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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 691 · 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 52 children, 30 enjoy drawing, 30 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  2. 2.In a group of 44 grown-ups, 27 drink tea, 18 drink coffee and 11 drink both. How many drink at least one of the two?
  3. 3.In a group of 36 children, 14 play cricket, 9 play football and 2 play both. How many play only football?
  4. 4.In a group of 37 children, 15 play cricket, 14 play football and 5 play both. How many play at least one of the two?
  5. 5.In a group of 48 children, 19 sing Hindi songs, 28 sing English songs and 10 sing both. How many sing only English songs?
  6. 6.In a group of 36 children, 12 play cricket, 24 play football and 8 play both. How many play neither of the two?
  7. 7.In a group of 56 children, 30 play cricket, 23 play football and 10 play both. How many play exactly one of the two?
  8. 8.In a group of 27 children, 16 play cricket, 8 play football and 5 play both. How many play only football?
  9. 9.In a group of 34 children, 19 play chess, 7 play carrom and 3 play both. How many play neither of the two?
  10. 10.In a group of 30 children, 24 enjoy drawing, 16 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  11. 11.In a group of 36 children, 24 enjoy drawing, 16 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  12. 12.In a group of 34 children, 26 enjoy drawing, 17 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  13. 13.In a group of 39 children, 17 play cricket, 29 play football and 10 play both. How many play exactly one of the two?
  14. 14.In a group of 52 children, 27 play cricket, 20 play football and 8 play both. How many play only cricket?
  15. 15.In a group of 43 children, 23 like mangoes, 16 like bananas and 3 like both. How many like neither of the two?
  16. 16.In a group of 31 children, 26 play chess, 15 play carrom and 12 play both. How many play only carrom?
  17. 17.In a group of 40 children, 22 play cricket, 9 play football and 3 play both. How many play exactly one of the two?
  18. 18.In a group of 25 children, 14 enjoy drawing, 11 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  19. 19.In a group of 42 children, 23 like mangoes, 21 like bananas and 12 like both. How many like exactly one of the two?
  20. 20.In a group of 31 children, 17 play cricket, 15 play football and 4 play both. How many play only football?
  21. 21.In a group of 41 children, 16 sing Hindi songs, 21 sing English songs and 3 sing both. How many sing only English songs?
  22. 22.In a group of 21 children, 9 sing Hindi songs, 12 sing English songs and 4 sing both. How many sing at least one of the two?
  23. 23.In a group of 43 children, 25 sing Hindi songs, 23 sing English songs and 7 sing both. How many sing only Hindi songs?
  24. 24.In a group of 19 children, 11 play chess, 11 play carrom and 7 play both. How many play at least one of the two?
  25. 25.In a group of 40 children, 17 enjoy drawing, 15 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  26. 26.In a group of 37 children, 10 enjoy drawing, 15 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  27. 27.In a group of 36 children, 20 like mangoes, 24 like bananas and 10 like both. How many like exactly one of the two?
  28. 28.In a group of 43 children, 18 sing Hindi songs, 18 sing English songs and 2 sing both. How many sing exactly one of the two?
  29. 29.In a group of 42 grown-ups, 20 drink tea, 31 drink coffee and 11 drink both. How many drink only coffee?
  30. 30.In a group of 34 children, 14 play cricket, 18 play football and 10 play both. How many play only football?
  31. 31.In a group of 34 grown-ups, 14 drink tea, 13 drink coffee and 3 drink both. How many drink at least one of the two?
  32. 32.In a group of 44 grown-ups, 27 drink tea, 23 drink coffee and 7 drink both. How many drink only tea?
  33. 33.In a group of 41 children, 24 like mangoes, 18 like bananas and 12 like both. How many like only bananas?
  34. 34.In a group of 33 children, 9 play chess, 17 play carrom and 5 play both. How many play exactly one of the two?
  35. 35.In a group of 21 grown-ups, 8 drink tea, 13 drink coffee and 5 drink both. How many drink only coffee?
  36. 36.In a group of 40 grown-ups, 14 drink tea, 25 drink coffee and 10 drink both. How many drink only tea?
  37. 37.In a group of 31 children, 12 enjoy drawing, 11 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  38. 38.In a group of 46 grown-ups, 21 drink tea, 14 drink coffee and 2 drink both. How many drink exactly one of the two?
  39. 39.In a group of 39 grown-ups, 25 drink tea, 22 drink coffee and 12 drink both. How many drink exactly one of the two?
  40. 40.In a group of 31 children, 9 like mangoes, 16 like bananas and 4 like both. How many like only bananas?

Answer key

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

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