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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 499 · 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 40 children, 25 sing Hindi songs, 19 sing English songs and 8 sing both. How many sing at least one of the two?
  2. 2.In a group of 36 children, 17 enjoy drawing, 20 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  3. 3.In a group of 43 children, 25 play chess, 13 play carrom and 6 play both. How many play at least one of the two?
  4. 4.In a group of 37 children, 15 play cricket, 19 play football and 11 play both. How many play only cricket?
  5. 5.In a group of 26 grown-ups, 14 drink tea, 14 drink coffee and 10 drink both. How many drink neither of the two?
  6. 6.In a group of 30 children, 17 enjoy drawing, 6 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  7. 7.In a group of 47 grown-ups, 19 drink tea, 30 drink coffee and 11 drink both. How many drink at least one of the two?
  8. 8.In a group of 19 children, 6 play cricket, 12 play football and 3 play both. How many play at least one of the two?
  9. 9.In a group of 52 children, 22 enjoy drawing, 22 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  10. 10.In a group of 33 children, 22 sing Hindi songs, 13 sing English songs and 10 sing both. How many sing at least one of the two?
  11. 11.In a group of 36 children, 21 enjoy drawing, 7 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  12. 12.In a group of 20 grown-ups, 16 drink tea, 11 drink coffee and 8 drink both. How many drink only coffee?
  13. 13.In a group of 36 children, 13 like mangoes, 12 like bananas and 4 like both. How many like neither of the two?
  14. 14.In a group of 24 children, 8 play chess, 15 play carrom and 4 play both. How many play exactly one of the two?
  15. 15.In a group of 34 children, 18 play cricket, 26 play football and 11 play both. How many play neither of the two?
  16. 16.In a group of 26 children, 19 play chess, 10 play carrom and 7 play both. How many play at least one of the two?
  17. 17.In a group of 26 children, 12 enjoy drawing, 12 enjoy dancing and 5 enjoy both. How many enjoy at least one of the two?
  18. 18.In a group of 21 children, 10 sing Hindi songs, 10 sing English songs and 3 sing both. How many sing at least one of the two?
  19. 19.In a group of 48 grown-ups, 30 drink tea, 28 drink coffee and 11 drink both. How many drink only tea?
  20. 20.In a group of 31 children, 5 sing Hindi songs, 16 sing English songs and 2 sing both. How many sing neither of the two?
  21. 21.In a group of 26 grown-ups, 18 drink tea, 13 drink coffee and 6 drink both. How many drink exactly one of the two?
  22. 22.In a group of 34 children, 7 sing Hindi songs, 22 sing English songs and 4 sing both. How many sing only Hindi songs?
  23. 23.In a group of 41 children, 23 play chess, 27 play carrom and 11 play both. How many play neither of the two?
  24. 24.In a group of 54 children, 23 play chess, 28 play carrom and 12 play both. How many play only carrom?
  25. 25.In a group of 30 children, 14 play chess, 18 play carrom and 7 play both. How many play neither of the two?
  26. 26.In a group of 29 children, 14 play chess, 16 play carrom and 3 play both. How many play neither of the two?
  27. 27.In a group of 33 children, 15 like mangoes, 18 like bananas and 10 like both. How many like at least one of the two?
  28. 28.In a group of 33 children, 9 play cricket, 14 play football and 5 play both. How many play only football?
  29. 29.In a group of 31 grown-ups, 16 drink tea, 25 drink coffee and 12 drink both. How many drink exactly one of the two?
  30. 30.In a group of 32 children, 14 like mangoes, 14 like bananas and 10 like both. How many like neither of the two?
  31. 31.In a group of 31 children, 21 sing Hindi songs, 11 sing English songs and 3 sing both. How many sing only English songs?
  32. 32.In a group of 38 children, 10 play cricket, 23 play football and 5 play both. How many play at least one of the two?
  33. 33.In a group of 21 grown-ups, 15 drink tea, 13 drink coffee and 9 drink both. How many drink exactly one of the two?
  34. 34.In a group of 39 children, 24 enjoy drawing, 11 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  35. 35.In a group of 25 grown-ups, 7 drink tea, 17 drink coffee and 3 drink both. How many drink only tea?
  36. 36.In a group of 53 children, 22 play chess, 25 play carrom and 6 play both. How many play exactly one of the two?
  37. 37.In a group of 32 children, 10 sing Hindi songs, 11 sing English songs and 2 sing both. How many sing neither of the two?
  38. 38.In a group of 47 children, 27 enjoy drawing, 22 enjoy dancing and 10 enjoy both. How many enjoy only dancing?
  39. 39.In a group of 34 children, 15 like mangoes, 14 like bananas and 9 like both. How many like only bananas?
  40. 40.In a group of 42 children, 26 sing Hindi songs, 13 sing English songs and 7 sing both. How many sing exactly one of the two?

Answer key

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

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