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Logical reasoning lesson 22: Venn diagrams · Set 44 · 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 34 children, 15 sing Hindi songs, 10 sing English songs and 3 sing both. How many sing exactly one of the two?
  2. 2.In a group of 43 children, 15 sing Hindi songs, 20 sing English songs and 7 sing both. How many sing at least one of the two?
  3. 3.In a group of 37 grown-ups, 26 drink tea, 16 drink coffee and 6 drink both. How many drink at least one of the two?
  4. 4.In a group of 43 grown-ups, 12 drink tea, 28 drink coffee and 9 drink both. How many drink exactly one of the two?
  5. 5.In a group of 39 children, 19 sing Hindi songs, 29 sing English songs and 12 sing both. How many sing exactly one of the two?
  6. 6.In a group of 31 children, 12 play cricket, 22 play football and 9 play both. How many play neither of the two?
  7. 7.In a group of 29 children, 20 enjoy drawing, 12 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  8. 8.In a group of 34 children, 21 enjoy drawing, 16 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  9. 9.In a group of 19 children, 13 like mangoes, 8 like bananas and 3 like both. How many like only mangoes?
  10. 10.In a group of 34 grown-ups, 13 drink tea, 21 drink coffee and 6 drink both. How many drink exactly one of the two?
  11. 11.In a group of 32 children, 17 like mangoes, 25 like bananas and 11 like both. How many like neither of the two?
  12. 12.In a group of 31 grown-ups, 18 drink tea, 19 drink coffee and 12 drink both. How many drink exactly one of the two?
  13. 13.In a group of 56 children, 32 enjoy drawing, 23 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  14. 14.In a group of 32 children, 13 like mangoes, 17 like bananas and 6 like both. How many like only mangoes?
  15. 15.In a group of 35 children, 26 play cricket, 13 play football and 7 play both. How many play only cricket?
  16. 16.In a group of 48 grown-ups, 25 drink tea, 29 drink coffee and 9 drink both. How many drink only coffee?
  17. 17.In a group of 45 children, 29 like mangoes, 24 like bananas and 9 like both. How many like exactly one of the two?
  18. 18.In a group of 42 children, 23 sing Hindi songs, 27 sing English songs and 11 sing both. How many sing neither of the two?
  19. 19.In a group of 31 children, 18 sing Hindi songs, 13 sing English songs and 10 sing both. How many sing at least one of the two?
  20. 20.In a group of 40 grown-ups, 20 drink tea, 20 drink coffee and 3 drink both. How many drink neither of the two?
  21. 21.In a group of 33 grown-ups, 12 drink tea, 18 drink coffee and 4 drink both. How many drink at least one of the two?
  22. 22.In a group of 44 children, 30 play cricket, 23 play football and 12 play both. How many play only cricket?
  23. 23.In a group of 37 children, 17 play cricket, 9 play football and 4 play both. How many play only football?
  24. 24.In a group of 41 children, 23 like mangoes, 17 like bananas and 11 like both. How many like exactly one of the two?
  25. 25.In a group of 35 children, 15 enjoy drawing, 27 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  26. 26.In a group of 37 grown-ups, 26 drink tea, 16 drink coffee and 10 drink both. How many drink exactly one of the two?
  27. 27.In a group of 38 children, 21 enjoy drawing, 19 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  28. 28.In a group of 41 children, 20 play chess, 30 play carrom and 11 play both. How many play only carrom?
  29. 29.In a group of 16 children, 9 enjoy drawing, 11 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  30. 30.In a group of 41 children, 13 sing Hindi songs, 24 sing English songs and 8 sing both. How many sing only Hindi songs?
  31. 31.In a group of 37 children, 9 sing Hindi songs, 22 sing English songs and 2 sing both. How many sing exactly one of the two?
  32. 32.In a group of 29 children, 11 play cricket, 18 play football and 4 play both. How many play at least one of the two?
  33. 33.In a group of 30 children, 7 enjoy drawing, 21 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  34. 34.In a group of 50 children, 27 like mangoes, 29 like bananas and 11 like both. How many like neither of the two?
  35. 35.In a group of 38 grown-ups, 17 drink tea, 11 drink coffee and 4 drink both. How many drink only coffee?
  36. 36.In a group of 50 children, 22 play chess, 31 play carrom and 11 play both. How many play only carrom?
  37. 37.In a group of 23 children, 13 play chess, 15 play carrom and 8 play both. How many play exactly one of the two?
  38. 38.In a group of 39 children, 17 like mangoes, 18 like bananas and 7 like both. How many like neither of the two?
  39. 39.In a group of 55 children, 29 enjoy drawing, 27 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  40. 40.In a group of 48 children, 30 like mangoes, 19 like bananas and 12 like both. How many like neither of the two?

Answer key

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

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