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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 61 · 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 37 children, 10 enjoy drawing, 17 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  2. 2.In a group of 26 children, 10 play chess, 9 play carrom and 6 play both. How many play exactly one of the two?
  3. 3.In a group of 37 children, 18 play chess, 11 play carrom and 6 play both. How many play only chess?
  4. 4.In a group of 39 grown-ups, 18 drink tea, 23 drink coffee and 10 drink both. How many drink only coffee?
  5. 5.In a group of 37 children, 18 sing Hindi songs, 17 sing English songs and 6 sing both. How many sing exactly one of the two?
  6. 6.In a group of 31 children, 16 play cricket, 9 play football and 3 play both. How many play at least one of the two?
  7. 7.In a group of 42 children, 20 sing Hindi songs, 20 sing English songs and 12 sing both. How many sing at least one of the two?
  8. 8.In a group of 21 children, 14 like mangoes, 9 like bananas and 4 like both. How many like only bananas?
  9. 9.In a group of 37 children, 24 play cricket, 10 play football and 4 play both. How many play only football?
  10. 10.In a group of 46 children, 16 sing Hindi songs, 18 sing English songs and 2 sing both. How many sing only English songs?
  11. 11.In a group of 29 children, 12 enjoy drawing, 7 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  12. 12.In a group of 35 children, 19 play cricket, 14 play football and 3 play both. How many play only cricket?
  13. 13.In a group of 25 children, 8 like mangoes, 17 like bananas and 2 like both. How many like at least one of the two?
  14. 14.In a group of 28 children, 19 enjoy drawing, 12 enjoy dancing and 5 enjoy both. How many enjoy at least one of the two?
  15. 15.In a group of 40 grown-ups, 20 drink tea, 19 drink coffee and 2 drink both. How many drink at least one of the two?
  16. 16.In a group of 21 children, 5 play chess, 17 play carrom and 2 play both. How many play exactly one of the two?
  17. 17.In a group of 27 children, 13 enjoy drawing, 6 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  18. 18.In a group of 38 children, 21 sing Hindi songs, 22 sing English songs and 6 sing both. How many sing neither of the two?
  19. 19.In a group of 25 children, 14 like mangoes, 15 like bananas and 9 like both. How many like at least one of the two?
  20. 20.In a group of 40 children, 23 enjoy drawing, 24 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  21. 21.In a group of 18 grown-ups, 9 drink tea, 9 drink coffee and 5 drink both. How many drink at least one of the two?
  22. 22.In a group of 45 children, 25 play cricket, 12 play football and 7 play both. How many play at least one of the two?
  23. 23.In a group of 34 children, 8 enjoy drawing, 23 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  24. 24.In a group of 31 children, 16 sing Hindi songs, 16 sing English songs and 10 sing both. How many sing exactly one of the two?
  25. 25.In a group of 21 children, 13 sing Hindi songs, 9 sing English songs and 5 sing both. How many sing only English songs?
  26. 26.In a group of 39 grown-ups, 19 drink tea, 23 drink coffee and 5 drink both. How many drink neither of the two?
  27. 27.In a group of 24 children, 13 like mangoes, 18 like bananas and 9 like both. How many like at least one of the two?
  28. 28.In a group of 38 children, 18 like mangoes, 16 like bananas and 3 like both. How many like only bananas?
  29. 29.In a group of 31 children, 20 like mangoes, 8 like bananas and 3 like both. How many like exactly one of the two?
  30. 30.In a group of 27 children, 13 enjoy drawing, 9 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  31. 31.In a group of 36 children, 15 play chess, 16 play carrom and 8 play both. How many play neither of the two?
  32. 32.In a group of 39 children, 14 play cricket, 25 play football and 9 play both. How many play only football?
  33. 33.In a group of 39 children, 19 enjoy drawing, 21 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  34. 34.In a group of 36 children, 22 play cricket, 19 play football and 11 play both. How many play only football?
  35. 35.In a group of 43 children, 27 sing Hindi songs, 12 sing English songs and 8 sing both. How many sing only English songs?
  36. 36.In a group of 44 children, 25 sing Hindi songs, 26 sing English songs and 11 sing both. How many sing only English songs?
  37. 37.In a group of 53 children, 27 like mangoes, 29 like bananas and 11 like both. How many like only bananas?
  38. 38.In a group of 32 grown-ups, 18 drink tea, 12 drink coffee and 5 drink both. How many drink at least one of the two?
  39. 39.In a group of 26 grown-ups, 8 drink tea, 22 drink coffee and 5 drink both. How many drink exactly one of the two?
  40. 40.In a group of 29 children, 9 play cricket, 20 play football and 3 play both. How many play only cricket?

Answer key

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

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