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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 416 · 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 34 children, 24 enjoy drawing, 10 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  2. 2.In a group of 29 grown-ups, 10 drink tea, 11 drink coffee and 7 drink both. How many drink at least one of the two?
  3. 3.In a group of 54 children, 21 play cricket, 25 play football and 7 play both. How many play exactly one of the two?
  4. 4.In a group of 40 children, 16 play cricket, 18 play football and 9 play both. How many play neither of the two?
  5. 5.In a group of 46 children, 18 sing Hindi songs, 19 sing English songs and 5 sing both. How many sing only English songs?
  6. 6.In a group of 32 children, 22 sing Hindi songs, 14 sing English songs and 6 sing both. How many sing only Hindi songs?
  7. 7.In a group of 37 children, 30 sing Hindi songs, 17 sing English songs and 12 sing both. How many sing only English songs?
  8. 8.In a group of 38 children, 27 enjoy drawing, 20 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  9. 9.In a group of 33 children, 19 sing Hindi songs, 18 sing English songs and 6 sing both. How many sing exactly one of the two?
  10. 10.In a group of 26 children, 9 play chess, 14 play carrom and 3 play both. How many play only carrom?
  11. 11.In a group of 17 children, 10 like mangoes, 11 like bananas and 5 like both. How many like only bananas?
  12. 12.In a group of 56 children, 22 play chess, 29 play carrom and 9 play both. How many play only chess?
  13. 13.In a group of 46 children, 23 play cricket, 22 play football and 4 play both. How many play at least one of the two?
  14. 14.In a group of 32 children, 14 sing Hindi songs, 20 sing English songs and 11 sing both. How many sing neither of the two?
  15. 15.In a group of 29 children, 24 like mangoes, 11 like bananas and 7 like both. How many like only bananas?
  16. 16.In a group of 29 grown-ups, 12 drink tea, 14 drink coffee and 3 drink both. How many drink only coffee?
  17. 17.In a group of 27 children, 14 enjoy drawing, 13 enjoy dancing and 5 enjoy both. How many enjoy at least one of the two?
  18. 18.In a group of 21 grown-ups, 11 drink tea, 11 drink coffee and 8 drink both. How many drink at least one of the two?
  19. 19.In a group of 36 children, 26 play chess, 17 play carrom and 10 play both. How many play neither of the two?
  20. 20.In a group of 52 grown-ups, 24 drink tea, 26 drink coffee and 10 drink both. How many drink at least one of the two?
  21. 21.In a group of 47 children, 16 play cricket, 30 play football and 12 play both. How many play exactly one of the two?
  22. 22.In a group of 45 children, 18 play cricket, 18 play football and 4 play both. How many play at least one of the two?
  23. 23.In a group of 40 children, 25 enjoy drawing, 20 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  24. 24.In a group of 23 children, 16 sing Hindi songs, 11 sing English songs and 6 sing both. How many sing neither of the two?
  25. 25.In a group of 21 children, 14 sing Hindi songs, 14 sing English songs and 8 sing both. How many sing exactly one of the two?
  26. 26.In a group of 36 children, 18 play chess, 25 play carrom and 10 play both. How many play only chess?
  27. 27.In a group of 46 children, 15 sing Hindi songs, 28 sing English songs and 11 sing both. How many sing at least one of the two?
  28. 28.In a group of 38 children, 23 like mangoes, 15 like bananas and 12 like both. How many like only bananas?
  29. 29.In a group of 30 children, 13 enjoy drawing, 16 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  30. 30.In a group of 43 children, 20 like mangoes, 27 like bananas and 7 like both. How many like only bananas?
  31. 31.In a group of 25 children, 14 like mangoes, 12 like bananas and 8 like both. How many like neither of the two?
  32. 32.In a group of 40 grown-ups, 15 drink tea, 17 drink coffee and 3 drink both. How many drink only coffee?
  33. 33.In a group of 33 children, 17 play cricket, 16 play football and 8 play both. How many play only cricket?
  34. 34.In a group of 24 children, 15 play cricket, 19 play football and 11 play both. How many play only football?
  35. 35.In a group of 35 children, 9 enjoy drawing, 18 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  36. 36.In a group of 35 children, 14 enjoy drawing, 17 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  37. 37.In a group of 37 children, 18 play cricket, 21 play football and 12 play both. How many play exactly one of the two?
  38. 38.In a group of 25 grown-ups, 15 drink tea, 16 drink coffee and 12 drink both. How many drink exactly one of the two?
  39. 39.In a group of 21 children, 14 enjoy drawing, 12 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  40. 40.In a group of 36 children, 11 play cricket, 16 play football and 2 play both. How many play at least one of the two?

Answer key

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

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