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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 230 · 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 32 children, 16 play cricket, 12 play football and 6 play both. How many play exactly one of the two?
  2. 2.In a group of 40 children, 17 sing Hindi songs, 20 sing English songs and 10 sing both. How many sing only English songs?
  3. 3.In a group of 37 grown-ups, 13 drink tea, 22 drink coffee and 9 drink both. How many drink neither of the two?
  4. 4.In a group of 29 children, 25 play cricket, 10 play football and 7 play both. How many play exactly one of the two?
  5. 5.In a group of 29 children, 17 play cricket, 14 play football and 4 play both. How many play only cricket?
  6. 6.In a group of 25 grown-ups, 18 drink tea, 16 drink coffee and 12 drink both. How many drink only coffee?
  7. 7.In a group of 36 children, 17 enjoy drawing, 25 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  8. 8.In a group of 38 grown-ups, 23 drink tea, 11 drink coffee and 5 drink both. How many drink only coffee?
  9. 9.In a group of 55 children, 26 sing Hindi songs, 30 sing English songs and 11 sing both. How many sing at least one of the two?
  10. 10.In a group of 56 children, 26 enjoy drawing, 31 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  11. 11.In a group of 28 children, 20 enjoy drawing, 13 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  12. 12.In a group of 30 children, 12 enjoy drawing, 16 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  13. 13.In a group of 32 children, 18 enjoy drawing, 17 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  14. 14.In a group of 47 children, 24 play chess, 18 play carrom and 5 play both. How many play neither of the two?
  15. 15.In a group of 40 grown-ups, 6 drink tea, 21 drink coffee and 2 drink both. How many drink neither of the two?
  16. 16.In a group of 29 children, 14 play chess, 20 play carrom and 9 play both. How many play neither of the two?
  17. 17.In a group of 37 children, 16 enjoy drawing, 26 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  18. 18.In a group of 19 grown-ups, 8 drink tea, 14 drink coffee and 4 drink both. How many drink neither of the two?
  19. 19.In a group of 42 children, 15 sing Hindi songs, 16 sing English songs and 2 sing both. How many sing only English songs?
  20. 20.In a group of 25 children, 14 enjoy drawing, 19 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  21. 21.In a group of 51 children, 24 sing Hindi songs, 20 sing English songs and 6 sing both. How many sing only Hindi songs?
  22. 22.In a group of 46 children, 28 like mangoes, 14 like bananas and 9 like both. How many like only bananas?
  23. 23.In a group of 42 grown-ups, 25 drink tea, 12 drink coffee and 7 drink both. How many drink only coffee?
  24. 24.In a group of 56 children, 29 like mangoes, 30 like bananas and 11 like both. How many like neither of the two?
  25. 25.In a group of 33 children, 13 enjoy drawing, 17 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  26. 26.In a group of 40 grown-ups, 15 drink tea, 31 drink coffee and 12 drink both. How many drink exactly one of the two?
  27. 27.In a group of 33 children, 12 sing Hindi songs, 19 sing English songs and 9 sing both. How many sing only Hindi songs?
  28. 28.In a group of 19 children, 11 like mangoes, 12 like bananas and 6 like both. How many like at least one of the two?
  29. 29.In a group of 42 grown-ups, 21 drink tea, 31 drink coffee and 12 drink both. How many drink neither of the two?
  30. 30.In a group of 33 children, 17 play cricket, 24 play football and 9 play both. How many play only cricket?
  31. 31.In a group of 41 grown-ups, 21 drink tea, 16 drink coffee and 6 drink both. How many drink only coffee?
  32. 32.In a group of 45 children, 30 like mangoes, 24 like bananas and 10 like both. How many like exactly one of the two?
  33. 33.In a group of 30 children, 9 enjoy drawing, 21 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  34. 34.In a group of 34 grown-ups, 17 drink tea, 18 drink coffee and 6 drink both. How many drink at least one of the two?
  35. 35.In a group of 49 children, 22 sing Hindi songs, 30 sing English songs and 12 sing both. How many sing neither of the two?
  36. 36.In a group of 41 children, 21 enjoy drawing, 23 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  37. 37.In a group of 28 children, 6 enjoy drawing, 14 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  38. 38.In a group of 40 children, 16 like mangoes, 22 like bananas and 10 like both. How many like neither of the two?
  39. 39.In a group of 28 children, 9 play cricket, 19 play football and 2 play both. How many play neither of the two?
  40. 40.In a group of 48 children, 23 play cricket, 18 play football and 5 play both. How many play only cricket?

Answer key

  1. 16
  2. 10
  3. 11
  4. 21
  5. 13
  6. 4
  7. 6
  8. 6
  9. 45
  10. 15
  11. 19
  12. 24
  13. 9
  14. 10
  15. 15
  16. 4
  17. 26
  18. 1
  19. 14
  20. 3
  21. 18
  22. 5
  23. 5
  24. 8
  25. 13
  26. 22
  27. 3
  28. 17
  29. 2
  30. 8
  31. 10
  32. 34
  33. 24
  34. 29
  35. 9
  36. 40
  37. 3
  38. 12
  39. 2
  40. 18

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