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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 177 · 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 27 children, 19 sing Hindi songs, 14 sing English songs and 7 sing both. How many sing exactly one of the two?
  2. 2.In a group of 23 children, 13 play cricket, 10 play football and 2 play both. How many play neither of the two?
  3. 3.In a group of 47 children, 22 play cricket, 25 play football and 12 play both. How many play only football?
  4. 4.In a group of 35 children, 25 sing Hindi songs, 14 sing English songs and 9 sing both. How many sing exactly one of the two?
  5. 5.In a group of 40 children, 17 like mangoes, 18 like bananas and 3 like both. How many like exactly one of the two?
  6. 6.In a group of 47 grown-ups, 27 drink tea, 14 drink coffee and 9 drink both. How many drink only coffee?
  7. 7.In a group of 41 children, 19 play cricket, 18 play football and 2 play both. How many play exactly one of the two?
  8. 8.In a group of 44 children, 24 enjoy drawing, 30 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  9. 9.In a group of 50 children, 22 like mangoes, 19 like bananas and 5 like both. How many like only bananas?
  10. 10.In a group of 54 children, 29 play chess, 24 play carrom and 11 play both. How many play only chess?
  11. 11.In a group of 22 children, 8 play cricket, 6 play football and 3 play both. How many play at least one of the two?
  12. 12.In a group of 50 children, 27 enjoy drawing, 27 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  13. 13.In a group of 35 children, 16 enjoy drawing, 13 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  14. 14.In a group of 36 children, 20 enjoy drawing, 18 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  15. 15.In a group of 50 children, 26 play cricket, 25 play football and 11 play both. How many play exactly one of the two?
  16. 16.In a group of 36 children, 8 play cricket, 20 play football and 3 play both. How many play only football?
  17. 17.In a group of 46 children, 27 enjoy drawing, 12 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  18. 18.In a group of 32 children, 18 enjoy drawing, 19 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  19. 19.In a group of 37 children, 25 play cricket, 15 play football and 10 play both. How many play at least one of the two?
  20. 20.In a group of 38 children, 16 like mangoes, 22 like bananas and 2 like both. How many like at least one of the two?
  21. 21.In a group of 27 children, 12 sing Hindi songs, 16 sing English songs and 7 sing both. How many sing neither of the two?
  22. 22.In a group of 42 children, 14 play chess, 23 play carrom and 3 play both. How many play at least one of the two?
  23. 23.In a group of 42 children, 27 enjoy drawing, 23 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  24. 24.In a group of 27 children, 10 play cricket, 12 play football and 7 play both. How many play at least one of the two?
  25. 25.In a group of 19 children, 7 enjoy drawing, 8 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  26. 26.In a group of 31 children, 12 play cricket, 14 play football and 2 play both. How many play at least one of the two?
  27. 27.In a group of 40 children, 16 like mangoes, 17 like bananas and 2 like both. How many like exactly one of the two?
  28. 28.In a group of 38 children, 29 enjoy drawing, 19 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  29. 29.In a group of 43 children, 21 like mangoes, 21 like bananas and 4 like both. How many like exactly one of the two?
  30. 30.In a group of 31 children, 17 play cricket, 15 play football and 4 play both. How many play at least one of the two?
  31. 31.In a group of 39 children, 15 enjoy drawing, 21 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  32. 32.In a group of 44 grown-ups, 17 drink tea, 19 drink coffee and 4 drink both. How many drink only coffee?
  33. 33.In a group of 38 grown-ups, 16 drink tea, 26 drink coffee and 9 drink both. How many drink only tea?
  34. 34.In a group of 32 children, 19 enjoy drawing, 17 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  35. 35.In a group of 32 children, 15 sing Hindi songs, 15 sing English songs and 4 sing both. How many sing only English songs?
  36. 36.In a group of 37 children, 19 enjoy drawing, 20 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  37. 37.In a group of 17 children, 13 sing Hindi songs, 9 sing English songs and 6 sing both. How many sing only Hindi songs?
  38. 38.In a group of 36 children, 21 play cricket, 10 play football and 6 play both. How many play only football?
  39. 39.In a group of 29 children, 9 like mangoes, 24 like bananas and 5 like both. How many like exactly one of the two?
  40. 40.In a group of 28 children, 14 play chess, 16 play carrom and 11 play both. How many play only carrom?

Answer key

  1. 19
  2. 2
  3. 13
  4. 21
  5. 29
  6. 5
  7. 33
  8. 13
  9. 14
  10. 18
  11. 11
  12. 43
  13. 22
  14. 34
  15. 29
  16. 17
  17. 15
  18. 6
  19. 30
  20. 36
  21. 6
  22. 34
  23. 17
  24. 15
  25. 4
  26. 24
  27. 29
  28. 2
  29. 34
  30. 28
  31. 25
  32. 15
  33. 7
  34. 10
  35. 11
  36. 5
  37. 7
  38. 4
  39. 23
  40. 5

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