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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 247 · 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 32 grown-ups, 19 drink tea, 15 drink coffee and 5 drink both. How many drink exactly one of the two?
  2. 2.In a group of 32 children, 16 sing Hindi songs, 21 sing English songs and 10 sing both. How many sing exactly one of the two?
  3. 3.In a group of 45 children, 18 play cricket, 20 play football and 8 play both. How many play exactly one of the two?
  4. 4.In a group of 41 children, 22 play chess, 14 play carrom and 9 play both. How many play at least one of the two?
  5. 5.In a group of 37 children, 19 sing Hindi songs, 18 sing English songs and 6 sing both. How many sing neither of the two?
  6. 6.In a group of 29 children, 12 sing Hindi songs, 16 sing English songs and 4 sing both. How many sing exactly one of the two?
  7. 7.In a group of 45 children, 26 sing Hindi songs, 13 sing English songs and 9 sing both. How many sing neither of the two?
  8. 8.In a group of 27 children, 13 like mangoes, 19 like bananas and 8 like both. How many like neither of the two?
  9. 9.In a group of 31 children, 9 play chess, 25 play carrom and 6 play both. How many play only chess?
  10. 10.In a group of 28 children, 16 play chess, 13 play carrom and 10 play both. How many play only carrom?
  11. 11.In a group of 34 children, 12 play cricket, 19 play football and 2 play both. How many play only cricket?
  12. 12.In a group of 30 grown-ups, 16 drink tea, 21 drink coffee and 9 drink both. How many drink at least one of the two?
  13. 13.In a group of 47 children, 24 enjoy drawing, 24 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  14. 14.In a group of 37 children, 29 enjoy drawing, 19 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  15. 15.In a group of 19 children, 9 play chess, 8 play carrom and 2 play both. How many play exactly one of the two?
  16. 16.In a group of 41 children, 24 enjoy drawing, 14 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  17. 17.In a group of 22 children, 12 play cricket, 9 play football and 2 play both. How many play only football?
  18. 18.In a group of 46 children, 21 enjoy drawing, 29 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  19. 19.In a group of 42 children, 24 sing Hindi songs, 12 sing English songs and 8 sing both. How many sing neither of the two?
  20. 20.In a group of 39 children, 14 enjoy drawing, 28 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  21. 21.In a group of 24 children, 7 enjoy drawing, 6 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  22. 22.In a group of 31 children, 6 enjoy drawing, 13 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  23. 23.In a group of 28 grown-ups, 16 drink tea, 16 drink coffee and 9 drink both. How many drink neither of the two?
  24. 24.In a group of 43 grown-ups, 22 drink tea, 19 drink coffee and 11 drink both. How many drink only coffee?
  25. 25.In a group of 30 children, 10 play cricket, 12 play football and 7 play both. How many play exactly one of the two?
  26. 26.In a group of 35 children, 13 sing Hindi songs, 27 sing English songs and 8 sing both. How many sing only Hindi songs?
  27. 27.In a group of 41 children, 16 play chess, 16 play carrom and 6 play both. How many play exactly one of the two?
  28. 28.In a group of 35 children, 16 play cricket, 15 play football and 9 play both. How many play only football?
  29. 29.In a group of 46 children, 26 play cricket, 16 play football and 10 play both. How many play at least one of the two?
  30. 30.In a group of 49 grown-ups, 29 drink tea, 17 drink coffee and 12 drink both. How many drink neither of the two?
  31. 31.In a group of 26 children, 14 enjoy drawing, 14 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  32. 32.In a group of 47 grown-ups, 24 drink tea, 19 drink coffee and 11 drink both. How many drink exactly one of the two?
  33. 33.In a group of 43 children, 11 sing Hindi songs, 26 sing English songs and 7 sing both. How many sing only English songs?
  34. 34.In a group of 35 children, 13 play cricket, 28 play football and 8 play both. How many play only football?
  35. 35.In a group of 27 children, 13 play cricket, 16 play football and 8 play both. How many play at least one of the two?
  36. 36.In a group of 43 children, 19 sing Hindi songs, 27 sing English songs and 10 sing both. How many sing exactly one of the two?
  37. 37.In a group of 37 grown-ups, 23 drink tea, 19 drink coffee and 8 drink both. How many drink only coffee?
  38. 38.In a group of 45 children, 17 enjoy drawing, 19 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  39. 39.In a group of 27 children, 9 enjoy drawing, 17 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  40. 40.In a group of 33 grown-ups, 9 drink tea, 12 drink coffee and 2 drink both. How many drink exactly one of the two?

Answer key

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

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