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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 122 · 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, 6 sing Hindi songs, 23 sing English songs and 3 sing both. How many sing neither of the two?
  2. 2.In a group of 33 children, 19 like mangoes, 15 like bananas and 9 like both. How many like only bananas?
  3. 3.In a group of 20 children, 8 sing Hindi songs, 8 sing English songs and 3 sing both. How many sing only Hindi songs?
  4. 4.In a group of 45 children, 23 like mangoes, 22 like bananas and 3 like both. How many like only mangoes?
  5. 5.In a group of 33 grown-ups, 25 drink tea, 16 drink coffee and 11 drink both. How many drink only tea?
  6. 6.In a group of 34 children, 15 like mangoes, 21 like bananas and 10 like both. How many like only mangoes?
  7. 7.In a group of 53 grown-ups, 20 drink tea, 29 drink coffee and 9 drink both. How many drink exactly one of the two?
  8. 8.In a group of 24 children, 5 play cricket, 6 play football and 2 play both. How many play at least one of the two?
  9. 9.In a group of 38 grown-ups, 22 drink tea, 12 drink coffee and 2 drink both. How many drink at least one of the two?
  10. 10.In a group of 37 children, 17 play cricket, 17 play football and 8 play both. How many play only football?
  11. 11.In a group of 29 children, 17 enjoy drawing, 18 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  12. 12.In a group of 48 grown-ups, 22 drink tea, 25 drink coffee and 7 drink both. How many drink neither of the two?
  13. 13.In a group of 17 children, 13 like mangoes, 13 like bananas and 10 like both. How many like only bananas?
  14. 14.In a group of 38 grown-ups, 16 drink tea, 22 drink coffee and 11 drink both. How many drink neither of the two?
  15. 15.In a group of 34 children, 17 like mangoes, 17 like bananas and 5 like both. How many like only bananas?
  16. 16.In a group of 44 children, 26 like mangoes, 21 like bananas and 6 like both. How many like exactly one of the two?
  17. 17.In a group of 49 grown-ups, 14 drink tea, 22 drink coffee and 2 drink both. How many drink at least one of the two?
  18. 18.In a group of 24 children, 8 like mangoes, 7 like bananas and 2 like both. How many like only bananas?
  19. 19.In a group of 36 children, 24 enjoy drawing, 19 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  20. 20.In a group of 35 grown-ups, 14 drink tea, 17 drink coffee and 4 drink both. How many drink only coffee?
  21. 21.In a group of 31 children, 16 like mangoes, 18 like bananas and 9 like both. How many like only bananas?
  22. 22.In a group of 25 children, 8 play chess, 9 play carrom and 5 play both. How many play only chess?
  23. 23.In a group of 24 children, 12 play chess, 14 play carrom and 7 play both. How many play neither of the two?
  24. 24.In a group of 40 grown-ups, 21 drink tea, 20 drink coffee and 12 drink both. How many drink neither of the two?
  25. 25.In a group of 19 children, 12 play cricket, 8 play football and 2 play both. How many play exactly one of the two?
  26. 26.In a group of 55 children, 24 enjoy drawing, 21 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  27. 27.In a group of 46 children, 24 play chess, 23 play carrom and 12 play both. How many play neither of the two?
  28. 28.In a group of 22 children, 12 like mangoes, 16 like bananas and 8 like both. How many like exactly one of the two?
  29. 29.In a group of 45 children, 22 play cricket, 24 play football and 8 play both. How many play at least one of the two?
  30. 30.In a group of 26 children, 18 play chess, 9 play carrom and 5 play both. How many play exactly one of the two?
  31. 31.In a group of 59 grown-ups, 30 drink tea, 31 drink coffee and 11 drink both. How many drink only coffee?
  32. 32.In a group of 27 children, 9 enjoy drawing, 11 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  33. 33.In a group of 50 children, 23 like mangoes, 20 like bananas and 4 like both. How many like at least one of the two?
  34. 34.In a group of 26 grown-ups, 11 drink tea, 7 drink coffee and 4 drink both. How many drink only tea?
  35. 35.In a group of 23 children, 13 play cricket, 16 play football and 10 play both. How many play at least one of the two?
  36. 36.In a group of 27 children, 10 play cricket, 10 play football and 5 play both. How many play only football?
  37. 37.In a group of 31 children, 6 play chess, 17 play carrom and 2 play both. How many play only chess?
  38. 38.In a group of 37 children, 23 enjoy drawing, 19 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  39. 39.In a group of 24 children, 8 play chess, 16 play carrom and 2 play both. How many play at least one of the two?
  40. 40.In a group of 25 children, 17 enjoy drawing, 15 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?

Answer key

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

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