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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 675 · 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, 19 enjoy drawing, 13 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  2. 2.In a group of 32 children, 7 like mangoes, 21 like bananas and 3 like both. How many like at least one of the two?
  3. 3.In a group of 44 children, 20 like mangoes, 22 like bananas and 2 like both. How many like neither of the two?
  4. 4.In a group of 40 children, 26 sing Hindi songs, 19 sing English songs and 6 sing both. How many sing exactly one of the two?
  5. 5.In a group of 29 children, 15 enjoy drawing, 13 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  6. 6.In a group of 31 children, 14 enjoy drawing, 20 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  7. 7.In a group of 42 children, 18 play chess, 18 play carrom and 8 play both. How many play only chess?
  8. 8.In a group of 31 children, 17 enjoy drawing, 12 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  9. 9.In a group of 34 children, 8 like mangoes, 23 like bananas and 3 like both. How many like only bananas?
  10. 10.In a group of 31 children, 11 play chess, 12 play carrom and 7 play both. How many play only chess?
  11. 11.In a group of 47 children, 17 enjoy drawing, 31 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  12. 12.In a group of 31 children, 18 play cricket, 21 play football and 10 play both. How many play only football?
  13. 13.In a group of 38 children, 19 play cricket, 17 play football and 12 play both. How many play at least one of the two?
  14. 14.In a group of 34 children, 16 like mangoes, 18 like bananas and 10 like both. How many like only mangoes?
  15. 15.In a group of 22 children, 8 like mangoes, 7 like bananas and 3 like both. How many like only bananas?
  16. 16.In a group of 20 children, 12 play chess, 13 play carrom and 6 play both. How many play neither of the two?
  17. 17.In a group of 34 children, 12 enjoy drawing, 15 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  18. 18.In a group of 47 children, 28 play cricket, 23 play football and 9 play both. How many play only football?
  19. 19.In a group of 43 children, 9 enjoy drawing, 25 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  20. 20.In a group of 24 grown-ups, 7 drink tea, 18 drink coffee and 2 drink both. How many drink only coffee?
  21. 21.In a group of 40 children, 17 play chess, 28 play carrom and 8 play both. How many play exactly one of the two?
  22. 22.In a group of 48 children, 25 like mangoes, 31 like bananas and 12 like both. How many like only bananas?
  23. 23.In a group of 28 children, 5 sing Hindi songs, 22 sing English songs and 2 sing both. How many sing only Hindi songs?
  24. 24.In a group of 26 children, 15 play chess, 11 play carrom and 4 play both. How many play exactly one of the two?
  25. 25.In a group of 20 grown-ups, 13 drink tea, 10 drink coffee and 5 drink both. How many drink only tea?
  26. 26.In a group of 41 children, 19 play cricket, 24 play football and 11 play both. How many play at least one of the two?
  27. 27.In a group of 35 grown-ups, 15 drink tea, 17 drink coffee and 11 drink both. How many drink exactly one of the two?
  28. 28.In a group of 32 grown-ups, 8 drink tea, 21 drink coffee and 2 drink both. How many drink neither of the two?
  29. 29.In a group of 53 children, 26 enjoy drawing, 26 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  30. 30.In a group of 38 children, 26 like mangoes, 18 like bananas and 12 like both. How many like neither of the two?
  31. 31.In a group of 37 children, 8 play chess, 20 play carrom and 5 play both. How many play exactly one of the two?
  32. 32.In a group of 42 children, 18 enjoy drawing, 21 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  33. 33.In a group of 27 children, 14 sing Hindi songs, 18 sing English songs and 6 sing both. How many sing exactly one of the two?
  34. 34.In a group of 27 grown-ups, 18 drink tea, 9 drink coffee and 6 drink both. How many drink neither of the two?
  35. 35.In a group of 34 children, 12 enjoy drawing, 20 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  36. 36.In a group of 30 children, 12 play chess, 11 play carrom and 2 play both. How many play exactly one of the two?
  37. 37.In a group of 47 children, 28 like mangoes, 16 like bananas and 12 like both. How many like at least one of the two?
  38. 38.In a group of 43 children, 14 play cricket, 25 play football and 6 play both. How many play exactly one of the two?
  39. 39.In a group of 45 grown-ups, 14 drink tea, 28 drink coffee and 10 drink both. How many drink only coffee?
  40. 40.In a group of 41 grown-ups, 29 drink tea, 18 drink coffee and 10 drink both. How many drink exactly one of the two?

Answer key

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

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