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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 209 · 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 17 children, 6 play chess, 5 play carrom and 2 play both. How many play neither of the two?
  2. 2.In a group of 66 children, 32 enjoy drawing, 32 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  3. 3.In a group of 36 children, 11 play cricket, 21 play football and 6 play both. How many play only cricket?
  4. 4.In a group of 43 children, 23 play chess, 22 play carrom and 4 play both. How many play exactly one of the two?
  5. 5.In a group of 33 children, 26 enjoy drawing, 11 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  6. 6.In a group of 25 children, 8 enjoy drawing, 16 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  7. 7.In a group of 32 children, 22 play cricket, 10 play football and 2 play both. How many play only football?
  8. 8.In a group of 31 children, 22 play cricket, 7 play football and 2 play both. How many play only cricket?
  9. 9.In a group of 37 children, 21 play chess, 21 play carrom and 11 play both. How many play at least one of the two?
  10. 10.In a group of 41 children, 21 play chess, 23 play carrom and 11 play both. How many play neither of the two?
  11. 11.In a group of 51 children, 23 play cricket, 23 play football and 6 play both. How many play at least one of the two?
  12. 12.In a group of 32 grown-ups, 22 drink tea, 19 drink coffee and 11 drink both. How many drink at least one of the two?
  13. 13.In a group of 60 children, 29 sing Hindi songs, 25 sing English songs and 9 sing both. How many sing only English songs?
  14. 14.In a group of 36 grown-ups, 15 drink tea, 27 drink coffee and 8 drink both. How many drink only coffee?
  15. 15.In a group of 34 grown-ups, 18 drink tea, 5 drink coffee and 2 drink both. How many drink at least one of the two?
  16. 16.In a group of 29 children, 19 sing Hindi songs, 12 sing English songs and 6 sing both. How many sing exactly one of the two?
  17. 17.In a group of 50 children, 20 play chess, 21 play carrom and 3 play both. How many play only carrom?
  18. 18.In a group of 37 children, 22 enjoy drawing, 10 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  19. 19.In a group of 48 children, 17 sing Hindi songs, 22 sing English songs and 2 sing both. How many sing exactly one of the two?
  20. 20.In a group of 61 children, 28 enjoy drawing, 29 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  21. 21.In a group of 52 grown-ups, 23 drink tea, 26 drink coffee and 10 drink both. How many drink exactly one of the two?
  22. 22.In a group of 41 children, 17 play cricket, 28 play football and 12 play both. How many play at least one of the two?
  23. 23.In a group of 30 grown-ups, 12 drink tea, 22 drink coffee and 7 drink both. How many drink exactly one of the two?
  24. 24.In a group of 35 grown-ups, 14 drink tea, 14 drink coffee and 6 drink both. How many drink at least one of the two?
  25. 25.In a group of 35 children, 12 play chess, 24 play carrom and 4 play both. How many play only chess?
  26. 26.In a group of 28 children, 13 play cricket, 11 play football and 6 play both. How many play at least one of the two?
  27. 27.In a group of 38 children, 14 play cricket, 20 play football and 7 play both. How many play neither of the two?
  28. 28.In a group of 18 children, 9 play cricket, 9 play football and 4 play both. How many play only football?
  29. 29.In a group of 41 children, 27 sing Hindi songs, 21 sing English songs and 11 sing both. How many sing exactly one of the two?
  30. 30.In a group of 40 children, 14 sing Hindi songs, 21 sing English songs and 7 sing both. How many sing only English songs?
  31. 31.In a group of 30 children, 16 play chess, 14 play carrom and 3 play both. How many play only carrom?
  32. 32.In a group of 41 grown-ups, 9 drink tea, 25 drink coffee and 5 drink both. How many drink only tea?
  33. 33.In a group of 28 children, 17 sing Hindi songs, 9 sing English songs and 3 sing both. How many sing at least one of the two?
  34. 34.In a group of 28 children, 21 enjoy drawing, 9 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  35. 35.In a group of 51 children, 19 play cricket, 20 play football and 2 play both. How many play at least one of the two?
  36. 36.In a group of 52 children, 23 play cricket, 28 play football and 9 play both. How many play only football?
  37. 37.In a group of 41 children, 18 like mangoes, 22 like bananas and 3 like both. How many like neither of the two?
  38. 38.In a group of 45 grown-ups, 19 drink tea, 29 drink coffee and 12 drink both. How many drink neither of the two?
  39. 39.In a group of 36 children, 10 enjoy drawing, 21 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  40. 40.In a group of 42 children, 20 play chess, 26 play carrom and 10 play both. How many play exactly one of the two?

Answer key

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

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