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Logical reasoning lesson 22: Venn diagrams · Set 29 · 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 20 grown-ups, 13 drink tea, 7 drink coffee and 3 drink both. How many drink at least one of the two?
  2. 2.In a group of 43 children, 14 sing Hindi songs, 19 sing English songs and 5 sing both. How many sing only English songs?
  3. 3.In a group of 32 grown-ups, 13 drink tea, 14 drink coffee and 7 drink both. How many drink only tea?
  4. 4.In a group of 35 children, 25 play chess, 16 play carrom and 9 play both. How many play exactly one of the two?
  5. 5.In a group of 33 grown-ups, 19 drink tea, 10 drink coffee and 7 drink both. How many drink exactly one of the two?
  6. 6.In a group of 40 children, 15 sing Hindi songs, 22 sing English songs and 5 sing both. How many sing exactly one of the two?
  7. 7.In a group of 22 children, 14 play cricket, 11 play football and 5 play both. How many play only football?
  8. 8.In a group of 41 children, 26 enjoy drawing, 22 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  9. 9.In a group of 21 children, 15 play cricket, 7 play football and 4 play both. How many play neither of the two?
  10. 10.In a group of 29 grown-ups, 22 drink tea, 6 drink coffee and 3 drink both. How many drink neither of the two?
  11. 11.In a group of 44 children, 26 enjoy drawing, 19 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  12. 12.In a group of 47 grown-ups, 27 drink tea, 18 drink coffee and 11 drink both. How many drink at least one of the two?
  13. 13.In a group of 46 children, 15 enjoy drawing, 25 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  14. 14.In a group of 48 children, 27 play chess, 18 play carrom and 7 play both. How many play neither of the two?
  15. 15.In a group of 40 grown-ups, 31 drink tea, 18 drink coffee and 11 drink both. How many drink at least one of the two?
  16. 16.In a group of 35 grown-ups, 27 drink tea, 14 drink coffee and 10 drink both. How many drink exactly one of the two?
  17. 17.In a group of 33 children, 21 play chess, 10 play carrom and 2 play both. How many play neither of the two?
  18. 18.In a group of 32 children, 14 play chess, 21 play carrom and 8 play both. How many play only carrom?
  19. 19.In a group of 26 children, 10 sing Hindi songs, 21 sing English songs and 6 sing both. How many sing only Hindi songs?
  20. 20.In a group of 25 children, 13 enjoy drawing, 12 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  21. 21.In a group of 28 children, 17 enjoy drawing, 15 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  22. 22.In a group of 41 children, 30 sing Hindi songs, 18 sing English songs and 11 sing both. How many sing only Hindi songs?
  23. 23.In a group of 28 children, 8 enjoy drawing, 21 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  24. 24.In a group of 32 children, 20 play chess, 15 play carrom and 4 play both. How many play only chess?
  25. 25.In a group of 17 children, 6 play chess, 12 play carrom and 3 play both. How many play exactly one of the two?
  26. 26.In a group of 17 children, 7 enjoy drawing, 12 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  27. 27.In a group of 24 children, 5 play chess, 9 play carrom and 2 play both. How many play neither of the two?
  28. 28.In a group of 45 children, 29 sing Hindi songs, 25 sing English songs and 11 sing both. How many sing only English songs?
  29. 29.In a group of 50 grown-ups, 18 drink tea, 30 drink coffee and 11 drink both. How many drink neither of the two?
  30. 30.In a group of 37 children, 21 play chess, 24 play carrom and 10 play both. How many play neither of the two?
  31. 31.In a group of 29 children, 6 play chess, 19 play carrom and 2 play both. How many play exactly one of the two?
  32. 32.In a group of 35 grown-ups, 20 drink tea, 16 drink coffee and 3 drink both. How many drink at least one of the two?
  33. 33.In a group of 24 children, 13 play chess, 6 play carrom and 3 play both. How many play exactly one of the two?
  34. 34.In a group of 25 children, 13 like mangoes, 19 like bananas and 9 like both. How many like only bananas?
  35. 35.In a group of 20 children, 6 enjoy drawing, 15 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  36. 36.In a group of 32 children, 12 play chess, 22 play carrom and 4 play both. How many play only chess?
  37. 37.In a group of 34 children, 20 play chess, 14 play carrom and 4 play both. How many play exactly one of the two?
  38. 38.In a group of 16 children, 7 play cricket, 9 play football and 3 play both. How many play exactly one of the two?
  39. 39.In a group of 18 children, 10 sing Hindi songs, 7 sing English songs and 3 sing both. How many sing only English songs?
  40. 40.In a group of 36 children, 17 play cricket, 11 play football and 2 play both. How many play neither of the two?

Answer key

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

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