Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 380 · 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 21 children, 12 like tea, 11 like coffee and 7 like both. How many like at least one of the two? (a) 21 (b) 9 (c) 23 (d) 16
2. 2.In a class of 17 children, 8 like maths, 12 like science and 4 like both. How many like neither? (a) 4 (b) 5 (c) 2 (d) 1
3. 3.In a class of 50 children, 29 like maths, 27 like science and 3 like neither. How many like both? (a) 6 (b) 3 (c) 9 (d) 47
4. 4.In a class of 40 children, 28 like maths, 16 like science and 9 like both. How many like at least one of the two? (a) 40 (b) 35 (c) 44 (d) 26
5. 5.In a class of 35 children, 19 like cricket, 18 like football and 9 like both. How many like only cricket? (a) 17 (b) 19 (c) 10 (d) 9
6. 6.In a class of 27 children, 8 like mangoes, 20 like bananas and 3 like both. How many like neither? (a) 5 (b) 1 (c) 3 (d) 2
7. 7.In a class of 35 children, 24 like mangoes, 20 like bananas and 3 like neither. How many like both? (a) 32 (b) 9 (c) 12 (d) 3
8. 8.In a class of 31 children, 25 like mangoes, 9 like bananas and 2 like neither. How many like both? (a) 3 (b) 2 (c) 29 (d) 5
9. 9.In a class of 32 children, 15 like dance, 18 like music and 11 like both. How many like only dance? (a) 14 (b) 4 (c) 15 (d) 7
10. 10.In a class of 51 children, 30 like maths, 31 like science and 2 like neither. How many like both? (a) 2 (b) 49 (c) 10 (d) 12
11. 11.In a class of 36 children, 16 like cricket, 22 like football and 5 like both. How many like at least one of the two? (a) 36 (b) 33 (c) 28 (d) 38
12. 12.In a class of 38 children, 17 like maths, 27 like science and 10 like both. How many like only maths? (a) 7 (b) 17 (c) 10 (d) 11
13. 13.In a class of 27 children, 11 like mangoes, 14 like bananas and 3 like both. How many like at least one of the two? (a) 27 (b) 25 (c) 19 (d) 22
14. 14.In a class of 38 children, 26 like cricket, 9 like football and 6 like both. How many like at least one of the two? (a) 35 (b) 29 (c) 38 (d) 23
15. 15.In a class of 38 children, 18 like maths, 24 like science and 9 like both. How many like at least one of the two? (a) 38 (b) 24 (c) 42 (d) 33
16. 16.In a class of 36 children, 16 like mangoes, 19 like bananas and 3 like neither. How many like both? (a) 1 (b) 33 (c) 2 (d) 3
17. 17.In a class of 24 children, 12 like mangoes, 6 like bananas and 2 like both. How many like at least one of the two? (a) 24 (b) 14 (c) 18 (d) 16
18. 18.In a class of 54 children, 25 like maths, 31 like science and 11 like both. How many like at least one of the two? (a) 56 (b) 45 (c) 34 (d) 54
19. 19.In a class of 24 children, 17 like maths, 15 like science and 10 like both. How many like only maths? (a) 7 (b) 5 (c) 9 (d) 17
20. 20.In a class of 19 children, 9 like tea, 7 like coffee and 3 like both. How many like neither? (a) 7 (b) 9 (c) 6 (d) 3
21. 21.In a class of 46 children, 20 like maths, 29 like science and 12 like both. How many like only maths? (a) 8 (b) 12 (c) 20 (d) 17
22. 22.In a class of 18 children, 8 like mangoes, 11 like bananas and 3 like both. How many like neither? (a) 5 (b) 1 (c) 2 (d) 3
23. 23.In a class of 24 children, 18 like mangoes, 8 like bananas and 3 like both. How many like at least one of the two? (a) 23 (b) 26 (c) 20 (d) 24
24. 24.In a class of 32 children, 13 like cricket, 18 like football and 8 like both. How many like neither? (a) 17 (b) 8 (c) 1 (d) 9
25. 25.In a class of 35 children, 22 like dance, 22 like music and 12 like both. How many like only dance? (a) 22 (b) 13 (c) 12 (d) 10
26. 26.In a class of 24 children, 12 like maths, 7 like science and 8 like neither. How many like both? (a) 8 (b) 16 (c) 3 (d) 4
27. 27.In a class of 27 children, 19 like cricket, 8 like football and 3 like both. How many like neither? (a) 6 (b) 4 (c) 3 (d) 0
28. 28.In a class of 30 children, 19 like mangoes, 9 like bananas and 2 like both. How many like neither? (a) 2 (b) 5 (c) 6 (d) 4
29. 29.In a class of 28 children, 13 like dance, 20 like music and 1 like neither. How many like both? (a) 27 (b) 1 (c) 5 (d) 6
30. 30.In a class of 43 children, 22 like maths, 20 like science and 3 like both. How many like at least one of the two? (a) 39 (b) 43 (c) 36 (d) 42
31. 31.In a class of 24 children, 18 like dance, 9 like music and 3 like neither. How many like both? (a) 3 (b) 7 (c) 21 (d) 6
32. 32.In a class of 39 children, 18 like tea, 30 like coffee and 12 like both. How many like neither? (a) 4 (b) 15 (c) 12 (d) 3
33. 33.In a class of 44 children, 26 like dance, 19 like music and 11 like both. How many like only dance? (a) 15 (b) 8 (c) 26 (d) 25
34. 34.In a class of 44 children, 25 like dance, 23 like music and 11 like both. How many like at least one of the two? (a) 44 (b) 48 (c) 37 (d) 26
35. 35.In a class of 38 children, 28 like dance, 19 like music and 11 like both. How many like at least one of the two? (a) 25 (b) 38 (c) 36 (d) 47
36. 36.In a class of 33 children, 18 like tea, 18 like coffee and 4 like neither. How many like both? (a) 4 (b) 29 (c) 3 (d) 7
37. 37.In a class of 39 children, 12 like dance, 22 like music and 3 like both. How many like at least one of the two? (a) 31 (b) 34 (c) 39 (d) 28
38. 38.In a class of 44 children, 26 like cricket, 25 like football and 11 like both. How many like only cricket? (a) 14 (b) 26 (c) 19 (d) 15
39. 39.In a class of 33 children, 26 like tea, 17 like coffee and 12 like both. How many like at least one of the two? (a) 19 (b) 31 (c) 43 (d) 33
40. 40.In a class of 49 children, 29 like mangoes, 28 like bananas and 12 like both. How many like at least one of the two? (a) 33 (b) 57 (c) 45 (d) 49

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