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Logical reasoning lesson 22: Venn diagrams · Set 32 · 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 24 children, 17 play cricket, 15 play football and 9 play both. How many play only cricket?
  2. 2.In a group of 26 children, 10 like mangoes, 16 like bananas and 3 like both. How many like exactly one of the two?
  3. 3.In a group of 44 children, 25 sing Hindi songs, 23 sing English songs and 5 sing both. How many sing exactly one of the two?
  4. 4.In a group of 41 grown-ups, 20 drink tea, 25 drink coffee and 10 drink both. How many drink only coffee?
  5. 5.In a group of 40 children, 21 like mangoes, 18 like bananas and 3 like both. How many like only bananas?
  6. 6.In a group of 54 children, 26 play chess, 25 play carrom and 8 play both. How many play exactly one of the two?
  7. 7.In a group of 26 grown-ups, 17 drink tea, 12 drink coffee and 6 drink both. How many drink at least one of the two?
  8. 8.In a group of 44 grown-ups, 11 drink tea, 22 drink coffee and 4 drink both. How many drink only tea?
  9. 9.In a group of 36 children, 12 enjoy drawing, 21 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  10. 10.In a group of 35 grown-ups, 13 drink tea, 20 drink coffee and 5 drink both. How many drink at least one of the two?
  11. 11.In a group of 42 children, 27 play cricket, 15 play football and 11 play both. How many play only cricket?
  12. 12.In a group of 28 children, 21 like mangoes, 11 like bananas and 7 like both. How many like only mangoes?
  13. 13.In a group of 39 children, 15 play cricket, 21 play football and 8 play both. How many play only cricket?
  14. 14.In a group of 44 children, 14 like mangoes, 24 like bananas and 4 like both. How many like at least one of the two?
  15. 15.In a group of 41 children, 17 enjoy drawing, 17 enjoy dancing and 5 enjoy both. How many enjoy at least one of the two?
  16. 16.In a group of 42 children, 18 play cricket, 18 play football and 4 play both. How many play only cricket?
  17. 17.In a group of 43 children, 23 enjoy drawing, 28 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  18. 18.In a group of 44 children, 22 like mangoes, 27 like bananas and 9 like both. How many like neither of the two?
  19. 19.In a group of 43 children, 26 sing Hindi songs, 10 sing English songs and 6 sing both. How many sing neither of the two?
  20. 20.In a group of 30 children, 10 sing Hindi songs, 16 sing English songs and 3 sing both. How many sing exactly one of the two?
  21. 21.In a group of 49 children, 18 play cricket, 25 play football and 7 play both. How many play only cricket?
  22. 22.In a group of 28 children, 12 play chess, 14 play carrom and 3 play both. How many play exactly one of the two?
  23. 23.In a group of 38 children, 27 sing Hindi songs, 15 sing English songs and 12 sing both. How many sing at least one of the two?
  24. 24.In a group of 41 grown-ups, 28 drink tea, 21 drink coffee and 12 drink both. How many drink at least one of the two?
  25. 25.In a group of 39 children, 19 sing Hindi songs, 18 sing English songs and 12 sing both. How many sing neither of the two?
  26. 26.In a group of 56 grown-ups, 22 drink tea, 30 drink coffee and 10 drink both. How many drink exactly one of the two?
  27. 27.In a group of 24 children, 5 enjoy drawing, 17 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  28. 28.In a group of 31 children, 11 sing Hindi songs, 20 sing English songs and 3 sing both. How many sing neither of the two?
  29. 29.In a group of 58 grown-ups, 29 drink tea, 25 drink coffee and 11 drink both. How many drink neither of the two?
  30. 30.In a group of 30 children, 5 enjoy drawing, 18 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  31. 31.In a group of 44 children, 23 play chess, 18 play carrom and 4 play both. How many play only chess?
  32. 32.In a group of 55 children, 20 sing Hindi songs, 24 sing English songs and 4 sing both. How many sing at least one of the two?
  33. 33.In a group of 57 children, 25 enjoy drawing, 25 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  34. 34.In a group of 33 children, 17 play cricket, 19 play football and 7 play both. How many play neither of the two?
  35. 35.In a group of 38 children, 21 sing Hindi songs, 15 sing English songs and 3 sing both. How many sing only Hindi songs?
  36. 36.In a group of 33 children, 19 like mangoes, 10 like bananas and 7 like both. How many like at least one of the two?
  37. 37.In a group of 26 children, 8 play cricket, 12 play football and 5 play both. How many play only football?
  38. 38.In a group of 31 children, 9 play cricket, 16 play football and 6 play both. How many play neither of the two?
  39. 39.In a group of 36 children, 12 enjoy drawing, 23 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  40. 40.In a group of 53 children, 27 play chess, 20 play carrom and 8 play both. How many play exactly one of the two?

Answer key

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

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