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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 110 · 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, 16 enjoy drawing, 7 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  2. 2.In a group of 41 children, 15 sing Hindi songs, 29 sing English songs and 9 sing both. How many sing exactly one of the two?
  3. 3.In a group of 41 children, 16 play cricket, 19 play football and 9 play both. How many play exactly one of the two?
  4. 4.In a group of 41 children, 26 play cricket, 11 play football and 8 play both. How many play at least one of the two?
  5. 5.In a group of 42 children, 10 play chess, 23 play carrom and 5 play both. How many play at least one of the two?
  6. 6.In a group of 29 grown-ups, 13 drink tea, 21 drink coffee and 6 drink both. How many drink exactly one of the two?
  7. 7.In a group of 54 grown-ups, 29 drink tea, 27 drink coffee and 11 drink both. How many drink only tea?
  8. 8.In a group of 52 children, 29 enjoy drawing, 22 enjoy dancing and 10 enjoy both. How many enjoy at least one of the two?
  9. 9.In a group of 41 children, 14 like mangoes, 28 like bananas and 10 like both. How many like at least one of the two?
  10. 10.In a group of 48 children, 26 enjoy drawing, 22 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  11. 11.In a group of 37 grown-ups, 29 drink tea, 15 drink coffee and 11 drink both. How many drink only tea?
  12. 12.In a group of 48 grown-ups, 16 drink tea, 22 drink coffee and 2 drink both. How many drink only tea?
  13. 13.In a group of 48 children, 18 enjoy drawing, 25 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  14. 14.In a group of 34 grown-ups, 19 drink tea, 6 drink coffee and 2 drink both. How many drink only coffee?
  15. 15.In a group of 18 children, 6 play chess, 10 play carrom and 3 play both. How many play only chess?
  16. 16.In a group of 40 children, 25 play cricket, 19 play football and 9 play both. How many play neither of the two?
  17. 17.In a group of 40 children, 31 play chess, 19 play carrom and 12 play both. How many play only carrom?
  18. 18.In a group of 33 children, 12 enjoy drawing, 21 enjoy dancing and 5 enjoy both. How many enjoy at least one of the two?
  19. 19.In a group of 36 grown-ups, 21 drink tea, 14 drink coffee and 2 drink both. How many drink only coffee?
  20. 20.In a group of 33 children, 23 play cricket, 19 play football and 10 play both. How many play exactly one of the two?
  21. 21.In a group of 43 children, 29 sing Hindi songs, 15 sing English songs and 12 sing both. How many sing neither of the two?
  22. 22.In a group of 39 children, 13 like mangoes, 19 like bananas and 6 like both. How many like only bananas?
  23. 23.In a group of 36 grown-ups, 12 drink tea, 21 drink coffee and 2 drink both. How many drink neither of the two?
  24. 24.In a group of 37 grown-ups, 23 drink tea, 17 drink coffee and 5 drink both. How many drink neither of the two?
  25. 25.In a group of 30 grown-ups, 20 drink tea, 13 drink coffee and 4 drink both. How many drink only tea?
  26. 26.In a group of 52 children, 27 enjoy drawing, 21 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  27. 27.In a group of 24 grown-ups, 16 drink tea, 8 drink coffee and 2 drink both. How many drink at least one of the two?
  28. 28.In a group of 17 children, 13 sing Hindi songs, 13 sing English songs and 10 sing both. How many sing at least one of the two?
  29. 29.In a group of 40 children, 21 play cricket, 17 play football and 12 play both. How many play at least one of the two?
  30. 30.In a group of 31 children, 20 play cricket, 11 play football and 6 play both. How many play only football?
  31. 31.In a group of 38 children, 11 enjoy drawing, 21 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  32. 32.In a group of 42 children, 30 sing Hindi songs, 19 sing English songs and 10 sing both. How many sing neither of the two?
  33. 33.In a group of 42 children, 26 play cricket, 14 play football and 11 play both. How many play only football?
  34. 34.In a group of 23 children, 12 play chess, 9 play carrom and 2 play both. How many play exactly one of the two?
  35. 35.In a group of 34 children, 15 enjoy drawing, 16 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  36. 36.In a group of 37 children, 20 play chess, 11 play carrom and 6 play both. How many play at least one of the two?
  37. 37.In a group of 23 children, 12 play cricket, 6 play football and 2 play both. How many play only football?
  38. 38.In a group of 33 grown-ups, 16 drink tea, 6 drink coffee and 3 drink both. How many drink only coffee?
  39. 39.In a group of 39 children, 23 play chess, 14 play carrom and 4 play both. How many play neither of the two?
  40. 40.In a group of 22 children, 10 enjoy drawing, 10 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?

Answer key

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

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