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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 382 · 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 35 grown-ups, 14 drink tea, 22 drink coffee and 9 drink both. How many drink neither of the two?
  2. 2.In a group of 25 children, 11 enjoy drawing, 8 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  3. 3.In a group of 18 children, 9 play chess, 5 play carrom and 2 play both. How many play only chess?
  4. 4.In a group of 31 children, 7 like mangoes, 13 like bananas and 4 like both. How many like at least one of the two?
  5. 5.In a group of 31 grown-ups, 12 drink tea, 13 drink coffee and 7 drink both. How many drink at least one of the two?
  6. 6.In a group of 35 grown-ups, 8 drink tea, 21 drink coffee and 2 drink both. How many drink only tea?
  7. 7.In a group of 41 children, 22 sing Hindi songs, 20 sing English songs and 6 sing both. How many sing at least one of the two?
  8. 8.In a group of 36 children, 15 play cricket, 10 play football and 3 play both. How many play only cricket?
  9. 9.In a group of 44 children, 31 like mangoes, 21 like bananas and 11 like both. How many like only mangoes?
  10. 10.In a group of 28 grown-ups, 20 drink tea, 14 drink coffee and 10 drink both. How many drink neither of the two?
  11. 11.In a group of 24 grown-ups, 19 drink tea, 13 drink coffee and 9 drink both. How many drink at least one of the two?
  12. 12.In a group of 54 children, 25 play chess, 21 play carrom and 7 play both. How many play exactly one of the two?
  13. 13.In a group of 33 children, 14 play chess, 19 play carrom and 2 play both. How many play neither of the two?
  14. 14.In a group of 41 children, 15 sing Hindi songs, 20 sing English songs and 4 sing both. How many sing exactly one of the two?
  15. 15.In a group of 36 grown-ups, 22 drink tea, 22 drink coffee and 10 drink both. How many drink only coffee?
  16. 16.In a group of 39 children, 21 play cricket, 12 play football and 4 play both. How many play neither of the two?
  17. 17.In a group of 35 children, 25 like mangoes, 16 like bananas and 12 like both. How many like only bananas?
  18. 18.In a group of 42 children, 18 play cricket, 30 play football and 12 play both. How many play only football?
  19. 19.In a group of 38 children, 30 sing Hindi songs, 18 sing English songs and 11 sing both. How many sing only Hindi songs?
  20. 20.In a group of 43 children, 26 play cricket, 26 play football and 10 play both. How many play at least one of the two?
  21. 21.In a group of 38 children, 30 sing Hindi songs, 16 sing English songs and 10 sing both. How many sing neither of the two?
  22. 22.In a group of 29 children, 11 play cricket, 13 play football and 3 play both. How many play exactly one of the two?
  23. 23.In a group of 30 children, 15 like mangoes, 17 like bananas and 9 like both. How many like neither of the two?
  24. 24.In a group of 44 children, 22 sing Hindi songs, 18 sing English songs and 5 sing both. How many sing exactly one of the two?
  25. 25.In a group of 47 children, 22 like mangoes, 22 like bananas and 2 like both. How many like exactly one of the two?
  26. 26.In a group of 38 children, 9 sing Hindi songs, 21 sing English songs and 2 sing both. How many sing neither of the two?
  27. 27.In a group of 32 grown-ups, 11 drink tea, 12 drink coffee and 4 drink both. How many drink at least one of the two?
  28. 28.In a group of 44 children, 26 sing Hindi songs, 20 sing English songs and 8 sing both. How many sing at least one of the two?
  29. 29.In a group of 40 children, 18 sing Hindi songs, 18 sing English songs and 3 sing both. How many sing only Hindi songs?
  30. 30.In a group of 22 children, 10 like mangoes, 8 like bananas and 3 like both. How many like only mangoes?
  31. 31.In a group of 37 children, 12 like mangoes, 20 like bananas and 7 like both. How many like exactly one of the two?
  32. 32.In a group of 50 children, 29 like mangoes, 22 like bananas and 10 like both. How many like exactly one of the two?
  33. 33.In a group of 27 children, 9 play chess, 7 play carrom and 2 play both. How many play only carrom?
  34. 34.In a group of 40 children, 28 play chess, 16 play carrom and 10 play both. How many play exactly one of the two?
  35. 35.In a group of 37 children, 23 like mangoes, 15 like bananas and 7 like both. How many like neither of the two?
  36. 36.In a group of 28 grown-ups, 12 drink tea, 21 drink coffee and 6 drink both. How many drink only coffee?
  37. 37.In a group of 38 grown-ups, 20 drink tea, 12 drink coffee and 6 drink both. How many drink only coffee?
  38. 38.In a group of 43 children, 13 enjoy drawing, 24 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  39. 39.In a group of 39 children, 26 sing Hindi songs, 18 sing English songs and 10 sing both. How many sing at least one of the two?
  40. 40.In a group of 19 children, 8 play cricket, 10 play football and 2 play both. How many play only cricket?

Answer key

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

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