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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 522 · 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 45 children, 21 enjoy drawing, 28 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  2. 2.In a group of 28 grown-ups, 15 drink tea, 20 drink coffee and 9 drink both. How many drink only coffee?
  3. 3.In a group of 41 children, 18 enjoy drawing, 18 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  4. 4.In a group of 26 grown-ups, 15 drink tea, 10 drink coffee and 3 drink both. How many drink exactly one of the two?
  5. 5.In a group of 33 children, 10 play chess, 24 play carrom and 4 play both. How many play at least one of the two?
  6. 6.In a group of 29 children, 24 play chess, 9 play carrom and 5 play both. How many play only carrom?
  7. 7.In a group of 47 children, 27 sing Hindi songs, 18 sing English songs and 10 sing both. How many sing only Hindi songs?
  8. 8.In a group of 54 children, 28 sing Hindi songs, 22 sing English songs and 9 sing both. How many sing exactly one of the two?
  9. 9.In a group of 45 children, 20 play cricket, 14 play football and 4 play both. How many play only cricket?
  10. 10.In a group of 29 children, 12 enjoy drawing, 11 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  11. 11.In a group of 49 children, 22 like mangoes, 24 like bananas and 7 like both. How many like only bananas?
  12. 12.In a group of 32 grown-ups, 19 drink tea, 16 drink coffee and 11 drink both. How many drink neither of the two?
  13. 13.In a group of 40 children, 26 sing Hindi songs, 19 sing English songs and 12 sing both. How many sing neither of the two?
  14. 14.In a group of 51 children, 17 like mangoes, 29 like bananas and 9 like both. How many like at least one of the two?
  15. 15.In a group of 49 children, 18 play chess, 22 play carrom and 5 play both. How many play exactly one of the two?
  16. 16.In a group of 45 children, 20 like mangoes, 31 like bananas and 11 like both. How many like at least one of the two?
  17. 17.In a group of 34 children, 18 play cricket, 9 play football and 3 play both. How many play only football?
  18. 18.In a group of 41 grown-ups, 19 drink tea, 27 drink coffee and 11 drink both. How many drink at least one of the two?
  19. 19.In a group of 37 grown-ups, 20 drink tea, 10 drink coffee and 6 drink both. How many drink only coffee?
  20. 20.In a group of 35 children, 26 like mangoes, 15 like bananas and 7 like both. How many like at least one of the two?
  21. 21.In a group of 38 children, 27 like mangoes, 21 like bananas and 12 like both. How many like neither of the two?
  22. 22.In a group of 33 grown-ups, 14 drink tea, 14 drink coffee and 9 drink both. How many drink exactly one of the two?
  23. 23.In a group of 23 children, 13 like mangoes, 13 like bananas and 9 like both. How many like neither of the two?
  24. 24.In a group of 26 children, 9 play chess, 12 play carrom and 6 play both. How many play exactly one of the two?
  25. 25.In a group of 48 children, 26 play chess, 23 play carrom and 10 play both. How many play only chess?
  26. 26.In a group of 44 grown-ups, 18 drink tea, 25 drink coffee and 8 drink both. How many drink only tea?
  27. 27.In a group of 29 children, 11 play cricket, 10 play football and 5 play both. How many play only cricket?
  28. 28.In a group of 42 children, 14 sing Hindi songs, 19 sing English songs and 3 sing both. How many sing only English songs?
  29. 29.In a group of 42 children, 19 play cricket, 23 play football and 9 play both. How many play exactly one of the two?
  30. 30.In a group of 33 children, 24 play cricket, 16 play football and 12 play both. How many play only cricket?
  31. 31.In a group of 23 children, 14 sing Hindi songs, 12 sing English songs and 9 sing both. How many sing neither of the two?
  32. 32.In a group of 28 children, 19 play cricket, 13 play football and 5 play both. How many play only cricket?
  33. 33.In a group of 33 grown-ups, 18 drink tea, 16 drink coffee and 6 drink both. How many drink only coffee?
  34. 34.In a group of 32 grown-ups, 9 drink tea, 12 drink coffee and 3 drink both. How many drink only coffee?
  35. 35.In a group of 35 children, 19 enjoy drawing, 22 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  36. 36.In a group of 38 children, 21 play chess, 19 play carrom and 6 play both. How many play at least one of the two?
  37. 37.In a group of 25 children, 14 play cricket, 15 play football and 9 play both. How many play exactly one of the two?
  38. 38.In a group of 55 children, 32 like mangoes, 21 like bananas and 12 like both. How many like only mangoes?
  39. 39.In a group of 35 children, 19 like mangoes, 10 like bananas and 6 like both. How many like only mangoes?
  40. 40.In a group of 34 children, 16 sing Hindi songs, 21 sing English songs and 7 sing both. How many sing exactly one of the two?

Answer key

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

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