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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 526 · 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 52 children, 23 enjoy drawing, 29 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  2. 2.In a group of 35 children, 13 like mangoes, 23 like bananas and 5 like both. How many like neither of the two?
  3. 3.In a group of 42 children, 21 like mangoes, 28 like bananas and 12 like both. How many like exactly one of the two?
  4. 4.In a group of 28 children, 8 like mangoes, 22 like bananas and 3 like both. How many like exactly one of the two?
  5. 5.In a group of 39 children, 13 sing Hindi songs, 24 sing English songs and 7 sing both. How many sing only English songs?
  6. 6.In a group of 24 grown-ups, 12 drink tea, 8 drink coffee and 2 drink both. How many drink exactly one of the two?
  7. 7.In a group of 53 children, 29 play chess, 26 play carrom and 9 play both. How many play neither of the two?
  8. 8.In a group of 36 children, 17 play chess, 15 play carrom and 6 play both. How many play only chess?
  9. 9.In a group of 32 children, 14 play cricket, 13 play football and 3 play both. How many play neither of the two?
  10. 10.In a group of 37 children, 16 play cricket, 32 play football and 12 play both. How many play only football?
  11. 11.In a group of 19 children, 11 play cricket, 10 play football and 3 play both. How many play neither of the two?
  12. 12.In a group of 33 children, 16 enjoy drawing, 10 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  13. 13.In a group of 41 children, 24 sing Hindi songs, 18 sing English songs and 5 sing both. How many sing only Hindi songs?
  14. 14.In a group of 24 children, 13 play chess, 7 play carrom and 2 play both. How many play exactly one of the two?
  15. 15.In a group of 38 grown-ups, 31 drink tea, 18 drink coffee and 12 drink both. How many drink only coffee?
  16. 16.In a group of 30 children, 14 play chess, 16 play carrom and 4 play both. How many play only carrom?
  17. 17.In a group of 18 children, 6 sing Hindi songs, 11 sing English songs and 3 sing both. How many sing neither of the two?
  18. 18.In a group of 39 children, 14 play chess, 20 play carrom and 2 play both. How many play neither of the two?
  19. 19.In a group of 47 grown-ups, 20 drink tea, 18 drink coffee and 5 drink both. How many drink neither of the two?
  20. 20.In a group of 42 children, 23 enjoy drawing, 26 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  21. 21.In a group of 44 children, 18 sing Hindi songs, 22 sing English songs and 10 sing both. How many sing exactly one of the two?
  22. 22.In a group of 38 grown-ups, 15 drink tea, 28 drink coffee and 8 drink both. How many drink only tea?
  23. 23.In a group of 31 grown-ups, 13 drink tea, 8 drink coffee and 4 drink both. How many drink only tea?
  24. 24.In a group of 23 grown-ups, 6 drink tea, 6 drink coffee and 2 drink both. How many drink exactly one of the two?
  25. 25.In a group of 39 children, 25 enjoy drawing, 22 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  26. 26.In a group of 46 children, 28 play cricket, 18 play football and 12 play both. How many play only football?
  27. 27.In a group of 26 children, 13 play chess, 15 play carrom and 4 play both. How many play exactly one of the two?
  28. 28.In a group of 50 children, 25 play chess, 24 play carrom and 6 play both. How many play only chess?
  29. 29.In a group of 42 children, 9 like mangoes, 22 like bananas and 4 like both. How many like only bananas?
  30. 30.In a group of 47 grown-ups, 27 drink tea, 27 drink coffee and 11 drink both. How many drink neither of the two?
  31. 31.In a group of 17 children, 13 sing Hindi songs, 10 sing English songs and 7 sing both. How many sing at least one of the two?
  32. 32.In a group of 32 children, 13 enjoy drawing, 20 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  33. 33.In a group of 44 children, 19 play chess, 24 play carrom and 8 play both. How many play only chess?
  34. 34.In a group of 25 children, 13 play cricket, 10 play football and 7 play both. How many play neither of the two?
  35. 35.In a group of 39 children, 23 sing Hindi songs, 18 sing English songs and 6 sing both. How many sing only English songs?
  36. 36.In a group of 41 children, 20 play cricket, 14 play football and 3 play both. How many play at least one of the two?
  37. 37.In a group of 37 children, 12 like mangoes, 19 like bananas and 5 like both. How many like at least one of the two?
  38. 38.In a group of 45 children, 16 play cricket, 24 play football and 9 play both. How many play at least one of the two?
  39. 39.In a group of 49 grown-ups, 23 drink tea, 26 drink coffee and 10 drink both. How many drink exactly one of the two?
  40. 40.In a group of 47 grown-ups, 28 drink tea, 14 drink coffee and 10 drink both. How many drink neither of the two?

Answer key

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

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