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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 266 · 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 22 children, 13 play chess, 10 play carrom and 4 play both. How many play neither of the two?
  2. 2.In a group of 38 children, 16 play cricket, 10 play football and 3 play both. How many play exactly one of the two?
  3. 3.In a group of 51 children, 25 enjoy drawing, 21 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  4. 4.In a group of 23 children, 13 like mangoes, 10 like bananas and 4 like both. How many like only bananas?
  5. 5.In a group of 44 children, 23 play cricket, 17 play football and 11 play both. How many play exactly one of the two?
  6. 6.In a group of 44 children, 24 enjoy drawing, 28 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  7. 7.In a group of 32 children, 18 play cricket, 19 play football and 11 play both. How many play exactly one of the two?
  8. 8.In a group of 47 children, 20 sing Hindi songs, 24 sing English songs and 4 sing both. How many sing only Hindi songs?
  9. 9.In a group of 25 children, 18 like mangoes, 13 like bananas and 7 like both. How many like exactly one of the two?
  10. 10.In a group of 27 children, 18 enjoy drawing, 13 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  11. 11.In a group of 38 children, 24 play chess, 22 play carrom and 9 play both. How many play neither of the two?
  12. 12.In a group of 35 children, 9 play cricket, 19 play football and 2 play both. How many play only football?
  13. 13.In a group of 42 grown-ups, 21 drink tea, 28 drink coffee and 10 drink both. How many drink at least one of the two?
  14. 14.In a group of 40 grown-ups, 22 drink tea, 20 drink coffee and 9 drink both. How many drink neither of the two?
  15. 15.In a group of 29 children, 15 like mangoes, 20 like bananas and 12 like both. How many like exactly one of the two?
  16. 16.In a group of 32 children, 12 play chess, 15 play carrom and 6 play both. How many play exactly one of the two?
  17. 17.In a group of 46 children, 31 play chess, 17 play carrom and 11 play both. How many play only chess?
  18. 18.In a group of 47 children, 26 like mangoes, 29 like bananas and 11 like both. How many like at least one of the two?
  19. 19.In a group of 37 children, 8 sing Hindi songs, 20 sing English songs and 4 sing both. How many sing only Hindi songs?
  20. 20.In a group of 37 children, 21 sing Hindi songs, 8 sing English songs and 5 sing both. How many sing at least one of the two?
  21. 21.In a group of 35 children, 13 play cricket, 23 play football and 4 play both. How many play exactly one of the two?
  22. 22.In a group of 37 grown-ups, 22 drink tea, 12 drink coffee and 7 drink both. How many drink neither of the two?
  23. 23.In a group of 40 grown-ups, 13 drink tea, 17 drink coffee and 2 drink both. How many drink only tea?
  24. 24.In a group of 37 children, 18 play chess, 24 play carrom and 10 play both. How many play neither of the two?
  25. 25.In a group of 31 grown-ups, 22 drink tea, 6 drink coffee and 2 drink both. How many drink at least one of the two?
  26. 26.In a group of 43 children, 14 play cricket, 24 play football and 4 play both. How many play only football?
  27. 27.In a group of 43 grown-ups, 21 drink tea, 32 drink coffee and 12 drink both. How many drink only coffee?
  28. 28.In a group of 32 children, 24 enjoy drawing, 14 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  29. 29.In a group of 40 children, 17 enjoy drawing, 17 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  30. 30.In a group of 29 children, 9 play chess, 9 play carrom and 3 play both. How many play neither of the two?
  31. 31.In a group of 33 children, 14 sing Hindi songs, 7 sing English songs and 3 sing both. How many sing neither of the two?
  32. 32.In a group of 53 children, 30 sing Hindi songs, 24 sing English songs and 12 sing both. How many sing exactly one of the two?
  33. 33.In a group of 36 children, 8 play cricket, 24 play football and 5 play both. How many play only football?
  34. 34.In a group of 41 children, 26 sing Hindi songs, 22 sing English songs and 10 sing both. How many sing only Hindi songs?
  35. 35.In a group of 37 children, 27 play chess, 16 play carrom and 10 play both. How many play exactly one of the two?
  36. 36.In a group of 38 children, 18 sing Hindi songs, 12 sing English songs and 5 sing both. How many sing at least one of the two?
  37. 37.In a group of 23 children, 10 play chess, 18 play carrom and 6 play both. How many play only carrom?
  38. 38.In a group of 36 children, 22 play chess, 16 play carrom and 12 play both. How many play only chess?
  39. 39.In a group of 38 children, 17 play cricket, 18 play football and 11 play both. How many play at least one of the two?
  40. 40.In a group of 33 children, 18 enjoy drawing, 18 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?

Answer key

  1. 3
  2. 20
  3. 13
  4. 6
  5. 18
  6. 19
  7. 15
  8. 16
  9. 17
  10. 7
  11. 1
  12. 17
  13. 39
  14. 7
  15. 11
  16. 15
  17. 20
  18. 44
  19. 4
  20. 24
  21. 28
  22. 10
  23. 11
  24. 5
  25. 26
  26. 20
  27. 20
  28. 1
  29. 14
  30. 14
  31. 15
  32. 30
  33. 19
  34. 16
  35. 23
  36. 25
  37. 12
  38. 10
  39. 24
  40. 9

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