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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 102 · 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 35 children, 11 enjoy drawing, 26 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  2. 2.In a group of 33 children, 13 sing Hindi songs, 14 sing English songs and 7 sing both. How many sing at least one of the two?
  3. 3.In a group of 20 children, 8 play cricket, 12 play football and 3 play both. How many play exactly one of the two?
  4. 4.In a group of 42 grown-ups, 28 drink tea, 14 drink coffee and 8 drink both. How many drink only coffee?
  5. 5.In a group of 25 children, 11 enjoy drawing, 13 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  6. 6.In a group of 44 children, 23 play chess, 23 play carrom and 4 play both. How many play at least one of the two?
  7. 7.In a group of 46 grown-ups, 15 drink tea, 28 drink coffee and 10 drink both. How many drink at least one of the two?
  8. 8.In a group of 36 children, 14 like mangoes, 23 like bananas and 3 like both. How many like neither of the two?
  9. 9.In a group of 32 children, 18 sing Hindi songs, 11 sing English songs and 8 sing both. How many sing exactly one of the two?
  10. 10.In a group of 40 children, 19 sing Hindi songs, 25 sing English songs and 12 sing both. How many sing only English songs?
  11. 11.In a group of 32 children, 19 sing Hindi songs, 12 sing English songs and 6 sing both. How many sing exactly one of the two?
  12. 12.In a group of 25 grown-ups, 20 drink tea, 5 drink coffee and 2 drink both. How many drink only tea?
  13. 13.In a group of 31 children, 15 like mangoes, 24 like bananas and 9 like both. How many like exactly one of the two?
  14. 14.In a group of 35 grown-ups, 17 drink tea, 25 drink coffee and 9 drink both. How many drink only tea?
  15. 15.In a group of 23 children, 8 enjoy drawing, 7 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  16. 16.In a group of 44 children, 24 like mangoes, 9 like bananas and 4 like both. How many like exactly one of the two?
  17. 17.In a group of 33 children, 7 play chess, 17 play carrom and 2 play both. How many play exactly one of the two?
  18. 18.In a group of 58 grown-ups, 29 drink tea, 31 drink coffee and 12 drink both. How many drink exactly one of the two?
  19. 19.In a group of 36 children, 28 like mangoes, 14 like bananas and 10 like both. How many like neither of the two?
  20. 20.In a group of 35 children, 20 sing Hindi songs, 9 sing English songs and 4 sing both. How many sing only Hindi songs?
  21. 21.In a group of 54 children, 31 play cricket, 27 play football and 11 play both. How many play at least one of the two?
  22. 22.In a group of 47 children, 18 sing Hindi songs, 16 sing English songs and 2 sing both. How many sing neither of the two?
  23. 23.In a group of 45 children, 11 play chess, 26 play carrom and 7 play both. How many play neither of the two?
  24. 24.In a group of 39 children, 18 enjoy drawing, 19 enjoy dancing and 5 enjoy both. How many enjoy at least one of the two?
  25. 25.In a group of 32 children, 7 play chess, 17 play carrom and 4 play both. How many play only chess?
  26. 26.In a group of 55 children, 25 like mangoes, 22 like bananas and 6 like both. How many like exactly one of the two?
  27. 27.In a group of 20 children, 10 play cricket, 10 play football and 4 play both. How many play exactly one of the two?
  28. 28.In a group of 39 children, 11 enjoy drawing, 26 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  29. 29.In a group of 47 children, 27 enjoy drawing, 26 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  30. 30.In a group of 35 children, 20 play cricket, 15 play football and 2 play both. How many play neither of the two?
  31. 31.In a group of 26 children, 18 sing Hindi songs, 18 sing English songs and 11 sing both. How many sing only English songs?
  32. 32.In a group of 48 children, 20 play cricket, 21 play football and 6 play both. How many play only football?
  33. 33.In a group of 22 children, 7 sing Hindi songs, 15 sing English songs and 4 sing both. How many sing exactly one of the two?
  34. 34.In a group of 54 children, 26 enjoy drawing, 27 enjoy dancing and 10 enjoy both. How many enjoy only dancing?
  35. 35.In a group of 39 children, 16 enjoy drawing, 23 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  36. 36.In a group of 47 children, 22 play cricket, 26 play football and 8 play both. How many play only football?
  37. 37.In a group of 29 children, 9 play chess, 14 play carrom and 3 play both. How many play only carrom?
  38. 38.In a group of 38 children, 26 play chess, 19 play carrom and 11 play both. How many play neither of the two?
  39. 39.In a group of 28 children, 14 play cricket, 9 play football and 6 play both. How many play neither of the two?
  40. 40.In a group of 38 children, 11 play cricket, 19 play football and 7 play both. How many play exactly one of the two?

Answer key

  1. 31
  2. 20
  3. 14
  4. 6
  5. 16
  6. 42
  7. 33
  8. 2
  9. 13
  10. 13
  11. 19
  12. 18
  13. 21
  14. 8
  15. 10
  16. 25
  17. 20
  18. 36
  19. 4
  20. 16
  21. 47
  22. 15
  23. 15
  24. 32
  25. 3
  26. 35
  27. 12
  28. 23
  29. 45
  30. 2
  31. 7
  32. 15
  33. 14
  34. 17
  35. 33
  36. 18
  37. 11
  38. 4
  39. 11
  40. 16

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