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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 78 · 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 30 children, 9 play cricket, 14 play football and 5 play both. How many play neither of the two?
  2. 2.In a group of 43 children, 15 play chess, 27 play carrom and 7 play both. How many play exactly one of the two?
  3. 3.In a group of 19 children, 11 sing Hindi songs, 11 sing English songs and 8 sing both. How many sing only Hindi songs?
  4. 4.In a group of 30 children, 12 like mangoes, 21 like bananas and 7 like both. How many like exactly one of the two?
  5. 5.In a group of 29 children, 8 like mangoes, 11 like bananas and 4 like both. How many like neither of the two?
  6. 6.In a group of 50 children, 22 sing Hindi songs, 25 sing English songs and 11 sing both. How many sing exactly one of the two?
  7. 7.In a group of 33 children, 11 enjoy drawing, 17 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  8. 8.In a group of 28 grown-ups, 8 drink tea, 11 drink coffee and 4 drink both. How many drink only coffee?
  9. 9.In a group of 50 grown-ups, 26 drink tea, 23 drink coffee and 10 drink both. How many drink only coffee?
  10. 10.In a group of 39 children, 15 sing Hindi songs, 20 sing English songs and 10 sing both. How many sing only English songs?
  11. 11.In a group of 41 children, 11 enjoy drawing, 23 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  12. 12.In a group of 51 children, 27 sing Hindi songs, 21 sing English songs and 7 sing both. How many sing exactly one of the two?
  13. 13.In a group of 19 grown-ups, 7 drink tea, 8 drink coffee and 3 drink both. How many drink only coffee?
  14. 14.In a group of 38 grown-ups, 19 drink tea, 13 drink coffee and 6 drink both. How many drink neither of the two?
  15. 15.In a group of 42 children, 14 play cricket, 22 play football and 4 play both. How many play only football?
  16. 16.In a group of 46 children, 20 like mangoes, 22 like bananas and 4 like both. How many like only bananas?
  17. 17.In a group of 30 children, 11 play chess, 13 play carrom and 3 play both. How many play only chess?
  18. 18.In a group of 49 children, 22 play chess, 25 play carrom and 12 play both. How many play only chess?
  19. 19.In a group of 39 children, 18 play chess, 18 play carrom and 11 play both. How many play only chess?
  20. 20.In a group of 28 children, 22 sing Hindi songs, 7 sing English songs and 2 sing both. How many sing neither of the two?
  21. 21.In a group of 46 children, 28 enjoy drawing, 26 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  22. 22.In a group of 42 grown-ups, 17 drink tea, 28 drink coffee and 12 drink both. How many drink only coffee?
  23. 23.In a group of 22 children, 11 play cricket, 16 play football and 7 play both. How many play only cricket?
  24. 24.In a group of 31 children, 17 like mangoes, 13 like bananas and 2 like both. How many like at least one of the two?
  25. 25.In a group of 29 children, 11 like mangoes, 20 like bananas and 3 like both. How many like only bananas?
  26. 26.In a group of 32 grown-ups, 22 drink tea, 20 drink coffee and 11 drink both. How many drink at least one of the two?
  27. 27.In a group of 32 children, 15 enjoy drawing, 17 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  28. 28.In a group of 35 children, 9 sing Hindi songs, 18 sing English songs and 3 sing both. How many sing neither of the two?
  29. 29.In a group of 27 children, 12 play cricket, 18 play football and 6 play both. How many play neither of the two?
  30. 30.In a group of 38 children, 20 play cricket, 22 play football and 6 play both. How many play only football?
  31. 31.In a group of 37 grown-ups, 24 drink tea, 18 drink coffee and 10 drink both. How many drink neither of the two?
  32. 32.In a group of 33 children, 12 like mangoes, 26 like bananas and 9 like both. How many like at least one of the two?
  33. 33.In a group of 44 children, 22 like mangoes, 22 like bananas and 12 like both. How many like neither of the two?
  34. 34.In a group of 29 children, 16 sing Hindi songs, 17 sing English songs and 9 sing both. How many sing only Hindi songs?
  35. 35.In a group of 37 children, 20 like mangoes, 9 like bananas and 5 like both. How many like neither of the two?
  36. 36.In a group of 47 children, 20 like mangoes, 29 like bananas and 9 like both. How many like at least one of the two?
  37. 37.In a group of 27 children, 13 enjoy drawing, 19 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  38. 38.In a group of 31 children, 11 enjoy drawing, 20 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  39. 39.In a group of 24 grown-ups, 16 drink tea, 10 drink coffee and 6 drink both. How many drink exactly one of the two?
  40. 40.In a group of 33 grown-ups, 21 drink tea, 8 drink coffee and 3 drink both. How many drink at least one of the two?

Answer key

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

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