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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 540 · 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 31 grown-ups, 16 drink tea, 16 drink coffee and 3 drink both. How many drink only tea?
  2. 2.In a group of 38 children, 27 enjoy drawing, 13 enjoy dancing and 10 enjoy both. How many enjoy at least one of the two?
  3. 3.In a group of 49 children, 21 like mangoes, 28 like bananas and 8 like both. How many like only mangoes?
  4. 4.In a group of 23 children, 7 sing Hindi songs, 8 sing English songs and 3 sing both. How many sing neither of the two?
  5. 5.In a group of 31 grown-ups, 7 drink tea, 16 drink coffee and 3 drink both. How many drink only tea?
  6. 6.In a group of 31 children, 16 like mangoes, 21 like bananas and 10 like both. How many like only mangoes?
  7. 7.In a group of 29 children, 11 enjoy drawing, 21 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  8. 8.In a group of 36 children, 16 sing Hindi songs, 20 sing English songs and 12 sing both. How many sing neither of the two?
  9. 9.In a group of 36 grown-ups, 15 drink tea, 30 drink coffee and 11 drink both. How many drink only tea?
  10. 10.In a group of 37 grown-ups, 13 drink tea, 18 drink coffee and 8 drink both. How many drink only tea?
  11. 11.In a group of 41 children, 22 sing Hindi songs, 16 sing English songs and 9 sing both. How many sing exactly one of the two?
  12. 12.In a group of 33 children, 18 play cricket, 22 play football and 12 play both. How many play neither of the two?
  13. 13.In a group of 23 grown-ups, 11 drink tea, 9 drink coffee and 4 drink both. How many drink at least one of the two?
  14. 14.In a group of 46 children, 23 enjoy drawing, 21 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  15. 15.In a group of 25 children, 17 sing Hindi songs, 10 sing English songs and 5 sing both. How many sing only Hindi songs?
  16. 16.In a group of 36 grown-ups, 21 drink tea, 13 drink coffee and 2 drink both. How many drink at least one of the two?
  17. 17.In a group of 42 children, 21 sing Hindi songs, 25 sing English songs and 12 sing both. How many sing at least one of the two?
  18. 18.In a group of 21 children, 15 enjoy drawing, 7 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  19. 19.In a group of 42 grown-ups, 20 drink tea, 17 drink coffee and 10 drink both. How many drink neither of the two?
  20. 20.In a group of 17 children, 13 like mangoes, 5 like bananas and 2 like both. How many like neither of the two?
  21. 21.In a group of 26 children, 15 like mangoes, 11 like bananas and 2 like both. How many like only mangoes?
  22. 22.In a group of 53 children, 22 sing Hindi songs, 22 sing English songs and 3 sing both. How many sing exactly one of the two?
  23. 23.In a group of 46 children, 17 sing Hindi songs, 28 sing English songs and 8 sing both. How many sing exactly one of the two?
  24. 24.In a group of 39 children, 25 sing Hindi songs, 15 sing English songs and 7 sing both. How many sing at least one of the two?
  25. 25.In a group of 56 children, 25 like mangoes, 26 like bananas and 7 like both. How many like at least one of the two?
  26. 26.In a group of 26 children, 12 enjoy drawing, 12 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  27. 27.In a group of 33 children, 7 play chess, 18 play carrom and 4 play both. How many play exactly one of the two?
  28. 28.In a group of 45 children, 24 play cricket, 23 play football and 11 play both. How many play only football?
  29. 29.In a group of 18 children, 10 like mangoes, 9 like bananas and 3 like both. How many like only bananas?
  30. 30.In a group of 19 grown-ups, 7 drink tea, 9 drink coffee and 4 drink both. How many drink at least one of the two?
  31. 31.In a group of 38 grown-ups, 23 drink tea, 8 drink coffee and 3 drink both. How many drink only coffee?
  32. 32.In a group of 26 children, 10 sing Hindi songs, 16 sing English songs and 5 sing both. How many sing only Hindi songs?
  33. 33.In a group of 30 children, 16 enjoy drawing, 15 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  34. 34.In a group of 41 grown-ups, 18 drink tea, 28 drink coffee and 11 drink both. How many drink only coffee?
  35. 35.In a group of 30 children, 7 sing Hindi songs, 22 sing English songs and 2 sing both. How many sing at least one of the two?
  36. 36.In a group of 37 children, 23 like mangoes, 18 like bananas and 12 like both. How many like only mangoes?
  37. 37.In a group of 35 children, 25 sing Hindi songs, 19 sing English songs and 11 sing both. How many sing only Hindi songs?
  38. 38.In a group of 41 children, 22 play cricket, 15 play football and 10 play both. How many play exactly one of the two?
  39. 39.In a group of 39 children, 24 like mangoes, 17 like bananas and 4 like both. How many like neither of the two?
  40. 40.In a group of 49 children, 31 like mangoes, 26 like bananas and 12 like both. How many like only bananas?

Answer key

  1. 13
  2. 30
  3. 13
  4. 11
  5. 4
  6. 6
  7. 4
  8. 12
  9. 4
  10. 5
  11. 20
  12. 5
  13. 16
  14. 40
  15. 12
  16. 32
  17. 34
  18. 18
  19. 15
  20. 1
  21. 13
  22. 38
  23. 29
  24. 33
  25. 44
  26. 12
  27. 17
  28. 12
  29. 6
  30. 12
  31. 5
  32. 5
  33. 7
  34. 17
  35. 27
  36. 11
  37. 14
  38. 17
  39. 2
  40. 14

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