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Logical reasoning lesson 22: Venn diagrams · Set 254 · 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 29 grown-ups, 17 drink tea, 11 drink coffee and 5 drink both. How many drink exactly one of the two?
  2. 2.In a group of 31 grown-ups, 10 drink tea, 10 drink coffee and 2 drink both. How many drink only coffee?
  3. 3.In a group of 36 grown-ups, 17 drink tea, 15 drink coffee and 10 drink both. How many drink at least one of the two?
  4. 4.In a group of 35 children, 27 like mangoes, 15 like bananas and 9 like both. How many like only bananas?
  5. 5.In a group of 36 children, 15 enjoy drawing, 9 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  6. 6.In a group of 30 children, 17 play chess, 17 play carrom and 7 play both. How many play only chess?
  7. 7.In a group of 34 grown-ups, 11 drink tea, 13 drink coffee and 4 drink both. How many drink only tea?
  8. 8.In a group of 21 children, 7 enjoy drawing, 17 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  9. 9.In a group of 32 children, 15 sing Hindi songs, 15 sing English songs and 2 sing both. How many sing only Hindi songs?
  10. 10.In a group of 26 grown-ups, 16 drink tea, 15 drink coffee and 12 drink both. How many drink only tea?
  11. 11.In a group of 39 children, 12 like mangoes, 27 like bananas and 9 like both. How many like neither of the two?
  12. 12.In a group of 33 grown-ups, 15 drink tea, 25 drink coffee and 8 drink both. How many drink only tea?
  13. 13.In a group of 42 children, 18 sing Hindi songs, 22 sing English songs and 5 sing both. How many sing neither of the two?
  14. 14.In a group of 31 children, 14 like mangoes, 13 like bananas and 2 like both. How many like at least one of the two?
  15. 15.In a group of 16 children, 9 enjoy drawing, 12 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  16. 16.In a group of 55 grown-ups, 24 drink tea, 26 drink coffee and 6 drink both. How many drink only tea?
  17. 17.In a group of 29 children, 16 play chess, 7 play carrom and 2 play both. How many play neither of the two?
  18. 18.In a group of 48 children, 23 play chess, 16 play carrom and 4 play both. How many play at least one of the two?
  19. 19.In a group of 46 children, 18 enjoy drawing, 22 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  20. 20.In a group of 47 children, 21 play chess, 22 play carrom and 8 play both. How many play exactly one of the two?
  21. 21.In a group of 29 children, 17 play chess, 18 play carrom and 12 play both. How many play only chess?
  22. 22.In a group of 47 children, 25 enjoy drawing, 18 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  23. 23.In a group of 42 children, 23 play chess, 23 play carrom and 10 play both. How many play neither of the two?
  24. 24.In a group of 31 children, 10 play cricket, 13 play football and 5 play both. How many play at least one of the two?
  25. 25.In a group of 23 children, 14 enjoy drawing, 15 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  26. 26.In a group of 20 children, 14 play cricket, 13 play football and 9 play both. How many play neither of the two?
  27. 27.In a group of 49 children, 31 play cricket, 26 play football and 12 play both. How many play at least one of the two?
  28. 28.In a group of 28 children, 12 sing Hindi songs, 10 sing English songs and 6 sing both. How many sing only Hindi songs?
  29. 29.In a group of 41 children, 26 play chess, 13 play carrom and 10 play both. How many play neither of the two?
  30. 30.In a group of 47 children, 31 enjoy drawing, 19 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  31. 31.In a group of 31 children, 15 play cricket, 8 play football and 3 play both. How many play exactly one of the two?
  32. 32.In a group of 31 children, 9 enjoy drawing, 16 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  33. 33.In a group of 20 children, 13 like mangoes, 15 like bananas and 9 like both. How many like neither of the two?
  34. 34.In a group of 28 children, 20 enjoy drawing, 15 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  35. 35.In a group of 45 children, 28 play cricket, 13 play football and 10 play both. How many play only cricket?
  36. 36.In a group of 22 children, 10 enjoy drawing, 8 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  37. 37.In a group of 33 children, 27 like mangoes, 13 like bananas and 8 like both. How many like neither of the two?
  38. 38.In a group of 38 grown-ups, 22 drink tea, 15 drink coffee and 3 drink both. How many drink neither of the two?
  39. 39.In a group of 36 children, 17 sing Hindi songs, 21 sing English songs and 6 sing both. How many sing only Hindi songs?
  40. 40.In a group of 34 children, 12 play cricket, 17 play football and 3 play both. How many play only football?

Answer key

  1. 18
  2. 8
  3. 22
  4. 6
  5. 14
  6. 10
  7. 7
  8. 1
  9. 13
  10. 4
  11. 9
  12. 7
  13. 7
  14. 25
  15. 6
  16. 18
  17. 8
  18. 35
  19. 13
  20. 27
  21. 5
  22. 13
  23. 6
  24. 18
  25. 7
  26. 2
  27. 45
  28. 6
  29. 12
  30. 8
  31. 17
  32. 7
  33. 1
  34. 11
  35. 18
  36. 6
  37. 1
  38. 4
  39. 11
  40. 14

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