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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 219 · 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 27 children, 20 sing Hindi songs, 8 sing English songs and 3 sing both. How many sing exactly one of the two?
  2. 2.In a group of 24 children, 13 sing Hindi songs, 8 sing English songs and 3 sing both. How many sing exactly one of the two?
  3. 3.In a group of 29 children, 12 play cricket, 10 play football and 4 play both. How many play only football?
  4. 4.In a group of 40 grown-ups, 17 drink tea, 20 drink coffee and 3 drink both. How many drink only coffee?
  5. 5.In a group of 31 children, 19 like mangoes, 15 like bananas and 5 like both. How many like neither of the two?
  6. 6.In a group of 30 children, 22 enjoy drawing, 9 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  7. 7.In a group of 35 children, 14 sing Hindi songs, 26 sing English songs and 9 sing both. How many sing at least one of the two?
  8. 8.In a group of 30 children, 14 enjoy drawing, 14 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  9. 9.In a group of 49 children, 25 enjoy drawing, 29 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  10. 10.In a group of 31 children, 19 play cricket, 12 play football and 8 play both. How many play exactly one of the two?
  11. 11.In a group of 43 children, 28 enjoy drawing, 15 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  12. 12.In a group of 52 children, 32 play chess, 18 play carrom and 12 play both. How many play only chess?
  13. 13.In a group of 43 children, 27 play cricket, 14 play football and 7 play both. How many play at least one of the two?
  14. 14.In a group of 54 children, 26 play cricket, 22 play football and 6 play both. How many play at least one of the two?
  15. 15.In a group of 29 children, 6 play chess, 20 play carrom and 3 play both. How many play exactly one of the two?
  16. 16.In a group of 30 children, 20 sing Hindi songs, 20 sing English songs and 12 sing both. How many sing at least one of the two?
  17. 17.In a group of 31 children, 14 sing Hindi songs, 18 sing English songs and 2 sing both. How many sing at least one of the two?
  18. 18.In a group of 35 children, 11 play cricket, 16 play football and 5 play both. How many play only cricket?
  19. 19.In a group of 23 grown-ups, 10 drink tea, 10 drink coffee and 5 drink both. How many drink only coffee?
  20. 20.In a group of 43 children, 26 play chess, 11 play carrom and 7 play both. How many play only carrom?
  21. 21.In a group of 42 children, 12 play chess, 25 play carrom and 7 play both. How many play only carrom?
  22. 22.In a group of 50 children, 24 enjoy drawing, 18 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  23. 23.In a group of 29 grown-ups, 16 drink tea, 9 drink coffee and 4 drink both. How many drink at least one of the two?
  24. 24.In a group of 42 grown-ups, 11 drink tea, 25 drink coffee and 8 drink both. How many drink at least one of the two?
  25. 25.In a group of 44 children, 26 like mangoes, 16 like bananas and 6 like both. How many like neither of the two?
  26. 26.In a group of 17 children, 7 enjoy drawing, 8 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  27. 27.In a group of 47 children, 18 play chess, 23 play carrom and 4 play both. How many play only chess?
  28. 28.In a group of 31 children, 16 sing Hindi songs, 17 sing English songs and 11 sing both. How many sing exactly one of the two?
  29. 29.In a group of 16 grown-ups, 10 drink tea, 9 drink coffee and 6 drink both. How many drink only coffee?
  30. 30.In a group of 45 children, 23 enjoy drawing, 21 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  31. 31.In a group of 36 children, 10 sing Hindi songs, 24 sing English songs and 5 sing both. How many sing exactly one of the two?
  32. 32.In a group of 33 children, 19 sing Hindi songs, 23 sing English songs and 11 sing both. How many sing only Hindi songs?
  33. 33.In a group of 29 grown-ups, 23 drink tea, 9 drink coffee and 5 drink both. How many drink at least one of the two?
  34. 34.In a group of 42 children, 16 like mangoes, 26 like bananas and 10 like both. How many like only mangoes?
  35. 35.In a group of 21 children, 8 enjoy drawing, 11 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  36. 36.In a group of 40 children, 30 play chess, 21 play carrom and 12 play both. How many play only carrom?
  37. 37.In a group of 53 grown-ups, 29 drink tea, 26 drink coffee and 12 drink both. How many drink only coffee?
  38. 38.In a group of 19 children, 10 play chess, 7 play carrom and 4 play both. How many play only carrom?
  39. 39.In a group of 30 children, 9 play cricket, 15 play football and 6 play both. How many play only football?
  40. 40.In a group of 21 children, 17 play chess, 11 play carrom and 8 play both. How many play neither of the two?

Answer key

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

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