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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 582 · 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 46 children, 25 enjoy drawing, 20 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  2. 2.In a group of 40 children, 18 like mangoes, 15 like bananas and 2 like both. How many like exactly one of the two?
  3. 3.In a group of 30 children, 14 play chess, 14 play carrom and 3 play both. How many play exactly one of the two?
  4. 4.In a group of 24 children, 14 play cricket, 13 play football and 7 play both. How many play neither of the two?
  5. 5.In a group of 43 children, 14 play chess, 29 play carrom and 11 play both. How many play only chess?
  6. 6.In a group of 47 children, 27 play chess, 17 play carrom and 11 play both. How many play neither of the two?
  7. 7.In a group of 36 children, 23 play chess, 17 play carrom and 5 play both. How many play neither of the two?
  8. 8.In a group of 38 children, 26 enjoy drawing, 14 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  9. 9.In a group of 36 children, 24 play cricket, 13 play football and 9 play both. How many play exactly one of the two?
  10. 10.In a group of 37 children, 18 like mangoes, 13 like bananas and 9 like both. How many like only mangoes?
  11. 11.In a group of 50 children, 22 enjoy drawing, 26 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  12. 12.In a group of 41 grown-ups, 10 drink tea, 24 drink coffee and 4 drink both. How many drink only tea?
  13. 13.In a group of 23 children, 10 play chess, 16 play carrom and 5 play both. How many play only chess?
  14. 14.In a group of 30 children, 6 play cricket, 16 play football and 2 play both. How many play only football?
  15. 15.In a group of 38 children, 13 like mangoes, 24 like bananas and 8 like both. How many like at least one of the two?
  16. 16.In a group of 45 children, 24 like mangoes, 21 like bananas and 5 like both. How many like neither of the two?
  17. 17.In a group of 46 grown-ups, 29 drink tea, 21 drink coffee and 10 drink both. How many drink exactly one of the two?
  18. 18.In a group of 42 children, 21 play chess, 13 play carrom and 6 play both. How many play only chess?
  19. 19.In a group of 20 grown-ups, 10 drink tea, 8 drink coffee and 3 drink both. How many drink at least one of the two?
  20. 20.In a group of 37 children, 16 sing Hindi songs, 10 sing English songs and 2 sing both. How many sing neither of the two?
  21. 21.In a group of 36 children, 22 enjoy drawing, 21 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  22. 22.In a group of 18 children, 7 play cricket, 8 play football and 2 play both. How many play at least one of the two?
  23. 23.In a group of 30 children, 13 like mangoes, 10 like bananas and 2 like both. How many like only mangoes?
  24. 24.In a group of 21 grown-ups, 8 drink tea, 7 drink coffee and 2 drink both. How many drink exactly one of the two?
  25. 25.In a group of 27 children, 10 enjoy drawing, 19 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  26. 26.In a group of 35 children, 15 sing Hindi songs, 21 sing English songs and 2 sing both. How many sing exactly one of the two?
  27. 27.In a group of 32 children, 17 enjoy drawing, 22 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  28. 28.In a group of 35 grown-ups, 18 drink tea, 21 drink coffee and 6 drink both. How many drink exactly one of the two?
  29. 29.In a group of 44 children, 27 like mangoes, 13 like bananas and 7 like both. How many like exactly one of the two?
  30. 30.In a group of 51 grown-ups, 21 drink tea, 22 drink coffee and 5 drink both. How many drink neither of the two?
  31. 31.In a group of 28 children, 20 play chess, 15 play carrom and 11 play both. How many play at least one of the two?
  32. 32.In a group of 51 children, 23 enjoy drawing, 27 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  33. 33.In a group of 19 children, 8 enjoy drawing, 6 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  34. 34.In a group of 39 children, 12 sing Hindi songs, 27 sing English songs and 7 sing both. How many sing exactly one of the two?
  35. 35.In a group of 25 children, 7 like mangoes, 11 like bananas and 2 like both. How many like only mangoes?
  36. 36.In a group of 41 children, 23 sing Hindi songs, 14 sing English songs and 3 sing both. How many sing only Hindi songs?
  37. 37.In a group of 31 children, 14 like mangoes, 24 like bananas and 11 like both. How many like only mangoes?
  38. 38.In a group of 38 children, 20 play cricket, 24 play football and 9 play both. How many play at least one of the two?
  39. 39.In a group of 32 children, 10 play chess, 9 play carrom and 2 play both. How many play neither of the two?
  40. 40.In a group of 26 children, 17 enjoy drawing, 11 enjoy dancing and 5 enjoy both. How many enjoy only dancing?

Answer key

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

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