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Logical reasoning lesson 22: Venn diagrams · Set 345 · 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 43 children, 31 enjoy drawing, 18 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  2. 2.In a group of 26 children, 6 sing Hindi songs, 18 sing English songs and 2 sing both. How many sing only Hindi songs?
  3. 3.In a group of 38 grown-ups, 27 drink tea, 17 drink coffee and 8 drink both. How many drink at least one of the two?
  4. 4.In a group of 32 grown-ups, 12 drink tea, 10 drink coffee and 4 drink both. How many drink neither of the two?
  5. 5.In a group of 40 grown-ups, 11 drink tea, 24 drink coffee and 4 drink both. How many drink neither of the two?
  6. 6.In a group of 30 children, 22 enjoy drawing, 11 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?
  7. 7.In a group of 32 grown-ups, 13 drink tea, 9 drink coffee and 3 drink both. How many drink neither of the two?
  8. 8.In a group of 25 children, 9 play cricket, 17 play football and 3 play both. How many play at least one of the two?
  9. 9.In a group of 42 grown-ups, 22 drink tea, 12 drink coffee and 6 drink both. How many drink exactly one of the two?
  10. 10.In a group of 31 grown-ups, 14 drink tea, 7 drink coffee and 3 drink both. How many drink neither of the two?
  11. 11.In a group of 42 children, 21 enjoy drawing, 13 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  12. 12.In a group of 36 children, 18 like mangoes, 17 like bananas and 4 like both. How many like only mangoes?
  13. 13.In a group of 32 children, 12 play chess, 20 play carrom and 2 play both. How many play at least one of the two?
  14. 14.In a group of 42 children, 24 sing Hindi songs, 21 sing English songs and 11 sing both. How many sing only Hindi songs?
  15. 15.In a group of 33 children, 17 enjoy drawing, 15 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  16. 16.In a group of 42 children, 20 sing Hindi songs, 25 sing English songs and 5 sing both. How many sing only Hindi songs?
  17. 17.In a group of 48 children, 19 play chess, 19 play carrom and 2 play both. How many play exactly one of the two?
  18. 18.In a group of 33 children, 15 sing Hindi songs, 21 sing English songs and 10 sing both. How many sing neither of the two?
  19. 19.In a group of 38 children, 22 play chess, 16 play carrom and 9 play both. How many play only chess?
  20. 20.In a group of 37 grown-ups, 17 drink tea, 23 drink coffee and 12 drink both. How many drink neither of the two?
  21. 21.In a group of 28 children, 14 sing Hindi songs, 19 sing English songs and 8 sing both. How many sing only English songs?
  22. 22.In a group of 32 children, 23 play chess, 13 play carrom and 7 play both. How many play exactly one of the two?
  23. 23.In a group of 33 grown-ups, 15 drink tea, 12 drink coffee and 4 drink both. How many drink neither of the two?
  24. 24.In a group of 18 children, 13 enjoy drawing, 12 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  25. 25.In a group of 26 grown-ups, 5 drink tea, 8 drink coffee and 2 drink both. How many drink at least one of the two?
  26. 26.In a group of 30 grown-ups, 20 drink tea, 14 drink coffee and 5 drink both. How many drink neither of the two?
  27. 27.In a group of 42 children, 27 sing Hindi songs, 21 sing English songs and 10 sing both. How many sing neither of the two?
  28. 28.In a group of 43 children, 26 like mangoes, 12 like bananas and 9 like both. How many like neither of the two?
  29. 29.In a group of 30 children, 14 enjoy drawing, 14 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  30. 30.In a group of 42 children, 26 play cricket, 20 play football and 12 play both. How many play exactly one of the two?
  31. 31.In a group of 45 grown-ups, 19 drink tea, 14 drink coffee and 2 drink both. How many drink only coffee?
  32. 32.In a group of 44 children, 13 enjoy drawing, 30 enjoy dancing and 10 enjoy both. How many enjoy at least one of the two?
  33. 33.In a group of 31 children, 13 enjoy drawing, 21 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  34. 34.In a group of 30 children, 10 play cricket, 19 play football and 4 play both. How many play only football?
  35. 35.In a group of 49 grown-ups, 21 drink tea, 26 drink coffee and 6 drink both. How many drink only coffee?
  36. 36.In a group of 62 children, 30 sing Hindi songs, 31 sing English songs and 12 sing both. How many sing neither of the two?
  37. 37.In a group of 35 children, 18 sing Hindi songs, 7 sing English songs and 4 sing both. How many sing neither of the two?
  38. 38.In a group of 50 children, 24 play chess, 30 play carrom and 12 play both. How many play at least one of the two?
  39. 39.In a group of 33 children, 12 sing Hindi songs, 29 sing English songs and 9 sing both. How many sing only Hindi songs?
  40. 40.In a group of 25 children, 5 play cricket, 10 play football and 2 play both. How many play only cricket?

Answer key

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

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