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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 549 · 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 33 children, 20 play cricket, 15 play football and 12 play both. How many play exactly one of the two?
  2. 2.In a group of 42 grown-ups, 14 drink tea, 23 drink coffee and 9 drink both. How many drink exactly one of the two?
  3. 3.In a group of 32 children, 18 like mangoes, 21 like bananas and 12 like both. How many like at least one of the two?
  4. 4.In a group of 23 children, 8 like mangoes, 8 like bananas and 2 like both. How many like at least one of the two?
  5. 5.In a group of 30 children, 21 play chess, 18 play carrom and 10 play both. How many play exactly one of the two?
  6. 6.In a group of 21 children, 10 like mangoes, 12 like bananas and 6 like both. How many like at least one of the two?
  7. 7.In a group of 52 grown-ups, 23 drink tea, 27 drink coffee and 9 drink both. How many drink only coffee?
  8. 8.In a group of 41 grown-ups, 18 drink tea, 15 drink coffee and 5 drink both. How many drink only tea?
  9. 9.In a group of 46 children, 25 enjoy drawing, 23 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  10. 10.In a group of 39 children, 23 like mangoes, 12 like bananas and 5 like both. How many like neither of the two?
  11. 11.In a group of 47 children, 20 play cricket, 23 play football and 6 play both. How many play neither of the two?
  12. 12.In a group of 42 children, 24 like mangoes, 15 like bananas and 5 like both. How many like only bananas?
  13. 13.In a group of 44 children, 14 enjoy drawing, 22 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  14. 14.In a group of 43 children, 17 sing Hindi songs, 31 sing English songs and 12 sing both. How many sing neither of the two?
  15. 15.In a group of 32 children, 22 play cricket, 8 play football and 4 play both. How many play only cricket?
  16. 16.In a group of 33 children, 15 play cricket, 19 play football and 3 play both. How many play exactly one of the two?
  17. 17.In a group of 36 children, 9 play chess, 18 play carrom and 4 play both. How many play exactly one of the two?
  18. 18.In a group of 21 grown-ups, 10 drink tea, 10 drink coffee and 2 drink both. How many drink only coffee?
  19. 19.In a group of 35 children, 30 play chess, 14 play carrom and 10 play both. How many play neither of the two?
  20. 20.In a group of 33 grown-ups, 14 drink tea, 13 drink coffee and 8 drink both. How many drink at least one of the two?
  21. 21.In a group of 35 children, 18 play cricket, 9 play football and 5 play both. How many play only football?
  22. 22.In a group of 40 children, 24 play chess, 18 play carrom and 6 play both. How many play neither of the two?
  23. 23.In a group of 42 children, 26 enjoy drawing, 16 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  24. 24.In a group of 49 children, 27 play cricket, 28 play football and 8 play both. How many play only football?
  25. 25.In a group of 43 children, 23 play chess, 23 play carrom and 12 play both. How many play only chess?
  26. 26.In a group of 24 children, 12 play cricket, 16 play football and 9 play both. How many play only cricket?
  27. 27.In a group of 31 children, 24 enjoy drawing, 15 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  28. 28.In a group of 28 children, 14 enjoy drawing, 23 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  29. 29.In a group of 45 grown-ups, 27 drink tea, 21 drink coffee and 9 drink both. How many drink only coffee?
  30. 30.In a group of 48 children, 22 sing Hindi songs, 27 sing English songs and 10 sing both. How many sing only English songs?
  31. 31.In a group of 44 children, 23 enjoy drawing, 31 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  32. 32.In a group of 40 children, 20 enjoy drawing, 17 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  33. 33.In a group of 29 grown-ups, 10 drink tea, 7 drink coffee and 3 drink both. How many drink neither of the two?
  34. 34.In a group of 36 children, 17 play chess, 13 play carrom and 6 play both. How many play at least one of the two?
  35. 35.In a group of 35 children, 16 like mangoes, 17 like bananas and 11 like both. How many like only bananas?
  36. 36.In a group of 47 grown-ups, 25 drink tea, 20 drink coffee and 11 drink both. How many drink at least one of the two?
  37. 37.In a group of 37 grown-ups, 16 drink tea, 25 drink coffee and 5 drink both. How many drink only coffee?
  38. 38.In a group of 21 children, 9 like mangoes, 9 like bananas and 4 like both. How many like only bananas?
  39. 39.In a group of 41 children, 21 like mangoes, 16 like bananas and 2 like both. How many like at least one of the two?
  40. 40.In a group of 33 children, 10 enjoy drawing, 22 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?

Answer key

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

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