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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 268 · 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 46 children, 21 enjoy drawing, 24 enjoy dancing and 10 enjoy both. How many enjoy at least one of the two?
  2. 2.In a group of 35 children, 19 enjoy drawing, 18 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  3. 3.In a group of 36 children, 29 play cricket, 16 play football and 10 play both. How many play only football?
  4. 4.In a group of 47 grown-ups, 26 drink tea, 17 drink coffee and 11 drink both. How many drink only tea?
  5. 5.In a group of 35 children, 26 play cricket, 13 play football and 6 play both. How many play only cricket?
  6. 6.In a group of 29 children, 7 play cricket, 17 play football and 4 play both. How many play neither of the two?
  7. 7.In a group of 45 children, 29 like mangoes, 19 like bananas and 9 like both. How many like at least one of the two?
  8. 8.In a group of 21 children, 7 sing Hindi songs, 8 sing English songs and 3 sing both. How many sing only English songs?
  9. 9.In a group of 38 children, 14 play chess, 19 play carrom and 2 play both. How many play only chess?
  10. 10.In a group of 48 grown-ups, 21 drink tea, 18 drink coffee and 3 drink both. How many drink only tea?
  11. 11.In a group of 24 grown-ups, 16 drink tea, 10 drink coffee and 7 drink both. How many drink exactly one of the two?
  12. 12.In a group of 27 children, 8 sing Hindi songs, 17 sing English songs and 3 sing both. How many sing only Hindi songs?
  13. 13.In a group of 35 children, 11 like mangoes, 18 like bananas and 5 like both. How many like at least one of the two?
  14. 14.In a group of 48 grown-ups, 21 drink tea, 26 drink coffee and 11 drink both. How many drink neither of the two?
  15. 15.In a group of 37 children, 15 enjoy drawing, 13 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  16. 16.In a group of 39 grown-ups, 21 drink tea, 8 drink coffee and 3 drink both. How many drink at least one of the two?
  17. 17.In a group of 34 children, 24 play cricket, 12 play football and 4 play both. How many play exactly one of the two?
  18. 18.In a group of 54 children, 28 play cricket, 23 play football and 9 play both. How many play at least one of the two?
  19. 19.In a group of 32 children, 16 like mangoes, 25 like bananas and 12 like both. How many like at least one of the two?
  20. 20.In a group of 39 grown-ups, 20 drink tea, 20 drink coffee and 4 drink both. How many drink exactly one of the two?
  21. 21.In a group of 23 children, 12 play cricket, 12 play football and 6 play both. How many play neither of the two?
  22. 22.In a group of 25 grown-ups, 16 drink tea, 11 drink coffee and 5 drink both. How many drink at least one of the two?
  23. 23.In a group of 47 children, 30 sing Hindi songs, 21 sing English songs and 11 sing both. How many sing at least one of the two?
  24. 24.In a group of 19 children, 12 sing Hindi songs, 13 sing English songs and 7 sing both. How many sing neither of the two?
  25. 25.In a group of 47 children, 19 enjoy drawing, 21 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  26. 26.In a group of 38 children, 16 play chess, 18 play carrom and 5 play both. How many play only carrom?
  27. 27.In a group of 32 children, 13 like mangoes, 11 like bananas and 4 like both. How many like only bananas?
  28. 28.In a group of 38 children, 23 play cricket, 11 play football and 3 play both. How many play only football?
  29. 29.In a group of 26 children, 12 play chess, 16 play carrom and 4 play both. How many play exactly one of the two?
  30. 30.In a group of 24 children, 17 enjoy drawing, 15 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  31. 31.In a group of 45 children, 32 sing Hindi songs, 16 sing English songs and 12 sing both. How many sing only English songs?
  32. 32.In a group of 37 children, 22 play chess, 15 play carrom and 10 play both. How many play at least one of the two?
  33. 33.In a group of 37 grown-ups, 12 drink tea, 22 drink coffee and 3 drink both. How many drink only coffee?
  34. 34.In a group of 32 children, 16 play cricket, 13 play football and 6 play both. How many play neither of the two?
  35. 35.In a group of 45 children, 30 play cricket, 25 play football and 12 play both. How many play only cricket?
  36. 36.In a group of 24 children, 8 play chess, 16 play carrom and 2 play both. How many play exactly one of the two?
  37. 37.In a group of 33 children, 13 like mangoes, 14 like bananas and 9 like both. How many like only bananas?
  38. 38.In a group of 45 children, 11 play chess, 26 play carrom and 6 play both. How many play neither of the two?
  39. 39.In a group of 32 children, 8 play cricket, 18 play football and 2 play both. How many play only cricket?
  40. 40.In a group of 41 children, 25 sing Hindi songs, 19 sing English songs and 5 sing both. How many sing neither of the two?

Answer key

  1. 35
  2. 6
  3. 6
  4. 15
  5. 20
  6. 9
  7. 39
  8. 5
  9. 12
  10. 18
  11. 12
  12. 5
  13. 24
  14. 12
  15. 24
  16. 26
  17. 28
  18. 42
  19. 29
  20. 32
  21. 5
  22. 22
  23. 40
  24. 1
  25. 33
  26. 13
  27. 7
  28. 8
  29. 20
  30. 4
  31. 4
  32. 27
  33. 19
  34. 9
  35. 18
  36. 20
  37. 5
  38. 14
  39. 6
  40. 2

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