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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 112 · 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 29 children, 14 enjoy drawing, 12 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  2. 2.In a group of 27 children, 21 enjoy drawing, 13 enjoy dancing and 10 enjoy both. How many enjoy at least one of the two?
  3. 3.In a group of 38 children, 26 like mangoes, 14 like bananas and 7 like both. How many like only mangoes?
  4. 4.In a group of 38 children, 18 enjoy drawing, 13 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  5. 5.In a group of 30 children, 16 play chess, 20 play carrom and 8 play both. How many play exactly one of the two?
  6. 6.In a group of 48 children, 32 enjoy drawing, 27 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  7. 7.In a group of 17 children, 8 play chess, 9 play carrom and 2 play both. How many play neither of the two?
  8. 8.In a group of 43 children, 11 play chess, 28 play carrom and 8 play both. How many play only carrom?
  9. 9.In a group of 46 children, 18 play chess, 30 play carrom and 12 play both. How many play at least one of the two?
  10. 10.In a group of 44 children, 10 play chess, 24 play carrom and 4 play both. How many play only carrom?
  11. 11.In a group of 21 children, 15 play chess, 12 play carrom and 8 play both. How many play neither of the two?
  12. 12.In a group of 39 children, 25 enjoy drawing, 8 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  13. 13.In a group of 44 children, 28 sing Hindi songs, 25 sing English songs and 12 sing both. How many sing exactly one of the two?
  14. 14.In a group of 38 children, 13 like mangoes, 15 like bananas and 3 like both. How many like exactly one of the two?
  15. 15.In a group of 48 children, 21 enjoy drawing, 22 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  16. 16.In a group of 25 grown-ups, 21 drink tea, 13 drink coffee and 10 drink both. How many drink at least one of the two?
  17. 17.In a group of 36 children, 17 sing Hindi songs, 18 sing English songs and 2 sing both. How many sing exactly one of the two?
  18. 18.In a group of 40 children, 26 play cricket, 17 play football and 8 play both. How many play exactly one of the two?
  19. 19.In a group of 28 children, 9 play cricket, 19 play football and 4 play both. How many play neither of the two?
  20. 20.In a group of 38 children, 16 like mangoes, 22 like bananas and 7 like both. How many like at least one of the two?
  21. 21.In a group of 36 children, 19 play cricket, 7 play football and 3 play both. How many play at least one of the two?
  22. 22.In a group of 20 children, 14 enjoy drawing, 11 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  23. 23.In a group of 42 children, 21 play cricket, 12 play football and 6 play both. How many play only football?
  24. 24.In a group of 36 children, 17 sing Hindi songs, 23 sing English songs and 10 sing both. How many sing neither of the two?
  25. 25.In a group of 36 children, 9 sing Hindi songs, 19 sing English songs and 6 sing both. How many sing neither of the two?
  26. 26.In a group of 17 children, 5 sing Hindi songs, 10 sing English songs and 2 sing both. How many sing only English songs?
  27. 27.In a group of 44 children, 22 play cricket, 19 play football and 12 play both. How many play neither of the two?
  28. 28.In a group of 43 children, 23 play cricket, 30 play football and 12 play both. How many play exactly one of the two?
  29. 29.In a group of 15 grown-ups, 10 drink tea, 7 drink coffee and 3 drink both. How many drink exactly one of the two?
  30. 30.In a group of 49 children, 20 sing Hindi songs, 30 sing English songs and 11 sing both. How many sing only English songs?
  31. 31.In a group of 38 children, 22 sing Hindi songs, 23 sing English songs and 12 sing both. How many sing only English songs?
  32. 32.In a group of 50 children, 32 sing Hindi songs, 29 sing English songs and 12 sing both. How many sing only Hindi songs?
  33. 33.In a group of 52 children, 29 like mangoes, 31 like bananas and 12 like both. How many like at least one of the two?
  34. 34.In a group of 28 children, 19 play chess, 16 play carrom and 10 play both. How many play at least one of the two?
  35. 35.In a group of 49 children, 19 sing Hindi songs, 25 sing English songs and 5 sing both. How many sing exactly one of the two?
  36. 36.In a group of 40 grown-ups, 25 drink tea, 18 drink coffee and 7 drink both. How many drink neither of the two?
  37. 37.In a group of 46 grown-ups, 30 drink tea, 19 drink coffee and 12 drink both. How many drink neither of the two?
  38. 38.In a group of 24 children, 9 enjoy drawing, 17 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  39. 39.In a group of 35 children, 15 play chess, 19 play carrom and 6 play both. How many play only carrom?
  40. 40.In a group of 48 children, 22 like mangoes, 23 like bananas and 9 like both. How many like neither of the two?

Answer key

  1. 18
  2. 24
  3. 19
  4. 24
  5. 20
  6. 35
  7. 2
  8. 20
  9. 36
  10. 20
  11. 2
  12. 3
  13. 29
  14. 22
  15. 27
  16. 24
  17. 31
  18. 27
  19. 4
  20. 31
  21. 23
  22. 3
  23. 6
  24. 6
  25. 14
  26. 8
  27. 15
  28. 29
  29. 11
  30. 19
  31. 11
  32. 20
  33. 48
  34. 25
  35. 34
  36. 4
  37. 9
  38. 2
  39. 13
  40. 12

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