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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 316 · 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 34 children, 12 sing Hindi songs, 22 sing English songs and 5 sing both. How many sing neither of the two?
  2. 2.In a group of 36 children, 20 sing Hindi songs, 10 sing English songs and 6 sing both. How many sing neither of the two?
  3. 3.In a group of 27 grown-ups, 18 drink tea, 14 drink coffee and 6 drink both. How many drink only tea?
  4. 4.In a group of 28 grown-ups, 14 drink tea, 15 drink coffee and 8 drink both. How many drink only tea?
  5. 5.In a group of 24 children, 18 sing Hindi songs, 7 sing English songs and 3 sing both. How many sing exactly one of the two?
  6. 6.In a group of 45 children, 25 play chess, 21 play carrom and 9 play both. How many play at least one of the two?
  7. 7.In a group of 28 grown-ups, 11 drink tea, 22 drink coffee and 7 drink both. How many drink only coffee?
  8. 8.In a group of 43 children, 24 play chess, 17 play carrom and 8 play both. How many play at least one of the two?
  9. 9.In a group of 44 grown-ups, 17 drink tea, 16 drink coffee and 4 drink both. How many drink exactly one of the two?
  10. 10.In a group of 58 children, 25 sing Hindi songs, 24 sing English songs and 6 sing both. How many sing exactly one of the two?
  11. 11.In a group of 40 grown-ups, 19 drink tea, 25 drink coffee and 7 drink both. How many drink at least one of the two?
  12. 12.In a group of 53 children, 19 play cricket, 22 play football and 2 play both. How many play neither of the two?
  13. 13.In a group of 43 children, 12 play cricket, 24 play football and 4 play both. How many play at least one of the two?
  14. 14.In a group of 41 children, 14 enjoy drawing, 22 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  15. 15.In a group of 47 grown-ups, 17 drink tea, 25 drink coffee and 10 drink both. How many drink neither of the two?
  16. 16.In a group of 36 children, 14 enjoy drawing, 26 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  17. 17.In a group of 38 children, 20 like mangoes, 16 like bananas and 8 like both. How many like neither of the two?
  18. 18.In a group of 52 grown-ups, 24 drink tea, 26 drink coffee and 12 drink both. How many drink at least one of the two?
  19. 19.In a group of 43 grown-ups, 24 drink tea, 17 drink coffee and 4 drink both. How many drink exactly one of the two?
  20. 20.In a group of 43 grown-ups, 22 drink tea, 15 drink coffee and 7 drink both. How many drink exactly one of the two?
  21. 21.In a group of 32 grown-ups, 19 drink tea, 10 drink coffee and 7 drink both. How many drink only tea?
  22. 22.In a group of 40 grown-ups, 19 drink tea, 20 drink coffee and 8 drink both. How many drink only coffee?
  23. 23.In a group of 46 children, 25 like mangoes, 16 like bananas and 6 like both. How many like at least one of the two?
  24. 24.In a group of 31 children, 9 like mangoes, 23 like bananas and 5 like both. How many like at least one of the two?
  25. 25.In a group of 36 children, 21 play chess, 6 play carrom and 2 play both. How many play only carrom?
  26. 26.In a group of 27 children, 9 play chess, 8 play carrom and 5 play both. How many play at least one of the two?
  27. 27.In a group of 18 children, 8 play cricket, 8 play football and 2 play both. How many play exactly one of the two?
  28. 28.In a group of 43 children, 27 enjoy drawing, 16 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  29. 29.In a group of 20 children, 14 play chess, 8 play carrom and 3 play both. How many play only carrom?
  30. 30.In a group of 20 children, 5 like mangoes, 16 like bananas and 2 like both. How many like exactly one of the two?
  31. 31.In a group of 45 grown-ups, 27 drink tea, 27 drink coffee and 10 drink both. How many drink only tea?
  32. 32.In a group of 38 children, 10 sing Hindi songs, 18 sing English songs and 4 sing both. How many sing only English songs?
  33. 33.In a group of 23 children, 6 play cricket, 5 play football and 2 play both. How many play exactly one of the two?
  34. 34.In a group of 53 children, 22 play chess, 32 play carrom and 12 play both. How many play at least one of the two?
  35. 35.In a group of 27 children, 10 like mangoes, 16 like bananas and 6 like both. How many like only bananas?
  36. 36.In a group of 18 children, 8 enjoy drawing, 8 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  37. 37.In a group of 37 children, 20 like mangoes, 14 like bananas and 8 like both. How many like at least one of the two?
  38. 38.In a group of 46 grown-ups, 27 drink tea, 24 drink coffee and 9 drink both. How many drink neither of the two?
  39. 39.In a group of 25 children, 8 play cricket, 18 play football and 5 play both. How many play neither of the two?
  40. 40.In a group of 48 grown-ups, 17 drink tea, 26 drink coffee and 8 drink both. How many drink at least one of the two?

Answer key

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

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