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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 81 · 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 50 children, 16 play cricket, 31 play football and 12 play both. How many play at least one of the two?
  2. 2.In a group of 34 children, 18 play cricket, 19 play football and 11 play both. How many play only football?
  3. 3.In a group of 45 children, 27 sing Hindi songs, 13 sing English songs and 8 sing both. How many sing exactly one of the two?
  4. 4.In a group of 37 children, 9 enjoy drawing, 18 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  5. 5.In a group of 23 grown-ups, 13 drink tea, 9 drink coffee and 2 drink both. How many drink only tea?
  6. 6.In a group of 28 children, 7 enjoy drawing, 22 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  7. 7.In a group of 42 children, 23 play chess, 21 play carrom and 7 play both. How many play at least one of the two?
  8. 8.In a group of 43 children, 30 like mangoes, 13 like bananas and 10 like both. How many like exactly one of the two?
  9. 9.In a group of 26 grown-ups, 12 drink tea, 10 drink coffee and 7 drink both. How many drink at least one of the two?
  10. 10.In a group of 38 children, 14 sing Hindi songs, 29 sing English songs and 9 sing both. How many sing neither of the two?
  11. 11.In a group of 32 grown-ups, 9 drink tea, 22 drink coffee and 2 drink both. How many drink only tea?
  12. 12.In a group of 42 children, 26 like mangoes, 14 like bananas and 9 like both. How many like exactly one of the two?
  13. 13.In a group of 53 children, 29 play chess, 28 play carrom and 9 play both. How many play only chess?
  14. 14.In a group of 24 children, 7 like mangoes, 12 like bananas and 4 like both. How many like exactly one of the two?
  15. 15.In a group of 25 children, 8 like mangoes, 18 like bananas and 2 like both. How many like at least one of the two?
  16. 16.In a group of 22 children, 7 like mangoes, 16 like bananas and 2 like both. How many like exactly one of the two?
  17. 17.In a group of 26 children, 8 play cricket, 15 play football and 5 play both. How many play only football?
  18. 18.In a group of 26 grown-ups, 11 drink tea, 7 drink coffee and 2 drink both. How many drink only tea?
  19. 19.In a group of 31 children, 15 sing Hindi songs, 16 sing English songs and 8 sing both. How many sing neither of the two?
  20. 20.In a group of 55 children, 24 enjoy drawing, 28 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  21. 21.In a group of 32 children, 18 enjoy drawing, 10 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?
  22. 22.In a group of 48 children, 17 sing Hindi songs, 28 sing English songs and 12 sing both. How many sing only Hindi songs?
  23. 23.In a group of 35 children, 18 enjoy drawing, 24 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  24. 24.In a group of 37 children, 13 play chess, 26 play carrom and 9 play both. How many play at least one of the two?
  25. 25.In a group of 37 children, 21 enjoy drawing, 11 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  26. 26.In a group of 42 children, 14 play chess, 29 play carrom and 10 play both. How many play at least one of the two?
  27. 27.In a group of 17 children, 8 enjoy drawing, 10 enjoy dancing and 5 enjoy both. How many enjoy at least one of the two?
  28. 28.In a group of 33 grown-ups, 16 drink tea, 24 drink coffee and 9 drink both. How many drink neither of the two?
  29. 29.In a group of 42 grown-ups, 16 drink tea, 18 drink coffee and 6 drink both. How many drink only tea?
  30. 30.In a group of 29 children, 16 play chess, 16 play carrom and 8 play both. How many play neither of the two?
  31. 31.In a group of 46 children, 17 play chess, 26 play carrom and 9 play both. How many play neither of the two?
  32. 32.In a group of 22 children, 7 play chess, 13 play carrom and 4 play both. How many play only chess?
  33. 33.In a group of 44 children, 23 play chess, 19 play carrom and 6 play both. How many play neither of the two?
  34. 34.In a group of 28 children, 12 sing Hindi songs, 22 sing English songs and 8 sing both. How many sing only English songs?
  35. 35.In a group of 24 children, 18 like mangoes, 15 like bananas and 12 like both. How many like only mangoes?
  36. 36.In a group of 47 children, 28 like mangoes, 20 like bananas and 8 like both. How many like exactly one of the two?
  37. 37.In a group of 22 grown-ups, 14 drink tea, 13 drink coffee and 7 drink both. How many drink neither of the two?
  38. 38.In a group of 26 grown-ups, 19 drink tea, 14 drink coffee and 10 drink both. How many drink only tea?
  39. 39.In a group of 47 children, 21 sing Hindi songs, 30 sing English songs and 11 sing both. How many sing only Hindi songs?
  40. 40.In a group of 48 children, 27 play cricket, 25 play football and 12 play both. How many play at least one of the two?

Answer key

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

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