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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 71 · 40 questions
TalentJR

How to think it through (Middle first): Put “both” in the overlap. Only A = A − both; only B = B − both; at least one = A + B − both. Neither = total − at least one; exactly one = only A + only B.

NameDateTime takenScore ___ / 40
  1. 1.In a group of 51 children, 20 enjoy drawing, 20 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  2. 2.In a group of 35 children, 10 play cricket, 19 play football and 5 play both. How many play exactly one of the two?
  3. 3.In a group of 27 children, 6 enjoy drawing, 19 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  4. 4.In a group of 39 grown-ups, 27 drink tea, 15 drink coffee and 7 drink both. How many drink only tea?
  5. 5.In a group of 35 children, 28 play cricket, 16 play football and 12 play both. How many play neither of the two?
  6. 6.In a group of 42 children, 22 play cricket, 20 play football and 12 play both. How many play only football?
  7. 7.In a group of 39 children, 17 enjoy drawing, 25 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  8. 8.In a group of 50 children, 25 enjoy drawing, 21 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  9. 9.In a group of 28 children, 17 enjoy drawing, 11 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  10. 10.In a group of 23 grown-ups, 9 drink tea, 13 drink coffee and 5 drink both. How many drink only tea?
  11. 11.In a group of 44 grown-ups, 32 drink tea, 15 drink coffee and 12 drink both. How many drink at least one of the two?
  12. 12.In a group of 40 children, 18 like mangoes, 22 like bananas and 2 like both. How many like only mangoes?
  13. 13.In a group of 29 children, 9 play chess, 18 play carrom and 6 play both. How many play at least one of the two?
  14. 14.In a group of 33 children, 14 like mangoes, 21 like bananas and 11 like both. How many like neither of the two?
  15. 15.In a group of 54 children, 23 enjoy drawing, 27 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  16. 16.In a group of 52 children, 18 enjoy drawing, 24 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  17. 17.In a group of 50 children, 24 play cricket, 17 play football and 5 play both. How many play exactly one of the two?
  18. 18.In a group of 17 children, 13 play chess, 5 play carrom and 2 play both. How many play only carrom?
  19. 19.In a group of 42 children, 24 play chess, 27 play carrom and 10 play both. How many play at least one of the two?
  20. 20.In a group of 52 children, 20 enjoy drawing, 22 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  21. 21.In a group of 36 children, 9 like mangoes, 22 like bananas and 5 like both. How many like exactly one of the two?
  22. 22.In a group of 38 children, 10 enjoy drawing, 22 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  23. 23.In a group of 48 children, 27 sing Hindi songs, 22 sing English songs and 9 sing both. How many sing at least one of the two?
  24. 24.In a group of 23 children, 11 like mangoes, 10 like bananas and 3 like both. How many like only bananas?
  25. 25.In a group of 36 children, 13 play cricket, 25 play football and 8 play both. How many play only cricket?
  26. 26.In a group of 54 children, 29 like mangoes, 21 like bananas and 11 like both. How many like only bananas?
  27. 27.In a group of 47 children, 24 play chess, 16 play carrom and 6 play both. How many play neither of the two?
  28. 28.In a group of 32 grown-ups, 13 drink tea, 12 drink coffee and 5 drink both. How many drink only coffee?
  29. 29.In a group of 28 grown-ups, 9 drink tea, 21 drink coffee and 3 drink both. How many drink only coffee?
  30. 30.In a group of 37 children, 6 play chess, 21 play carrom and 2 play both. How many play exactly one of the two?
  31. 31.In a group of 38 children, 22 play cricket, 12 play football and 9 play both. How many play exactly one of the two?
  32. 32.In a group of 19 children, 8 like mangoes, 8 like bananas and 4 like both. How many like neither of the two?
  33. 33.In a group of 43 grown-ups, 21 drink tea, 29 drink coffee and 11 drink both. How many drink only coffee?
  34. 34.In a group of 16 children, 6 enjoy drawing, 8 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  35. 35.In a group of 37 children, 23 enjoy drawing, 13 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  36. 36.In a group of 37 children, 17 enjoy drawing, 25 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  37. 37.In a group of 30 children, 12 enjoy drawing, 10 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  38. 38.In a group of 14 children, 6 play cricket, 10 play football and 3 play both. How many play at least one of the two?
  39. 39.In a group of 30 children, 16 play cricket, 11 play football and 2 play both. How many play only cricket?
  40. 40.In a group of 37 children, 16 sing Hindi songs, 22 sing English songs and 9 sing both. How many sing neither of the two?

Answer key

  1. 18
  2. 19
  3. 23
  4. 20
  5. 3
  6. 8
  7. 9
  8. 15
  9. 20
  10. 4
  11. 35
  12. 16
  13. 21
  14. 9
  15. 12
  16. 13
  17. 31
  18. 3
  19. 41
  20. 14
  21. 21
  22. 28
  23. 40
  24. 7
  25. 5
  26. 10
  27. 13
  28. 7
  29. 18
  30. 23
  31. 16
  32. 7
  33. 18
  34. 3
  35. 30
  36. 14
  37. 15
  38. 13
  39. 14
  40. 8

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