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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 437 · 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 25 children, 11 sing Hindi songs, 11 sing English songs and 2 sing both. How many sing at least one of the two?
  2. 2.In a group of 47 children, 25 like mangoes, 30 like bananas and 11 like both. How many like exactly one of the two?
  3. 3.In a group of 26 children, 16 play chess, 13 play carrom and 6 play both. How many play only carrom?
  4. 4.In a group of 38 children, 16 sing Hindi songs, 25 sing English songs and 6 sing both. How many sing exactly one of the two?
  5. 5.In a group of 46 children, 20 like mangoes, 25 like bananas and 12 like both. How many like neither of the two?
  6. 6.In a group of 18 children, 6 sing Hindi songs, 11 sing English songs and 2 sing both. How many sing only English songs?
  7. 7.In a group of 55 children, 30 play chess, 23 play carrom and 10 play both. How many play exactly one of the two?
  8. 8.In a group of 27 children, 18 enjoy drawing, 7 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  9. 9.In a group of 44 children, 19 sing Hindi songs, 19 sing English songs and 5 sing both. How many sing exactly one of the two?
  10. 10.In a group of 29 children, 10 like mangoes, 22 like bananas and 5 like both. How many like exactly one of the two?
  11. 11.In a group of 40 children, 19 play cricket, 23 play football and 5 play both. How many play exactly one of the two?
  12. 12.In a group of 32 children, 9 play cricket, 16 play football and 3 play both. How many play exactly one of the two?
  13. 13.In a group of 27 grown-ups, 9 drink tea, 12 drink coffee and 3 drink both. How many drink only tea?
  14. 14.In a group of 34 children, 20 play chess, 20 play carrom and 8 play both. How many play only chess?
  15. 15.In a group of 59 children, 29 sing Hindi songs, 27 sing English songs and 9 sing both. How many sing only Hindi songs?
  16. 16.In a group of 39 children, 19 play chess, 14 play carrom and 6 play both. How many play only chess?
  17. 17.In a group of 44 children, 29 enjoy drawing, 17 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  18. 18.In a group of 32 grown-ups, 11 drink tea, 15 drink coffee and 2 drink both. How many drink neither of the two?
  19. 19.In a group of 20 children, 14 like mangoes, 7 like bananas and 2 like both. How many like only bananas?
  20. 20.In a group of 35 grown-ups, 14 drink tea, 15 drink coffee and 2 drink both. How many drink only tea?
  21. 21.In a group of 45 children, 27 sing Hindi songs, 16 sing English songs and 9 sing both. How many sing only Hindi songs?
  22. 22.In a group of 38 children, 16 sing Hindi songs, 9 sing English songs and 2 sing both. How many sing exactly one of the two?
  23. 23.In a group of 47 children, 19 enjoy drawing, 27 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  24. 24.In a group of 47 children, 24 play chess, 24 play carrom and 11 play both. How many play only carrom?
  25. 25.In a group of 28 children, 14 like mangoes, 15 like bananas and 8 like both. How many like only bananas?
  26. 26.In a group of 29 grown-ups, 7 drink tea, 12 drink coffee and 4 drink both. How many drink at least one of the two?
  27. 27.In a group of 47 children, 18 enjoy drawing, 27 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  28. 28.In a group of 29 children, 19 like mangoes, 15 like bananas and 6 like both. How many like at least one of the two?
  29. 29.In a group of 50 children, 27 play chess, 26 play carrom and 9 play both. How many play at least one of the two?
  30. 30.In a group of 55 children, 25 enjoy drawing, 25 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  31. 31.In a group of 37 children, 14 play cricket, 25 play football and 11 play both. How many play only football?
  32. 32.In a group of 36 children, 25 sing Hindi songs, 16 sing English songs and 8 sing both. How many sing only English songs?
  33. 33.In a group of 44 children, 25 enjoy drawing, 16 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?
  34. 34.In a group of 47 children, 22 play chess, 27 play carrom and 7 play both. How many play at least one of the two?
  35. 35.In a group of 42 children, 17 enjoy drawing, 23 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  36. 36.In a group of 34 grown-ups, 15 drink tea, 26 drink coffee and 12 drink both. How many drink at least one of the two?
  37. 37.In a group of 39 children, 18 enjoy drawing, 14 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?
  38. 38.In a group of 38 children, 14 like mangoes, 17 like bananas and 3 like both. How many like only bananas?
  39. 39.In a group of 31 grown-ups, 20 drink tea, 21 drink coffee and 11 drink both. How many drink at least one of the two?
  40. 40.In a group of 35 children, 18 sing Hindi songs, 18 sing English songs and 3 sing both. How many sing exactly one of the two?

Answer key

  1. 20
  2. 33
  3. 7
  4. 29
  5. 13
  6. 9
  7. 33
  8. 14
  9. 28
  10. 22
  11. 32
  12. 19
  13. 6
  14. 12
  15. 20
  16. 13
  17. 6
  18. 8
  19. 5
  20. 12
  21. 18
  22. 21
  23. 38
  24. 13
  25. 7
  26. 15
  27. 36
  28. 28
  29. 44
  30. 32
  31. 14
  32. 8
  33. 9
  34. 42
  35. 18
  36. 29
  37. 13
  38. 14
  39. 30
  40. 30

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