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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 137 · 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 38 children, 20 play chess, 13 play carrom and 9 play both. How many play exactly one of the two?
  2. 2.In a group of 28 children, 15 enjoy drawing, 15 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  3. 3.In a group of 31 children, 14 enjoy drawing, 18 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  4. 4.In a group of 18 children, 11 play chess, 13 play carrom and 7 play both. How many play only chess?
  5. 5.In a group of 40 children, 13 play cricket, 25 play football and 8 play both. How many play only football?
  6. 6.In a group of 27 children, 8 enjoy drawing, 14 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  7. 7.In a group of 44 children, 30 play chess, 18 play carrom and 12 play both. How many play only chess?
  8. 8.In a group of 31 children, 16 enjoy drawing, 10 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  9. 9.In a group of 40 grown-ups, 20 drink tea, 27 drink coffee and 10 drink both. How many drink exactly one of the two?
  10. 10.In a group of 32 children, 17 sing Hindi songs, 17 sing English songs and 8 sing both. How many sing neither of the two?
  11. 11.In a group of 32 children, 24 sing Hindi songs, 11 sing English songs and 7 sing both. How many sing only English songs?
  12. 12.In a group of 44 children, 11 like mangoes, 20 like bananas and 2 like both. How many like exactly one of the two?
  13. 13.In a group of 42 children, 29 enjoy drawing, 18 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  14. 14.In a group of 40 children, 10 play cricket, 19 play football and 2 play both. How many play exactly one of the two?
  15. 15.In a group of 51 children, 20 play chess, 20 play carrom and 3 play both. How many play only carrom?
  16. 16.In a group of 38 children, 24 like mangoes, 20 like bananas and 11 like both. How many like at least one of the two?
  17. 17.In a group of 27 grown-ups, 10 drink tea, 12 drink coffee and 6 drink both. How many drink only coffee?
  18. 18.In a group of 32 grown-ups, 13 drink tea, 18 drink coffee and 7 drink both. How many drink at least one of the two?
  19. 19.In a group of 24 grown-ups, 13 drink tea, 15 drink coffee and 6 drink both. How many drink only tea?
  20. 20.In a group of 32 children, 19 play chess, 7 play carrom and 2 play both. How many play neither of the two?
  21. 21.In a group of 26 children, 17 enjoy drawing, 11 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  22. 22.In a group of 25 children, 15 enjoy drawing, 18 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  23. 23.In a group of 19 children, 10 sing Hindi songs, 12 sing English songs and 5 sing both. How many sing at least one of the two?
  24. 24.In a group of 33 children, 27 play chess, 14 play carrom and 10 play both. How many play exactly one of the two?
  25. 25.In a group of 38 grown-ups, 20 drink tea, 13 drink coffee and 8 drink both. How many drink only coffee?
  26. 26.In a group of 19 children, 13 enjoy drawing, 8 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  27. 27.In a group of 35 grown-ups, 19 drink tea, 6 drink coffee and 3 drink both. How many drink only coffee?
  28. 28.In a group of 40 children, 7 play cricket, 22 play football and 3 play both. How many play only cricket?
  29. 29.In a group of 38 children, 14 enjoy drawing, 22 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  30. 30.In a group of 41 children, 21 play chess, 13 play carrom and 7 play both. How many play only carrom?
  31. 31.In a group of 41 children, 10 sing Hindi songs, 26 sing English songs and 6 sing both. How many sing at least one of the two?
  32. 32.In a group of 25 grown-ups, 8 drink tea, 8 drink coffee and 4 drink both. How many drink only tea?
  33. 33.In a group of 26 children, 8 sing Hindi songs, 17 sing English songs and 5 sing both. How many sing only English songs?
  34. 34.In a group of 40 children, 22 play chess, 23 play carrom and 11 play both. How many play exactly one of the two?
  35. 35.In a group of 51 grown-ups, 21 drink tea, 21 drink coffee and 3 drink both. How many drink only tea?
  36. 36.In a group of 38 children, 9 play cricket, 22 play football and 3 play both. How many play only football?
  37. 37.In a group of 58 children, 27 play chess, 27 play carrom and 9 play both. How many play only chess?
  38. 38.In a group of 37 grown-ups, 18 drink tea, 18 drink coffee and 4 drink both. How many drink exactly one of the two?
  39. 39.In a group of 39 children, 30 sing Hindi songs, 17 sing English songs and 10 sing both. How many sing only English songs?
  40. 40.In a group of 48 children, 23 play chess, 24 play carrom and 12 play both. How many play neither of the two?

Answer key

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

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