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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 197 · 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 children, 11 enjoy drawing, 21 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  2. 2.In a group of 53 children, 25 sing Hindi songs, 26 sing English songs and 9 sing both. How many sing at least one of the two?
  3. 3.In a group of 33 children, 15 play cricket, 15 play football and 4 play both. How many play at least one of the two?
  4. 4.In a group of 44 children, 19 play chess, 23 play carrom and 10 play both. How many play neither of the two?
  5. 5.In a group of 29 children, 13 sing Hindi songs, 12 sing English songs and 6 sing both. How many sing exactly one of the two?
  6. 6.In a group of 25 children, 8 play cricket, 13 play football and 3 play both. How many play at least one of the two?
  7. 7.In a group of 25 children, 6 play chess, 7 play carrom and 3 play both. How many play neither of the two?
  8. 8.In a group of 34 children, 20 enjoy drawing, 22 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  9. 9.In a group of 39 grown-ups, 8 drink tea, 23 drink coffee and 4 drink both. How many drink at least one of the two?
  10. 10.In a group of 30 children, 21 sing Hindi songs, 12 sing English songs and 4 sing both. How many sing at least one of the two?
  11. 11.In a group of 28 children, 17 enjoy drawing, 21 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  12. 12.In a group of 54 children, 29 play cricket, 30 play football and 10 play both. How many play exactly one of the two?
  13. 13.In a group of 49 grown-ups, 20 drink tea, 21 drink coffee and 7 drink both. How many drink exactly one of the two?
  14. 14.In a group of 57 children, 26 like mangoes, 24 like bananas and 8 like both. How many like neither of the two?
  15. 15.In a group of 48 children, 31 like mangoes, 15 like bananas and 11 like both. How many like only bananas?
  16. 16.In a group of 33 children, 20 like mangoes, 12 like bananas and 7 like both. How many like only mangoes?
  17. 17.In a group of 55 children, 21 sing Hindi songs, 26 sing English songs and 7 sing both. How many sing only English songs?
  18. 18.In a group of 32 children, 20 play cricket, 7 play football and 4 play both. How many play only football?
  19. 19.In a group of 34 children, 19 enjoy drawing, 18 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  20. 20.In a group of 40 children, 13 play cricket, 22 play football and 2 play both. How many play at least one of the two?
  21. 21.In a group of 47 children, 19 like mangoes, 31 like bananas and 11 like both. How many like only mangoes?
  22. 22.In a group of 45 children, 26 like mangoes, 28 like bananas and 11 like both. How many like only mangoes?
  23. 23.In a group of 48 grown-ups, 13 drink tea, 25 drink coffee and 5 drink both. How many drink at least one of the two?
  24. 24.In a group of 41 children, 12 like mangoes, 23 like bananas and 8 like both. How many like only mangoes?
  25. 25.In a group of 38 children, 21 sing Hindi songs, 13 sing English songs and 2 sing both. How many sing at least one of the two?
  26. 26.In a group of 26 children, 21 play cricket, 6 play football and 3 play both. How many play only cricket?
  27. 27.In a group of 26 children, 13 sing Hindi songs, 7 sing English songs and 2 sing both. How many sing at least one of the two?
  28. 28.In a group of 22 grown-ups, 13 drink tea, 6 drink coffee and 2 drink both. How many drink exactly one of the two?
  29. 29.In a group of 44 children, 24 sing Hindi songs, 26 sing English songs and 12 sing both. How many sing neither of the two?
  30. 30.In a group of 23 grown-ups, 9 drink tea, 10 drink coffee and 6 drink both. How many drink exactly one of the two?
  31. 31.In a group of 31 grown-ups, 15 drink tea, 17 drink coffee and 8 drink both. How many drink exactly one of the two?
  32. 32.In a group of 31 children, 11 like mangoes, 12 like bananas and 6 like both. How many like exactly one of the two?
  33. 33.In a group of 27 children, 18 sing Hindi songs, 11 sing English songs and 5 sing both. How many sing at least one of the two?
  34. 34.In a group of 18 children, 9 play cricket, 11 play football and 3 play both. How many play only football?
  35. 35.In a group of 29 children, 9 like mangoes, 13 like bananas and 4 like both. How many like only mangoes?
  36. 36.In a group of 52 children, 31 sing Hindi songs, 21 sing English songs and 12 sing both. How many sing neither of the two?
  37. 37.In a group of 39 children, 14 enjoy drawing, 19 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  38. 38.In a group of 51 children, 19 sing Hindi songs, 28 sing English songs and 9 sing both. How many sing neither of the two?
  39. 39.In a group of 25 children, 8 enjoy drawing, 18 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  40. 40.In a group of 35 children, 11 enjoy drawing, 20 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?

Answer key

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

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