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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 547 · 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, 16 play cricket, 17 play football and 6 play both. How many play only football?
  2. 2.In a group of 36 children, 23 enjoy drawing, 23 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  3. 3.In a group of 32 children, 23 sing Hindi songs, 13 sing English songs and 9 sing both. How many sing only Hindi songs?
  4. 4.In a group of 40 children, 19 like mangoes, 25 like bananas and 6 like both. How many like only mangoes?
  5. 5.In a group of 43 children, 24 sing Hindi songs, 21 sing English songs and 8 sing both. How many sing exactly one of the two?
  6. 6.In a group of 49 children, 18 play cricket, 20 play football and 4 play both. How many play only football?
  7. 7.In a group of 42 children, 21 like mangoes, 20 like bananas and 10 like both. How many like exactly one of the two?
  8. 8.In a group of 29 children, 14 play chess, 19 play carrom and 11 play both. How many play neither of the two?
  9. 9.In a group of 33 children, 17 like mangoes, 23 like bananas and 12 like both. How many like at least one of the two?
  10. 10.In a group of 50 children, 28 like mangoes, 25 like bananas and 11 like both. How many like only mangoes?
  11. 11.In a group of 38 grown-ups, 13 drink tea, 16 drink coffee and 2 drink both. How many drink exactly one of the two?
  12. 12.In a group of 26 children, 13 sing Hindi songs, 15 sing English songs and 5 sing both. How many sing exactly one of the two?
  13. 13.In a group of 43 children, 19 sing Hindi songs, 17 sing English songs and 8 sing both. How many sing at least one of the two?
  14. 14.In a group of 26 children, 12 enjoy drawing, 11 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  15. 15.In a group of 41 children, 26 play chess, 22 play carrom and 11 play both. How many play only carrom?
  16. 16.In a group of 37 children, 17 play cricket, 27 play football and 12 play both. How many play only cricket?
  17. 17.In a group of 32 grown-ups, 22 drink tea, 15 drink coffee and 10 drink both. How many drink at least one of the two?
  18. 18.In a group of 39 children, 18 sing Hindi songs, 20 sing English songs and 2 sing both. How many sing neither of the two?
  19. 19.In a group of 31 children, 13 play chess, 22 play carrom and 9 play both. How many play at least one of the two?
  20. 20.In a group of 34 children, 16 sing Hindi songs, 18 sing English songs and 7 sing both. How many sing only Hindi songs?
  21. 21.In a group of 55 grown-ups, 21 drink tea, 29 drink coffee and 10 drink both. How many drink exactly one of the two?
  22. 22.In a group of 45 children, 21 like mangoes, 30 like bananas and 12 like both. How many like at least one of the two?
  23. 23.In a group of 26 children, 16 enjoy drawing, 15 enjoy dancing and 10 enjoy both. How many enjoy only dancing?
  24. 24.In a group of 26 children, 19 enjoy drawing, 17 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  25. 25.In a group of 38 children, 8 enjoy drawing, 22 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  26. 26.In a group of 28 children, 15 enjoy drawing, 15 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  27. 27.In a group of 32 children, 16 like mangoes, 6 like bananas and 3 like both. How many like exactly one of the two?
  28. 28.In a group of 39 children, 23 enjoy drawing, 16 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  29. 29.In a group of 45 children, 19 like mangoes, 16 like bananas and 2 like both. How many like only bananas?
  30. 30.In a group of 49 children, 26 play chess, 25 play carrom and 7 play both. How many play neither of the two?
  31. 31.In a group of 24 grown-ups, 10 drink tea, 5 drink coffee and 2 drink both. How many drink at least one of the two?
  32. 32.In a group of 46 children, 18 sing Hindi songs, 22 sing English songs and 3 sing both. How many sing at least one of the two?
  33. 33.In a group of 35 children, 16 sing Hindi songs, 15 sing English songs and 10 sing both. How many sing neither of the two?
  34. 34.In a group of 39 children, 16 play cricket, 20 play football and 8 play both. How many play neither of the two?
  35. 35.In a group of 45 children, 25 enjoy drawing, 28 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  36. 36.In a group of 41 children, 23 sing Hindi songs, 6 sing English songs and 3 sing both. How many sing only English songs?
  37. 37.In a group of 57 grown-ups, 24 drink tea, 31 drink coffee and 11 drink both. How many drink exactly one of the two?
  38. 38.In a group of 39 children, 23 sing Hindi songs, 25 sing English songs and 10 sing both. How many sing at least one of the two?
  39. 39.In a group of 37 children, 11 like mangoes, 23 like bananas and 5 like both. How many like exactly one of the two?
  40. 40.In a group of 33 children, 14 play chess, 17 play carrom and 8 play both. How many play only chess?

Answer key

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

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