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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 59 · 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 39 children, 18 enjoy drawing, 14 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  2. 2.In a group of 19 children, 11 like mangoes, 14 like bananas and 8 like both. How many like at least one of the two?
  3. 3.In a group of 29 children, 15 enjoy drawing, 18 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  4. 4.In a group of 36 children, 26 sing Hindi songs, 18 sing English songs and 10 sing both. How many sing neither of the two?
  5. 5.In a group of 31 children, 16 enjoy drawing, 22 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  6. 6.In a group of 35 children, 15 like mangoes, 28 like bananas and 11 like both. How many like only mangoes?
  7. 7.In a group of 47 children, 19 play chess, 26 play carrom and 11 play both. How many play exactly one of the two?
  8. 8.In a group of 28 children, 13 like mangoes, 7 like bananas and 4 like both. How many like only bananas?
  9. 9.In a group of 31 children, 20 sing Hindi songs, 16 sing English songs and 12 sing both. How many sing at least one of the two?
  10. 10.In a group of 32 children, 12 play cricket, 11 play football and 6 play both. How many play neither of the two?
  11. 11.In a group of 26 children, 14 enjoy drawing, 5 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  12. 12.In a group of 32 children, 15 play cricket, 14 play football and 7 play both. How many play at least one of the two?
  13. 13.In a group of 34 children, 15 play cricket, 19 play football and 8 play both. How many play only football?
  14. 14.In a group of 48 children, 29 play chess, 30 play carrom and 12 play both. How many play exactly one of the two?
  15. 15.In a group of 37 grown-ups, 24 drink tea, 14 drink coffee and 8 drink both. How many drink neither of the two?
  16. 16.In a group of 29 children, 13 enjoy drawing, 16 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  17. 17.In a group of 33 children, 14 enjoy drawing, 23 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  18. 18.In a group of 26 grown-ups, 15 drink tea, 17 drink coffee and 12 drink both. How many drink only coffee?
  19. 19.In a group of 25 children, 13 play chess, 19 play carrom and 8 play both. How many play exactly one of the two?
  20. 20.In a group of 30 children, 22 play chess, 13 play carrom and 7 play both. How many play only carrom?
  21. 21.In a group of 52 children, 26 play chess, 27 play carrom and 7 play both. How many play exactly one of the two?
  22. 22.In a group of 35 grown-ups, 17 drink tea, 18 drink coffee and 11 drink both. How many drink neither of the two?
  23. 23.In a group of 40 children, 27 enjoy drawing, 11 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  24. 24.In a group of 41 children, 21 like mangoes, 24 like bananas and 11 like both. How many like at least one of the two?
  25. 25.In a group of 34 children, 19 play cricket, 21 play football and 8 play both. How many play neither of the two?
  26. 26.In a group of 40 children, 20 sing Hindi songs, 30 sing English songs and 12 sing both. How many sing exactly one of the two?
  27. 27.In a group of 30 children, 11 like mangoes, 11 like bananas and 5 like both. How many like only mangoes?
  28. 28.In a group of 38 children, 18 enjoy drawing, 17 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  29. 29.In a group of 21 children, 13 sing Hindi songs, 11 sing English songs and 7 sing both. How many sing exactly one of the two?
  30. 30.In a group of 41 children, 31 play cricket, 15 play football and 12 play both. How many play neither of the two?
  31. 31.In a group of 34 children, 15 like mangoes, 24 like bananas and 7 like both. How many like only mangoes?
  32. 32.In a group of 31 children, 11 sing Hindi songs, 11 sing English songs and 3 sing both. How many sing only English songs?
  33. 33.In a group of 31 children, 23 sing Hindi songs, 11 sing English songs and 6 sing both. How many sing only English songs?
  34. 34.In a group of 53 grown-ups, 25 drink tea, 26 drink coffee and 12 drink both. How many drink exactly one of the two?
  35. 35.In a group of 29 children, 16 play chess, 19 play carrom and 8 play both. How many play only carrom?
  36. 36.In a group of 36 children, 13 like mangoes, 19 like bananas and 2 like both. How many like only bananas?
  37. 37.In a group of 36 children, 15 enjoy drawing, 20 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  38. 38.In a group of 25 children, 7 like mangoes, 19 like bananas and 2 like both. How many like only bananas?
  39. 39.In a group of 38 children, 9 play cricket, 17 play football and 2 play both. How many play only football?
  40. 40.In a group of 30 children, 13 play chess, 16 play carrom and 8 play both. How many play exactly one of the two?

Answer key

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

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