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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 244 · 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 50 children, 32 enjoy drawing, 21 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  2. 2.In a group of 41 grown-ups, 21 drink tea, 16 drink coffee and 3 drink both. How many drink at least one of the two?
  3. 3.In a group of 34 children, 21 play chess, 7 play carrom and 4 play both. How many play at least one of the two?
  4. 4.In a group of 50 children, 16 like mangoes, 23 like bananas and 4 like both. How many like at least one of the two?
  5. 5.In a group of 27 children, 14 play chess, 10 play carrom and 6 play both. How many play at least one of the two?
  6. 6.In a group of 29 children, 13 sing Hindi songs, 14 sing English songs and 6 sing both. How many sing neither of the two?
  7. 7.In a group of 41 children, 26 sing Hindi songs, 21 sing English songs and 11 sing both. How many sing only Hindi songs?
  8. 8.In a group of 39 grown-ups, 19 drink tea, 25 drink coffee and 12 drink both. How many drink only coffee?
  9. 9.In a group of 47 grown-ups, 16 drink tea, 26 drink coffee and 10 drink both. How many drink neither of the two?
  10. 10.In a group of 35 children, 23 sing Hindi songs, 8 sing English songs and 3 sing both. How many sing at least one of the two?
  11. 11.In a group of 36 children, 20 play chess, 24 play carrom and 12 play both. How many play only carrom?
  12. 12.In a group of 31 children, 16 enjoy drawing, 14 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  13. 13.In a group of 27 children, 9 play cricket, 18 play football and 5 play both. How many play only football?
  14. 14.In a group of 35 grown-ups, 19 drink tea, 26 drink coffee and 12 drink both. How many drink at least one of the two?
  15. 15.In a group of 25 grown-ups, 9 drink tea, 5 drink coffee and 2 drink both. How many drink exactly one of the two?
  16. 16.In a group of 32 children, 17 like mangoes, 11 like bananas and 8 like both. How many like at least one of the two?
  17. 17.In a group of 24 children, 14 enjoy drawing, 12 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  18. 18.In a group of 27 children, 15 sing Hindi songs, 12 sing English songs and 7 sing both. How many sing only Hindi songs?
  19. 19.In a group of 47 children, 15 play chess, 19 play carrom and 2 play both. How many play only chess?
  20. 20.In a group of 25 grown-ups, 17 drink tea, 6 drink coffee and 3 drink both. How many drink only tea?
  21. 21.In a group of 38 children, 10 play chess, 19 play carrom and 3 play both. How many play exactly one of the two?
  22. 22.In a group of 47 children, 28 enjoy drawing, 18 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  23. 23.In a group of 30 children, 23 play cricket, 7 play football and 4 play both. How many play only cricket?
  24. 24.In a group of 53 children, 21 enjoy drawing, 32 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  25. 25.In a group of 28 children, 14 play cricket, 11 play football and 8 play both. How many play neither of the two?
  26. 26.In a group of 49 children, 25 sing Hindi songs, 24 sing English songs and 12 sing both. How many sing only English songs?
  27. 27.In a group of 50 children, 22 play chess, 19 play carrom and 5 play both. How many play only chess?
  28. 28.In a group of 38 children, 8 sing Hindi songs, 23 sing English songs and 5 sing both. How many sing neither of the two?
  29. 29.In a group of 46 children, 17 enjoy drawing, 30 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  30. 30.In a group of 35 children, 18 enjoy drawing, 7 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  31. 31.In a group of 35 children, 17 like mangoes, 18 like bananas and 10 like both. How many like exactly one of the two?
  32. 32.In a group of 45 children, 16 like mangoes, 17 like bananas and 2 like both. How many like only bananas?
  33. 33.In a group of 33 children, 22 play chess, 7 play carrom and 3 play both. How many play at least one of the two?
  34. 34.In a group of 41 grown-ups, 20 drink tea, 27 drink coffee and 10 drink both. How many drink neither of the two?
  35. 35.In a group of 48 grown-ups, 22 drink tea, 22 drink coffee and 10 drink both. How many drink neither of the two?
  36. 36.In a group of 28 children, 15 like mangoes, 16 like bananas and 5 like both. How many like exactly one of the two?
  37. 37.In a group of 34 children, 21 sing Hindi songs, 7 sing English songs and 3 sing both. How many sing neither of the two?
  38. 38.In a group of 51 children, 26 play cricket, 23 play football and 6 play both. How many play neither of the two?
  39. 39.In a group of 20 children, 10 like mangoes, 10 like bananas and 4 like both. How many like only bananas?
  40. 40.In a group of 40 children, 23 enjoy drawing, 20 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?

Answer key

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

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