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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 109 · 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 36 children, 24 like mangoes, 16 like bananas and 5 like both. How many like exactly one of the two?
  2. 2.In a group of 19 children, 7 enjoy drawing, 6 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  3. 3.In a group of 40 children, 9 play cricket, 24 play football and 6 play both. How many play only football?
  4. 4.In a group of 34 children, 13 like mangoes, 20 like bananas and 5 like both. How many like at least one of the two?
  5. 5.In a group of 40 children, 24 play cricket, 15 play football and 8 play both. How many play neither of the two?
  6. 6.In a group of 33 grown-ups, 14 drink tea, 28 drink coffee and 11 drink both. How many drink neither of the two?
  7. 7.In a group of 39 children, 27 play cricket, 15 play football and 7 play both. How many play only football?
  8. 8.In a group of 66 grown-ups, 32 drink tea, 32 drink coffee and 12 drink both. How many drink at least one of the two?
  9. 9.In a group of 47 children, 21 sing Hindi songs, 28 sing English songs and 11 sing both. How many sing only Hindi songs?
  10. 10.In a group of 42 grown-ups, 23 drink tea, 22 drink coffee and 10 drink both. How many drink only tea?
  11. 11.In a group of 44 grown-ups, 21 drink tea, 24 drink coffee and 4 drink both. How many drink only tea?
  12. 12.In a group of 42 grown-ups, 25 drink tea, 13 drink coffee and 9 drink both. How many drink at least one of the two?
  13. 13.In a group of 40 grown-ups, 9 drink tea, 24 drink coffee and 4 drink both. How many drink neither of the two?
  14. 14.In a group of 50 grown-ups, 23 drink tea, 26 drink coffee and 8 drink both. How many drink exactly one of the two?
  15. 15.In a group of 31 children, 13 enjoy drawing, 25 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  16. 16.In a group of 35 children, 18 play cricket, 18 play football and 7 play both. How many play only cricket?
  17. 17.In a group of 34 children, 16 sing Hindi songs, 15 sing English songs and 8 sing both. How many sing exactly one of the two?
  18. 18.In a group of 28 children, 11 enjoy drawing, 17 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  19. 19.In a group of 48 children, 29 like mangoes, 25 like bananas and 11 like both. How many like exactly one of the two?
  20. 20.In a group of 52 children, 31 sing Hindi songs, 20 sing English songs and 12 sing both. How many sing exactly one of the two?
  21. 21.In a group of 32 children, 18 play cricket, 8 play football and 2 play both. How many play at least one of the two?
  22. 22.In a group of 40 children, 8 enjoy drawing, 24 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  23. 23.In a group of 52 children, 32 sing Hindi songs, 21 sing English songs and 12 sing both. How many sing neither of the two?
  24. 24.In a group of 54 children, 28 play chess, 26 play carrom and 8 play both. How many play only chess?
  25. 25.In a group of 24 grown-ups, 13 drink tea, 16 drink coffee and 7 drink both. How many drink neither of the two?
  26. 26.In a group of 21 children, 15 play cricket, 12 play football and 9 play both. How many play at least one of the two?
  27. 27.In a group of 37 children, 16 like mangoes, 15 like bananas and 2 like both. How many like only bananas?
  28. 28.In a group of 52 grown-ups, 31 drink tea, 20 drink coffee and 12 drink both. How many drink at least one of the two?
  29. 29.In a group of 46 children, 29 play cricket, 20 play football and 9 play both. How many play at least one of the two?
  30. 30.In a group of 53 children, 26 play chess, 24 play carrom and 6 play both. How many play at least one of the two?
  31. 31.In a group of 47 children, 18 play cricket, 28 play football and 12 play both. How many play neither of the two?
  32. 32.In a group of 45 children, 21 play chess, 26 play carrom and 8 play both. How many play neither of the two?
  33. 33.In a group of 35 children, 17 play cricket, 24 play football and 7 play both. How many play only football?
  34. 34.In a group of 40 children, 12 play chess, 24 play carrom and 4 play both. How many play exactly one of the two?
  35. 35.In a group of 42 children, 28 enjoy drawing, 19 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  36. 36.In a group of 39 children, 15 enjoy drawing, 24 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  37. 37.In a group of 58 children, 29 like mangoes, 30 like bananas and 11 like both. How many like neither of the two?
  38. 38.In a group of 49 children, 29 play chess, 28 play carrom and 12 play both. How many play neither of the two?
  39. 39.In a group of 21 children, 10 like mangoes, 13 like bananas and 6 like both. How many like only mangoes?
  40. 40.In a group of 29 children, 8 like mangoes, 11 like bananas and 3 like both. How many like exactly one of the two?

Answer key

  1. 30
  2. 10
  3. 18
  4. 28
  5. 9
  6. 2
  7. 8
  8. 52
  9. 10
  10. 13
  11. 17
  12. 29
  13. 11
  14. 33
  15. 3
  16. 11
  17. 15
  18. 5
  19. 32
  20. 27
  21. 24
  22. 12
  23. 11
  24. 20
  25. 2
  26. 18
  27. 13
  28. 39
  29. 40
  30. 44
  31. 13
  32. 6
  33. 17
  34. 28
  35. 4
  36. 15
  37. 10
  38. 4
  39. 4
  40. 13

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