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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 43 · 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 48 grown-ups, 31 drink tea, 28 drink coffee and 12 drink both. How many drink neither of the two?
  2. 2.In a group of 28 children, 11 play cricket, 15 play football and 5 play both. How many play only cricket?
  3. 3.In a group of 36 children, 18 enjoy drawing, 15 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  4. 4.In a group of 54 children, 29 enjoy drawing, 25 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  5. 5.In a group of 31 children, 15 enjoy drawing, 11 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?
  6. 6.In a group of 47 children, 15 enjoy drawing, 30 enjoy dancing and 10 enjoy both. How many enjoy at least one of the two?
  7. 7.In a group of 41 children, 13 sing Hindi songs, 15 sing English songs and 2 sing both. How many sing only English songs?
  8. 8.In a group of 39 children, 15 play chess, 16 play carrom and 7 play both. How many play only chess?
  9. 9.In a group of 32 children, 12 like mangoes, 12 like bananas and 6 like both. How many like neither of the two?
  10. 10.In a group of 49 children, 15 sing Hindi songs, 25 sing English songs and 6 sing both. How many sing at least one of the two?
  11. 11.In a group of 32 children, 23 sing Hindi songs, 11 sing English songs and 8 sing both. How many sing only English songs?
  12. 12.In a group of 23 children, 13 play cricket, 19 play football and 10 play both. How many play only cricket?
  13. 13.In a group of 38 grown-ups, 20 drink tea, 16 drink coffee and 4 drink both. How many drink only coffee?
  14. 14.In a group of 31 children, 12 play cricket, 14 play football and 3 play both. How many play exactly one of the two?
  15. 15.In a group of 49 children, 31 like mangoes, 18 like bananas and 12 like both. How many like neither of the two?
  16. 16.In a group of 44 children, 21 play chess, 23 play carrom and 11 play both. How many play only carrom?
  17. 17.In a group of 45 children, 26 enjoy drawing, 18 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  18. 18.In a group of 41 children, 14 enjoy drawing, 28 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  19. 19.In a group of 21 children, 11 enjoy drawing, 15 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  20. 20.In a group of 23 children, 19 play cricket, 6 play football and 3 play both. How many play at least one of the two?
  21. 21.In a group of 39 grown-ups, 23 drink tea, 19 drink coffee and 6 drink both. How many drink neither of the two?
  22. 22.In a group of 31 grown-ups, 21 drink tea, 8 drink coffee and 4 drink both. How many drink exactly one of the two?
  23. 23.In a group of 27 children, 22 play chess, 6 play carrom and 3 play both. How many play exactly one of the two?
  24. 24.In a group of 58 children, 24 play cricket, 23 play football and 4 play both. How many play exactly one of the two?
  25. 25.In a group of 30 children, 18 like mangoes, 17 like bananas and 9 like both. How many like at least one of the two?
  26. 26.In a group of 50 children, 19 play cricket, 29 play football and 12 play both. How many play exactly one of the two?
  27. 27.In a group of 33 children, 15 sing Hindi songs, 25 sing English songs and 10 sing both. How many sing at least one of the two?
  28. 28.In a group of 29 children, 9 sing Hindi songs, 20 sing English songs and 4 sing both. How many sing exactly one of the two?
  29. 29.In a group of 32 children, 9 sing Hindi songs, 17 sing English songs and 5 sing both. How many sing only Hindi songs?
  30. 30.In a group of 39 children, 20 like mangoes, 21 like bananas and 3 like both. How many like only mangoes?
  31. 31.In a group of 26 children, 6 sing Hindi songs, 12 sing English songs and 2 sing both. How many sing only English songs?
  32. 32.In a group of 45 children, 23 play chess, 16 play carrom and 9 play both. How many play at least one of the two?
  33. 33.In a group of 24 children, 12 sing Hindi songs, 12 sing English songs and 7 sing both. How many sing neither of the two?
  34. 34.In a group of 41 children, 26 sing Hindi songs, 15 sing English songs and 8 sing both. How many sing at least one of the two?
  35. 35.In a group of 36 children, 13 sing Hindi songs, 15 sing English songs and 4 sing both. How many sing neither of the two?
  36. 36.In a group of 32 children, 19 play cricket, 14 play football and 6 play both. How many play only football?
  37. 37.In a group of 27 children, 11 like mangoes, 22 like bananas and 8 like both. How many like at least one of the two?
  38. 38.In a group of 26 children, 9 like mangoes, 20 like bananas and 5 like both. How many like at least one of the two?
  39. 39.In a group of 37 children, 21 sing Hindi songs, 26 sing English songs and 11 sing both. How many sing only Hindi songs?
  40. 40.In a group of 49 children, 24 sing Hindi songs, 20 sing English songs and 6 sing both. How many sing at least one of the two?

Answer key

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

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