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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 104 · 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 41 children, 19 enjoy drawing, 21 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  2. 2.In a group of 33 children, 17 like mangoes, 12 like bananas and 7 like both. How many like only bananas?
  3. 3.In a group of 46 children, 27 play cricket, 13 play football and 7 play both. How many play only cricket?
  4. 4.In a group of 23 children, 11 play chess, 14 play carrom and 4 play both. How many play only carrom?
  5. 5.In a group of 28 children, 19 play cricket, 8 play football and 3 play both. How many play exactly one of the two?
  6. 6.In a group of 46 children, 22 play cricket, 19 play football and 10 play both. How many play only football?
  7. 7.In a group of 35 children, 19 sing Hindi songs, 16 sing English songs and 11 sing both. How many sing at least one of the two?
  8. 8.In a group of 29 children, 15 play chess, 18 play carrom and 10 play both. How many play only chess?
  9. 9.In a group of 50 children, 24 like mangoes, 25 like bananas and 9 like both. How many like exactly one of the two?
  10. 10.In a group of 50 children, 19 sing Hindi songs, 29 sing English songs and 12 sing both. How many sing only Hindi songs?
  11. 11.In a group of 32 children, 11 sing Hindi songs, 17 sing English songs and 2 sing both. How many sing only English songs?
  12. 12.In a group of 42 children, 18 play chess, 18 play carrom and 6 play both. How many play only chess?
  13. 13.In a group of 32 children, 16 play cricket, 17 play football and 3 play both. How many play at least one of the two?
  14. 14.In a group of 25 children, 13 play chess, 19 play carrom and 9 play both. How many play only carrom?
  15. 15.In a group of 41 children, 21 like mangoes, 17 like bananas and 6 like both. How many like neither of the two?
  16. 16.In a group of 39 grown-ups, 21 drink tea, 21 drink coffee and 6 drink both. How many drink only coffee?
  17. 17.In a group of 50 children, 22 play cricket, 26 play football and 8 play both. How many play only cricket?
  18. 18.In a group of 33 children, 18 sing Hindi songs, 14 sing English songs and 7 sing both. How many sing at least one of the two?
  19. 19.In a group of 28 children, 24 enjoy drawing, 10 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  20. 20.In a group of 42 children, 17 sing Hindi songs, 24 sing English songs and 6 sing both. How many sing neither of the two?
  21. 21.In a group of 26 children, 18 sing Hindi songs, 17 sing English songs and 11 sing both. How many sing only English songs?
  22. 22.In a group of 32 grown-ups, 18 drink tea, 9 drink coffee and 3 drink both. How many drink only coffee?
  23. 23.In a group of 27 children, 9 enjoy drawing, 13 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  24. 24.In a group of 36 grown-ups, 19 drink tea, 22 drink coffee and 11 drink both. How many drink exactly one of the two?
  25. 25.In a group of 36 children, 15 sing Hindi songs, 18 sing English songs and 8 sing both. How many sing neither of the two?
  26. 26.In a group of 15 children, 9 like mangoes, 6 like bananas and 3 like both. How many like only bananas?
  27. 27.In a group of 40 children, 15 sing Hindi songs, 17 sing English songs and 6 sing both. How many sing only English songs?
  28. 28.In a group of 43 children, 25 like mangoes, 14 like bananas and 11 like both. How many like at least one of the two?
  29. 29.In a group of 45 children, 18 enjoy drawing, 22 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?
  30. 30.In a group of 45 children, 13 enjoy drawing, 26 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  31. 31.In a group of 39 children, 12 play chess, 24 play carrom and 4 play both. How many play only chess?
  32. 32.In a group of 39 children, 11 like mangoes, 21 like bananas and 7 like both. How many like exactly one of the two?
  33. 33.In a group of 22 children, 5 enjoy drawing, 15 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  34. 34.In a group of 27 children, 8 play chess, 15 play carrom and 5 play both. How many play only carrom?
  35. 35.In a group of 43 grown-ups, 22 drink tea, 27 drink coffee and 8 drink both. How many drink at least one of the two?
  36. 36.In a group of 31 children, 11 enjoy drawing, 16 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  37. 37.In a group of 48 children, 14 like mangoes, 26 like bananas and 7 like both. How many like at least one of the two?
  38. 38.In a group of 51 grown-ups, 22 drink tea, 29 drink coffee and 12 drink both. How many drink neither of the two?
  39. 39.In a group of 41 children, 14 enjoy drawing, 22 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  40. 40.In a group of 32 children, 24 sing Hindi songs, 11 sing English songs and 5 sing both. How many sing only Hindi songs?

Answer key

  1. 8
  2. 5
  3. 20
  4. 10
  5. 21
  6. 9
  7. 24
  8. 5
  9. 31
  10. 7
  11. 15
  12. 12
  13. 30
  14. 10
  15. 9
  16. 15
  17. 14
  18. 25
  19. 20
  20. 7
  21. 6
  22. 6
  23. 19
  24. 19
  25. 11
  26. 3
  27. 11
  28. 28
  29. 11
  30. 4
  31. 8
  32. 18
  33. 13
  34. 10
  35. 41
  36. 19
  37. 33
  38. 12
  39. 19
  40. 19

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