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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 275 · 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 38 children, 12 enjoy drawing, 26 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  2. 2.In a group of 25 children, 19 play cricket, 7 play football and 2 play both. How many play exactly one of the two?
  3. 3.In a group of 20 children, 9 play cricket, 10 play football and 4 play both. How many play neither of the two?
  4. 4.In a group of 28 grown-ups, 21 drink tea, 10 drink coffee and 4 drink both. How many drink only tea?
  5. 5.In a group of 39 children, 23 play cricket, 18 play football and 8 play both. How many play at least one of the two?
  6. 6.In a group of 32 children, 22 enjoy drawing, 12 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  7. 7.In a group of 34 children, 15 enjoy drawing, 24 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  8. 8.In a group of 33 grown-ups, 11 drink tea, 13 drink coffee and 2 drink both. How many drink only tea?
  9. 9.In a group of 56 children, 30 sing Hindi songs, 30 sing English songs and 12 sing both. How many sing at least one of the two?
  10. 10.In a group of 25 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 51 children, 21 sing Hindi songs, 27 sing English songs and 8 sing both. How many sing only Hindi songs?
  12. 12.In a group of 24 grown-ups, 11 drink tea, 16 drink coffee and 7 drink both. How many drink at least one of the two?
  13. 13.In a group of 19 children, 8 like mangoes, 15 like bananas and 5 like both. How many like at least one of the two?
  14. 14.In a group of 28 grown-ups, 14 drink tea, 10 drink coffee and 7 drink both. How many drink neither of the two?
  15. 15.In a group of 27 children, 19 sing Hindi songs, 17 sing English songs and 10 sing both. How many sing at least one of the two?
  16. 16.In a group of 37 children, 21 sing Hindi songs, 18 sing English songs and 4 sing both. How many sing neither of the two?
  17. 17.In a group of 36 children, 26 play chess, 18 play carrom and 11 play both. How many play only chess?
  18. 18.In a group of 26 children, 12 play chess, 11 play carrom and 7 play both. How many play only chess?
  19. 19.In a group of 49 grown-ups, 24 drink tea, 31 drink coffee and 11 drink both. How many drink at least one of the two?
  20. 20.In a group of 38 children, 18 like mangoes, 18 like bananas and 8 like both. How many like neither of the two?
  21. 21.In a group of 29 grown-ups, 15 drink tea, 20 drink coffee and 10 drink both. How many drink neither of the two?
  22. 22.In a group of 17 children, 7 like mangoes, 12 like bananas and 4 like both. How many like only bananas?
  23. 23.In a group of 21 children, 9 play chess, 7 play carrom and 2 play both. How many play neither of the two?
  24. 24.In a group of 45 children, 24 play chess, 13 play carrom and 7 play both. How many play exactly one of the two?
  25. 25.In a group of 47 children, 23 sing Hindi songs, 20 sing English songs and 6 sing both. How many sing neither of the two?
  26. 26.In a group of 36 children, 14 enjoy drawing, 22 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  27. 27.In a group of 29 children, 21 play cricket, 7 play football and 2 play both. How many play exactly one of the two?
  28. 28.In a group of 41 children, 24 play cricket, 17 play football and 5 play both. How many play exactly one of the two?
  29. 29.In a group of 28 children, 14 play chess, 7 play carrom and 2 play both. How many play at least one of the two?
  30. 30.In a group of 44 children, 29 play cricket, 25 play football and 11 play both. How many play only cricket?
  31. 31.In a group of 34 children, 13 play cricket, 23 play football and 5 play both. How many play at least one of the two?
  32. 32.In a group of 28 children, 10 enjoy drawing, 17 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  33. 33.In a group of 37 children, 21 sing Hindi songs, 10 sing English songs and 3 sing both. How many sing neither of the two?
  34. 34.In a group of 35 children, 13 play chess, 11 play carrom and 4 play both. How many play only chess?
  35. 35.In a group of 29 children, 16 sing Hindi songs, 20 sing English songs and 12 sing both. How many sing neither of the two?
  36. 36.In a group of 29 children, 16 like mangoes, 14 like bananas and 6 like both. How many like only bananas?
  37. 37.In a group of 35 children, 16 enjoy drawing, 19 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  38. 38.In a group of 48 grown-ups, 26 drink tea, 26 drink coffee and 6 drink both. How many drink at least one of the two?
  39. 39.In a group of 49 grown-ups, 17 drink tea, 24 drink coffee and 4 drink both. How many drink exactly one of the two?
  40. 40.In a group of 30 children, 14 like mangoes, 19 like bananas and 6 like both. How many like only bananas?

Answer key

  1. 7
  2. 22
  3. 5
  4. 17
  5. 33
  6. 9
  7. 32
  8. 9
  9. 48
  10. 1
  11. 13
  12. 20
  13. 18
  14. 11
  15. 26
  16. 2
  17. 15
  18. 5
  19. 44
  20. 10
  21. 4
  22. 8
  23. 7
  24. 23
  25. 10
  26. 7
  27. 24
  28. 31
  29. 19
  30. 18
  31. 31
  32. 23
  33. 9
  34. 9
  35. 5
  36. 8
  37. 13
  38. 46
  39. 33
  40. 13

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