, 15 like coffee and 7 like both. How many like neither? (a) 1 (b) 8 (c) 2 (d) 7
36. 36.In a class of 28 children, 23 like maths, 13 like science and 2 like neither. How many like both? (a) 2 (b) 8 (c) 26 (d) 10
37. 37.In a class of 44 children, 25 like maths, 28 like science and 2 like neither. How many like both? (a) 2 (b) 42 (c) 9 (d) 11
38. 38.In a class of 51 children, 23 like dance, 25 like music and 7 like both. How many like only dance? (a) 16 (b) 26 (c) 23 (d) 18
39. 39.In a class of 26 children, 5 like dance, 19 like music and 2 like both. How many like neither? (a) 6 (b) 2 (c) 4 (d) 5
40. 40.In a class of 31 children, 17 like maths, 20 like science and 12 like both. How many like only maths? (a) 11 (b) 5 (c) 17 (d) 8

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