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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 226 · 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 26 children, 20 play cricket, 6 play football and 3 play both. How many play exactly one of the two?
  2. 2.In a group of 32 children, 13 play cricket, 11 play football and 2 play both. How many play only football?
  3. 3.In a group of 36 children, 14 sing Hindi songs, 18 sing English songs and 7 sing both. How many sing only English songs?
  4. 4.In a group of 41 grown-ups, 18 drink tea, 20 drink coffee and 4 drink both. How many drink exactly one of the two?
  5. 5.In a group of 31 grown-ups, 19 drink tea, 12 drink coffee and 3 drink both. How many drink only tea?
  6. 6.In a group of 38 grown-ups, 16 drink tea, 27 drink coffee and 11 drink both. How many drink only tea?
  7. 7.In a group of 42 children, 28 enjoy drawing, 15 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  8. 8.In a group of 26 children, 18 play cricket, 10 play football and 4 play both. How many play only football?
  9. 9.In a group of 27 children, 15 sing Hindi songs, 11 sing English songs and 6 sing both. How many sing neither of the two?
  10. 10.In a group of 26 grown-ups, 17 drink tea, 11 drink coffee and 8 drink both. How many drink at least one of the two?
  11. 11.In a group of 33 children, 17 play cricket, 12 play football and 6 play both. How many play only football?
  12. 12.In a group of 40 children, 24 play cricket, 13 play football and 6 play both. How many play exactly one of the two?
  13. 13.In a group of 37 children, 17 play cricket, 26 play football and 12 play both. How many play only football?
  14. 14.In a group of 30 children, 10 play chess, 8 play carrom and 2 play both. How many play only chess?
  15. 15.In a group of 52 children, 23 like mangoes, 22 like bananas and 3 like both. How many like only bananas?
  16. 16.In a group of 30 children, 16 like mangoes, 11 like bananas and 2 like both. How many like only mangoes?
  17. 17.In a group of 32 children, 16 play cricket, 23 play football and 10 play both. How many play neither of the two?
  18. 18.In a group of 41 grown-ups, 12 drink tea, 21 drink coffee and 2 drink both. How many drink exactly one of the two?
  19. 19.In a group of 31 grown-ups, 26 drink tea, 10 drink coffee and 7 drink both. How many drink at least one of the two?
  20. 20.In a group of 14 children, 8 sing Hindi songs, 9 sing English songs and 4 sing both. How many sing only English songs?
  21. 21.In a group of 29 grown-ups, 17 drink tea, 9 drink coffee and 5 drink both. How many drink only tea?
  22. 22.In a group of 32 children, 20 enjoy drawing, 9 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  23. 23.In a group of 19 children, 9 like mangoes, 13 like bananas and 5 like both. How many like neither of the two?
  24. 24.In a group of 38 children, 24 play chess, 17 play carrom and 12 play both. How many play at least one of the two?
  25. 25.In a group of 27 grown-ups, 20 drink tea, 17 drink coffee and 11 drink both. How many drink neither of the two?
  26. 26.In a group of 41 children, 21 sing Hindi songs, 8 sing English songs and 2 sing both. How many sing at least one of the two?
  27. 27.In a group of 33 children, 9 enjoy drawing, 15 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  28. 28.In a group of 34 children, 17 sing Hindi songs, 20 sing English songs and 5 sing both. How many sing only Hindi songs?
  29. 29.In a group of 36 children, 14 play cricket, 21 play football and 6 play both. How many play at least one of the two?
  30. 30.In a group of 25 grown-ups, 10 drink tea, 10 drink coffee and 7 drink both. How many drink at least one of the two?
  31. 31.In a group of 41 children, 27 like mangoes, 18 like bananas and 7 like both. How many like only bananas?
  32. 32.In a group of 51 children, 28 play cricket, 26 play football and 12 play both. How many play at least one of the two?
  33. 33.In a group of 38 children, 18 play chess, 16 play carrom and 10 play both. How many play at least one of the two?
  34. 34.In a group of 21 children, 9 like mangoes, 7 like bananas and 4 like both. How many like only bananas?
  35. 35.In a group of 34 children, 12 enjoy drawing, 24 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  36. 36.In a group of 34 grown-ups, 20 drink tea, 16 drink coffee and 4 drink both. How many drink only coffee?
  37. 37.In a group of 34 children, 16 play chess, 19 play carrom and 6 play both. How many play only carrom?
  38. 38.In a group of 52 children, 27 play cricket, 27 play football and 11 play both. How many play exactly one of the two?
  39. 39.In a group of 40 children, 23 like mangoes, 14 like bananas and 4 like both. How many like neither of the two?
  40. 40.In a group of 53 grown-ups, 25 drink tea, 21 drink coffee and 7 drink both. How many drink at least one of the two?

Answer key

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

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