Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 719 · 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 38 children, 9 like maths, 26 like science and 6 like both. How many like only maths? (a) 12 (b) 9 (c) 3 (d) 20
2. 2.In a class of 37 children, 20 like cricket, 22 like football and 6 like both. How many like at least one of the two? (a) 37 (b) 30 (c) 36 (d) 42
3. 3.In a class of 36 children, 14 like maths, 18 like science and 4 like both. How many like only maths? (a) 4 (b) 14 (c) 18 (d) 10
4. 4.In a class of 18 children, 7 like tea, 6 like coffee and 3 like both. How many like at least one of the two? (a) 10 (b) 7 (c) 18 (d) 13
5. 5.In a class of 27 children, 14 like mangoes, 19 like bananas and 9 like both. How many like neither? (a) 4 (b) 9 (c) 3 (d) 12
6. 6.In a class of 37 children, 23 like cricket, 22 like football and 2 like neither. How many like both? (a) 35 (b) 2 (c) 8 (d) 10
7. 7.In a class of 51 children, 26 like maths, 28 like science and 9 like both. How many like at least one of the two? (a) 54 (b) 51 (c) 36 (d) 45
8. 8.In a class of 23 children, 15 like maths, 9 like science and 4 like both. How many like at least one of the two? (a) 16 (b) 24 (c) 20 (d) 23
9. 9.In a class of 35 children, 21 like cricket, 17 like football and 4 like both. How many like at least one of the two? (a) 34 (b) 35 (c) 30 (d) 38
10. 10.In a class of 32 children, 21 like mangoes, 13 like bananas and 5 like both. How many like neither? (a) 3 (b) 4 (c) 8 (d) 5
11. 11.In a class of 25 children, 8 like tea, 12 like coffee and 7 like neither. How many like both? (a) 3 (b) 7 (c) 2 (d) 18
12. 12.In a class of 39 children, 25 like mangoes, 22 like bananas and 11 like both. How many like neither? (a) 11 (b) 14 (c) 3 (d) 4
13. 13.In a class of 40 children, 14 like cricket, 21 like football and 4 like both. How many like neither? (a) 4 (b) 13 (c) 9 (d) 5
14. 14.In a class of 18 children, 10 like cricket, 9 like football and 4 like both. How many like neither? (a) 2 (b) 7 (c) 4 (d) 3
15. 15.In a class of 40 children, 19 like mangoes, 16 like bananas and 2 like both. How many like at least one of the two? (a) 31 (b) 35 (c) 33 (d) 40
16. 16.In a class of 22 children, 14 like cricket, 11 like football and 1 like neither. How many like both? (a) 21 (b) 4 (c) 1 (d) 3
17. 17.In a class of 34 children, 14 like tea, 21 like coffee and 4 like both. How many like neither? (a) 2 (b) 7 (c) 4 (d) 3
18. 18.In a class of 43 children, 17 like maths, 19 like science and 2 like both. How many like neither? (a) 11 (b) 2 (c) 7 (d) 9
19. 19.In a class of 19 children, 11 like dance, 13 like music and 6 like both. How many like neither? (a) 2 (b) 6 (c) 7 (d) 1
20. 20.In a class of 27 children, 9 like maths, 21 like science and 4 like both. How many like at least one of the two? (a) 30 (b) 22 (c) 27 (d) 26
21. 21.In a class of 25 children, 9 like tea, 20 like coffee and 5 like both. How many like at least one of the two? (a) 25 (b) 19 (c) 24 (d) 29
22. 22.In a class of 28 children, 13 like dance, 17 like music and 6 like neither. How many like both? (a) 2 (b) 6 (c) 8 (d) 22
23. 23.In a class of 20 children, 14 like maths, 14 like science and 10 like both. How many like at least one of the two? (a) 8 (b) 20 (c) 28 (d) 18
24. 24.In a class of 28 children, 14 like dance, 14 like music and 10 like both. How many like at least one of the two? (a) 28 (b) 19 (c) 18 (d) 8
25. 25.In a class of 41 children, 25 like dance, 18 like music and 5 like neither. How many like both? (a) 7 (b) 5 (c) 2 (d) 36
26. 26.In a class of 30 children, 13 like dance, 16 like music and 9 like both. How many like only dance? (a) 7 (b) 14 (c) 4 (d) 13
27. 27.In a class of 32 children, 23 like mangoes, 11 like bananas and 7 like both. How many like neither? (a) 12 (b) 7 (c) 6 (d) 5
28. 28.In a class of 34 children, 13 like cricket, 18 like football and 4 like both. How many like neither? (a) 11 (b) 4 (c) 7 (d) 3
29. 29.In a class of 38 children, 22 like dance, 16 like music and 6 like both. How many like only dance? (a) 22 (b) 10 (c) 16 (d) 6
30. 30.In a class of 28 children, 13 like dance, 20 like music and 7 like both. How many like only dance? (a) 13 (b) 6 (c) 8 (d) 7
31. 31.In a class of 36 children, 22 like maths, 18 like science and 7 like both. How many like only maths? (a) 11 (b) 18 (c) 22 (d) 15
32. 32.In a class of 29 children, 20 like tea, 13 like coffee and 8 like both. How many like at least one of the two? (a) 17 (b) 25 (c) 29 (d) 33
33. 33.In a class of 47 children, 24 like tea, 25 like coffee and 5 like neither. How many like both? (a) 7 (b) 5 (c) 42 (d) 2
34. 34.In a class of 30 children, 21 like dance, 7 like music and 3 like both. How many like only dance? (a) 23 (b) 4 (c) 21 (d) 18
35. 35.In a class of 23 children, 10 like dance, 9 like music and 5 like both. How many like at least one of the two? (a) 23 (b) 9 (c) 14 (d) 19
36. 36.In a class of 52 children, 29 like maths, 24 like science and 9 like both. How many like at least one of the two? (a) 44 (b) 35 (c) 52 (d) 53
37. 37.In a class of 44 children, 21 like cricket, 25 like football and 5 like both. How many like only cricket? (a) 20 (b) 16 (c) 21 (d) 19
38. 38.In a class of 28 children, 15 like cricket, 19 like football and 7 like both. How many like at least one of the two? (a) 20 (b) 34 (c) 27 (d) 28
39. 39.In a class of 42 children, 15 like mangoes, 22 like bananas and 4 like both. How many like at least one of the two? (a) 42 (b) 37 (c) 33 (d) 29
40. 40.In a class of 37 children, 27 like tea, 19 like coffee and 10 like both. How many like neither? (a) 10 (b) 11 (c) 2 (d) 1

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