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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 314 · 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, 26 sing Hindi songs, 21 sing English songs and 11 sing both. How many sing neither of the two?
  2. 2.In a group of 32 children, 11 like mangoes, 27 like bananas and 7 like both. How many like only bananas?
  3. 3.In a group of 48 children, 27 play chess, 29 play carrom and 9 play both. How many play only carrom?
  4. 4.In a group of 38 children, 25 play cricket, 20 play football and 8 play both. How many play neither of the two?
  5. 5.In a group of 39 grown-ups, 9 drink tea, 20 drink coffee and 3 drink both. How many drink neither of the two?
  6. 6.In a group of 34 children, 16 enjoy drawing, 17 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  7. 7.In a group of 22 children, 14 like mangoes, 12 like bananas and 8 like both. How many like neither of the two?
  8. 8.In a group of 30 children, 11 play chess, 23 play carrom and 8 play both. How many play only carrom?
  9. 9.In a group of 55 children, 23 play cricket, 24 play football and 7 play both. How many play only cricket?
  10. 10.In a group of 48 grown-ups, 18 drink tea, 19 drink coffee and 2 drink both. How many drink at least one of the two?
  11. 11.In a group of 37 grown-ups, 23 drink tea, 22 drink coffee and 9 drink both. How many drink at least one of the two?
  12. 12.In a group of 35 children, 16 play cricket, 25 play football and 8 play both. How many play only football?
  13. 13.In a group of 29 children, 17 play cricket, 17 play football and 11 play both. How many play neither of the two?
  14. 14.In a group of 46 children, 26 play chess, 18 play carrom and 7 play both. How many play at least one of the two?
  15. 15.In a group of 26 children, 11 sing Hindi songs, 7 sing English songs and 3 sing both. How many sing only English songs?
  16. 16.In a group of 30 grown-ups, 18 drink tea, 11 drink coffee and 4 drink both. How many drink at least one of the two?
  17. 17.In a group of 29 children, 14 play chess, 18 play carrom and 5 play both. How many play neither of the two?
  18. 18.In a group of 21 children, 7 sing Hindi songs, 9 sing English songs and 3 sing both. How many sing only English songs?
  19. 19.In a group of 30 children, 12 play cricket, 12 play football and 5 play both. How many play only football?
  20. 20.In a group of 31 grown-ups, 11 drink tea, 21 drink coffee and 8 drink both. How many drink exactly one of the two?
  21. 21.In a group of 30 children, 9 enjoy drawing, 24 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  22. 22.In a group of 36 children, 15 sing Hindi songs, 28 sing English songs and 12 sing both. How many sing exactly one of the two?
  23. 23.In a group of 46 children, 14 play cricket, 26 play football and 7 play both. How many play neither of the two?
  24. 24.In a group of 34 children, 27 sing Hindi songs, 12 sing English songs and 9 sing both. How many sing only Hindi songs?
  25. 25.In a group of 48 children, 26 enjoy drawing, 20 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  26. 26.In a group of 39 children, 19 play cricket, 27 play football and 8 play both. How many play exactly one of the two?
  27. 27.In a group of 30 children, 13 play chess, 18 play carrom and 9 play both. How many play only chess?
  28. 28.In a group of 38 children, 19 play cricket, 27 play football and 11 play both. How many play only cricket?
  29. 29.In a group of 34 grown-ups, 12 drink tea, 14 drink coffee and 7 drink both. How many drink neither of the two?
  30. 30.In a group of 32 grown-ups, 16 drink tea, 12 drink coffee and 8 drink both. How many drink only coffee?
  31. 31.In a group of 41 children, 22 play chess, 17 play carrom and 9 play both. How many play at least one of the two?
  32. 32.In a group of 35 children, 19 play cricket, 11 play football and 7 play both. How many play only football?
  33. 33.In a group of 52 children, 17 sing Hindi songs, 29 sing English songs and 9 sing both. How many sing exactly one of the two?
  34. 34.In a group of 37 children, 18 play cricket, 22 play football and 10 play both. How many play neither of the two?
  35. 35.In a group of 25 children, 17 enjoy drawing, 12 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  36. 36.In a group of 34 children, 20 enjoy drawing, 11 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  37. 37.In a group of 48 children, 16 like mangoes, 20 like bananas and 2 like both. How many like at least one of the two?
  38. 38.In a group of 34 children, 11 play cricket, 19 play football and 2 play both. How many play neither of the two?
  39. 39.In a group of 27 children, 5 play cricket, 18 play football and 2 play both. How many play only football?
  40. 40.In a group of 26 children, 12 play cricket, 17 play football and 4 play both. How many play only cricket?

Answer key

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

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