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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 227 · 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 36 children, 19 enjoy drawing, 16 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  2. 2.In a group of 37 children, 22 enjoy drawing, 12 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  3. 3.In a group of 38 grown-ups, 11 drink tea, 19 drink coffee and 7 drink both. How many drink neither of the two?
  4. 4.In a group of 44 children, 15 play cricket, 25 play football and 9 play both. How many play neither of the two?
  5. 5.In a group of 47 children, 27 play cricket, 25 play football and 7 play both. How many play only football?
  6. 6.In a group of 40 children, 20 play cricket, 22 play football and 12 play both. How many play only cricket?
  7. 7.In a group of 49 children, 20 play chess, 28 play carrom and 8 play both. How many play exactly one of the two?
  8. 8.In a group of 24 grown-ups, 11 drink tea, 12 drink coffee and 2 drink both. How many drink exactly one of the two?
  9. 9.In a group of 26 children, 8 sing Hindi songs, 13 sing English songs and 2 sing both. How many sing only Hindi songs?
  10. 10.In a group of 40 children, 13 play chess, 18 play carrom and 3 play both. How many play exactly one of the two?
  11. 11.In a group of 52 children, 27 play cricket, 25 play football and 11 play both. How many play exactly one of the two?
  12. 12.In a group of 22 children, 12 like mangoes, 9 like bananas and 2 like both. How many like neither of the two?
  13. 13.In a group of 13 children, 7 play cricket, 8 play football and 3 play both. How many play at least one of the two?
  14. 14.In a group of 49 children, 21 enjoy drawing, 22 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  15. 15.In a group of 21 children, 13 play cricket, 10 play football and 3 play both. How many play at least one of the two?
  16. 16.In a group of 47 children, 21 play cricket, 20 play football and 9 play both. How many play only football?
  17. 17.In a group of 42 children, 21 play chess, 19 play carrom and 10 play both. How many play only chess?
  18. 18.In a group of 37 children, 18 play chess, 11 play carrom and 3 play both. How many play exactly one of the two?
  19. 19.In a group of 49 children, 27 play cricket, 17 play football and 9 play both. How many play exactly one of the two?
  20. 20.In a group of 39 children, 23 play cricket, 20 play football and 11 play both. How many play at least one of the two?
  21. 21.In a group of 44 children, 21 like mangoes, 20 like bananas and 11 like both. How many like at least one of the two?
  22. 22.In a group of 36 children, 14 play chess, 21 play carrom and 8 play both. How many play neither of the two?
  23. 23.In a group of 37 children, 25 play cricket, 18 play football and 9 play both. How many play at least one of the two?
  24. 24.In a group of 40 children, 23 like mangoes, 13 like bananas and 7 like both. How many like at least one of the two?
  25. 25.In a group of 47 children, 20 play chess, 22 play carrom and 9 play both. How many play neither of the two?
  26. 26.In a group of 13 children, 7 play chess, 5 play carrom and 2 play both. How many play exactly one of the two?
  27. 27.In a group of 47 grown-ups, 30 drink tea, 19 drink coffee and 10 drink both. How many drink at least one of the two?
  28. 28.In a group of 41 grown-ups, 21 drink tea, 16 drink coffee and 7 drink both. How many drink only tea?
  29. 29.In a group of 25 children, 8 like mangoes, 11 like bananas and 4 like both. How many like neither of the two?
  30. 30.In a group of 29 children, 11 play cricket, 14 play football and 7 play both. How many play exactly one of the two?
  31. 31.In a group of 55 children, 22 play cricket, 31 play football and 12 play both. How many play at least one of the two?
  32. 32.In a group of 41 children, 27 play cricket, 20 play football and 12 play both. How many play neither of the two?
  33. 33.In a group of 30 children, 14 sing Hindi songs, 9 sing English songs and 2 sing both. How many sing only English songs?
  34. 34.In a group of 44 children, 17 play cricket, 24 play football and 10 play both. How many play at least one of the two?
  35. 35.In a group of 36 children, 18 play chess, 15 play carrom and 9 play both. How many play at least one of the two?
  36. 36.In a group of 52 children, 20 sing Hindi songs, 27 sing English songs and 8 sing both. How many sing neither of the two?
  37. 37.In a group of 45 children, 24 sing Hindi songs, 22 sing English songs and 6 sing both. How many sing only English songs?
  38. 38.In a group of 17 children, 6 like mangoes, 10 like bananas and 3 like both. How many like only bananas?
  39. 39.In a group of 40 grown-ups, 25 drink tea, 20 drink coffee and 10 drink both. How many drink only tea?
  40. 40.In a group of 28 children, 20 play chess, 11 play carrom and 6 play both. How many play exactly one of the two?

Answer key

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

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