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Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 722 · 40 questions
TalentJR

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).

NameDateTime takenScore ___ / 40
  1. 1.In a class of 31 children, 18 like maths, 12 like science and 5 like both. How many like only maths? (a) 19 (b) 18 (c) 7 (d) 13
  2. 2.In a class of 41 children, 15 like maths, 21 like science and 4 like both. How many like only maths? (a) 20 (b) 17 (c) 11 (d) 15
  3. 3.In a class of 52 children, 31 like mangoes, 30 like bananas and 12 like both. How many like at least one of the two? (a) 37 (b) 49 (c) 61 (d) 52
  4. 4.In a class of 37 children, 21 like cricket, 20 like football and 10 like both. How many like at least one of the two? (a) 31 (b) 37 (c) 21 (d) 41
  5. 5.In a class of 38 children, 19 like mangoes, 16 like bananas and 4 like both. How many like neither? (a) 3 (b) 11 (c) 7 (d) 4
  6. 6.In a class of 45 children, 15 like maths, 31 like science and 11 like both. How many like neither? (a) 10 (b) 9 (c) 11 (d) 21
  7. 7.In a class of 18 children, 9 like cricket, 8 like football and 5 like both. How many like neither? (a) 1 (b) 6 (c) 11 (d) 5
  8. 8.In a class of 30 children, 13 like mangoes, 13 like bananas and 2 like both. How many like only mangoes? (a) 11 (b) 2 (c) 13 (d) 17
  9. 9.In a class of 30 children, 22 like cricket, 15 like football and 1 like neither. How many like both? (a) 29 (b) 8 (c) 7 (d) 1
  10. 10.In a class of 28 children, 21 like dance, 11 like music and 7 like both. How many like neither? (a) 3 (b) 7 (c) 10 (d) 4
  11. 11.In a class of 52 children, 24 like maths, 30 like science and 10 like neither. How many like both? (a) 42 (b) 10 (c) 2 (d) 12
  12. 12.In a class of 25 children, 13 like cricket, 16 like football and 7 like both. How many like only cricket? (a) 9 (b) 7 (c) 13 (d) 6
  13. 13.In a class of 42 children, 28 like mangoes, 24 like bananas and 12 like both. How many like neither? (a) 12 (b) 14 (c) 3 (d) 2
  14. 14.In a class of 25 children, 7 like cricket, 16 like football and 5 like neither. How many like both? (a) 4 (b) 20 (c) 3 (d) 5
  15. 15.In a class of 36 children, 28 like cricket, 15 like football and 9 like both. How many like only cricket? (a) 28 (b) 21 (c) 6 (d) 19
  16. 16.In a class of 36 children, 15 like cricket, 30 like football and 11 like both. How many like only cricket? (a) 6 (b) 4 (c) 19 (d) 15
  17. 17.In a class of 38 children, 16 like dance, 28 like music and 8 like both. How many like only dance? (a) 20 (b) 16 (c) 8 (d) 10
  18. 18.In a class of 42 children, 20 like maths, 20 like science and 2 like both. How many like neither? (a) 2 (b) 4 (c) 6 (d) 5
  19. 19.In a class of 30 children, 21 like mangoes, 10 like bananas and 2 like both. How many like only mangoes? (a) 20 (b) 21 (c) 8 (d) 19
  20. 20.In a class of 33 children, 14 like dance, 21 like music and 10 like both. How many like neither? (a) 10 (b) 8 (c) 9 (d) 18
  21. 21.In a class of 45 children, 24 like dance, 23 like music and 10 like both. How many like at least one of the two? (a) 45 (b) 37 (c) 27 (d) 47
  22. 22.In a class of 43 children, 29 like mangoes, 25 like bananas and 12 like both. How many like only mangoes? (a) 18 (b) 13 (c) 29 (d) 17
  23. 23.In a class of 37 children, 19 like dance, 15 like music and 5 like both. How many like only dance? (a) 19 (b) 22 (c) 14 (d) 10
  24. 24.In a class of 29 children, 18 like maths, 21 like science and 11 like both. How many like neither? (a) 11 (b) 12 (c) 1 (d) 2
  25. 25.In a class of 49 children, 27 like dance, 21 like music and 8 like both. How many like only dance? (a) 28 (b) 27 (c) 13 (d) 19
  26. 26.In a class of 41 children, 23 like dance, 14 like music and 4 like both. How many like at least one of the two? (a) 41 (b) 37 (c) 29 (d) 33
  27. 27.In a class of 26 children, 17 like cricket, 18 like football and 12 like both. How many like only cricket? (a) 5 (b) 17 (c) 8 (d) 6
  28. 28.In a class of 41 children, 28 like mangoes, 15 like bananas and 12 like both. How many like only mangoes? (a) 26 (b) 16 (c) 3 (d) 28
  29. 29.In a class of 39 children, 23 like dance, 17 like music and 9 like both. How many like only dance? (a) 22 (b) 14 (c) 23 (d) 8
  30. 30.In a class of 29 children, 18 like maths, 9 like science and 6 like neither. How many like both? (a) 23 (b) 4 (c) 5 (d) 6
  31. 31.In a class of 31 children, 23 like dance, 13 like music and 2 like neither. How many like both? (a) 7 (b) 5 (c) 2 (d) 29
  32. 32.In a class of 24 children, 18 like maths, 7 like science and 2 like both. How many like at least one of the two? (a) 23 (b) 21 (c) 24 (d) 25
  33. 33.In a class of 32 children, 16 like dance, 11 like music and 4 like both. How many like only dance? (a) 21 (b) 12 (c) 16 (d) 7
  34. 34.In a class of 37 children, 19 like maths, 25 like science and 9 like both. How many like only maths? (a) 10 (b) 12 (c) 19 (d) 16
  35. 35.In a class of 38 children, 19 like cricket, 26 like football and 10 like both. How many like only cricket? (a) 9 (b) 16 (c) 12 (d) 19
  36. 36.In a class of 36 children, 17 like tea, 24 like coffee and 6 like both. How many like at least one of the two? (a) 29 (b) 36 (c) 35 (d) 41
  37. 37.In a class of 33 children, 20 like mangoes, 16 like bananas and 7 like both. How many like neither? (a) 7 (b) 4 (c) 11 (d) 5
  38. 38.In a class of 24 children, 18 like cricket, 10 like football and 1 like neither. How many like both? (a) 4 (b) 23 (c) 5 (d) 1
  39. 39.In a class of 38 children, 24 like maths, 19 like science and 8 like both. How many like at least one of the two? (a) 38 (b) 43 (c) 35 (d) 27
  40. 40.In a class of 29 children, 21 like maths, 13 like science and 6 like both. How many like at least one of the two? (a) 28 (b) 22 (c) 34 (d) 29

Answer key

  1. 13
  2. 11
  3. 49
  4. 31
  5. 7
  6. 10
  7. 6
  8. 11
  9. 8
  10. 3
  11. 12
  12. 6
  13. 2
  14. 3
  15. 19
  16. 4
  17. 8
  18. 4
  19. 19
  20. 8
  21. 37
  22. 17
  23. 14
  24. 1
  25. 19
  26. 33
  27. 5
  28. 16
  29. 14
  30. 4
  31. 7
  32. 23
  33. 12
  34. 10
  35. 9
  36. 35
  37. 4
  38. 5
  39. 35
  40. 28

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