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Logical reasoning lesson 22: Venn diagrams · Set 22 · 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 53 children, 27 like mangoes, 29 like bananas and 9 like both. How many like at least one of the two?
  2. 2.In a group of 19 children, 7 like mangoes, 11 like bananas and 3 like both. How many like at least one of the two?
  3. 3.In a group of 28 grown-ups, 16 drink tea, 19 drink coffee and 9 drink both. How many drink at least one of the two?
  4. 4.In a group of 22 children, 12 enjoy drawing, 12 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  5. 5.In a group of 14 children, 6 play chess, 9 play carrom and 2 play both. How many play only chess?
  6. 6.In a group of 54 children, 24 enjoy drawing, 26 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  7. 7.In a group of 48 children, 19 sing Hindi songs, 25 sing English songs and 9 sing both. How many sing only Hindi songs?
  8. 8.In a group of 17 children, 10 play cricket, 9 play football and 4 play both. How many play neither of the two?
  9. 9.In a group of 36 children, 15 play cricket, 20 play football and 4 play both. How many play neither of the two?
  10. 10.In a group of 40 children, 27 play chess, 20 play carrom and 11 play both. How many play only carrom?
  11. 11.In a group of 28 children, 7 like mangoes, 11 like bananas and 3 like both. How many like at least one of the two?
  12. 12.In a group of 52 children, 32 play cricket, 19 play football and 12 play both. How many play at least one of the two?
  13. 13.In a group of 38 children, 23 play chess, 18 play carrom and 9 play both. How many play only carrom?
  14. 14.In a group of 37 children, 18 sing Hindi songs, 25 sing English songs and 11 sing both. How many sing only Hindi songs?
  15. 15.In a group of 33 children, 19 enjoy drawing, 12 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  16. 16.In a group of 55 children, 26 enjoy drawing, 23 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?
  17. 17.In a group of 29 children, 19 enjoy drawing, 11 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  18. 18.In a group of 26 children, 18 play chess, 10 play carrom and 6 play both. How many play exactly one of the two?
  19. 19.In a group of 24 children, 14 play chess, 6 play carrom and 2 play both. How many play only chess?
  20. 20.In a group of 35 children, 16 play chess, 14 play carrom and 2 play both. How many play at least one of the two?
  21. 21.In a group of 42 children, 22 like mangoes, 25 like bananas and 7 like both. How many like only mangoes?
  22. 22.In a group of 20 children, 11 enjoy drawing, 13 enjoy dancing and 5 enjoy both. How many enjoy at least one of the two?
  23. 23.In a group of 45 children, 16 play chess, 17 play carrom and 3 play both. How many play at least one of the two?
  24. 24.In a group of 53 children, 32 play chess, 27 play carrom and 12 play both. How many play neither of the two?
  25. 25.In a group of 36 children, 18 play chess, 11 play carrom and 7 play both. How many play at least one of the two?
  26. 26.In a group of 51 grown-ups, 19 drink tea, 28 drink coffee and 8 drink both. How many drink only coffee?
  27. 27.In a group of 30 children, 9 like mangoes, 10 like bananas and 4 like both. How many like only mangoes?
  28. 28.In a group of 31 children, 10 play cricket, 16 play football and 4 play both. How many play exactly one of the two?
  29. 29.In a group of 34 children, 19 enjoy drawing, 15 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  30. 30.In a group of 30 grown-ups, 17 drink tea, 19 drink coffee and 7 drink both. How many drink exactly one of the two?
  31. 31.In a group of 45 children, 18 like mangoes, 22 like bananas and 8 like both. How many like only mangoes?
  32. 32.In a group of 35 children, 15 like mangoes, 21 like bananas and 2 like both. How many like only mangoes?
  33. 33.In a group of 39 children, 19 enjoy drawing, 18 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  34. 34.In a group of 26 children, 16 play chess, 18 play carrom and 10 play both. How many play only carrom?
  35. 35.In a group of 35 children, 15 play chess, 25 play carrom and 8 play both. How many play at least one of the two?
  36. 36.In a group of 29 grown-ups, 18 drink tea, 9 drink coffee and 2 drink both. How many drink only tea?
  37. 37.In a group of 38 children, 18 play chess, 24 play carrom and 5 play both. How many play at least one of the two?
  38. 38.In a group of 39 children, 21 sing Hindi songs, 26 sing English songs and 12 sing both. How many sing exactly one of the two?
  39. 39.In a group of 32 children, 12 play chess, 20 play carrom and 4 play both. How many play only chess?
  40. 40.In a group of 51 children, 20 like mangoes, 24 like bananas and 5 like both. How many like only bananas?

Answer key

  1. 47
  2. 15
  3. 26
  4. 18
  5. 4
  6. 32
  7. 10
  8. 2
  9. 5
  10. 9
  11. 15
  12. 39
  13. 9
  14. 7
  15. 27
  16. 12
  17. 23
  18. 16
  19. 12
  20. 28
  21. 15
  22. 19
  23. 30
  24. 6
  25. 22
  26. 20
  27. 5
  28. 18
  29. 12
  30. 22
  31. 10
  32. 13
  33. 11
  34. 8
  35. 32
  36. 16
  37. 37
  38. 23
  39. 8
  40. 19

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