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Logical reasoning lesson 22: Venn diagrams · Set 229 · 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 39 children, 19 enjoy drawing, 23 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  2. 2.In a group of 42 children, 27 like mangoes, 13 like bananas and 8 like both. How many like exactly one of the two?
  3. 3.In a group of 24 grown-ups, 8 drink tea, 12 drink coffee and 2 drink both. How many drink at least one of the two?
  4. 4.In a group of 40 children, 27 play cricket, 20 play football and 10 play both. How many play neither of the two?
  5. 5.In a group of 39 grown-ups, 21 drink tea, 25 drink coffee and 9 drink both. How many drink neither of the two?
  6. 6.In a group of 29 children, 12 like mangoes, 7 like bananas and 3 like both. How many like only bananas?
  7. 7.In a group of 38 children, 18 like mangoes, 25 like bananas and 11 like both. How many like exactly one of the two?
  8. 8.In a group of 38 grown-ups, 14 drink tea, 27 drink coffee and 9 drink both. How many drink neither of the two?
  9. 9.In a group of 36 children, 19 sing Hindi songs, 24 sing English songs and 9 sing both. How many sing at least one of the two?
  10. 10.In a group of 23 children, 8 enjoy drawing, 7 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  11. 11.In a group of 20 children, 12 play cricket, 10 play football and 4 play both. How many play at least one of the two?
  12. 12.In a group of 36 children, 22 play chess, 14 play carrom and 2 play both. How many play neither of the two?
  13. 13.In a group of 43 children, 23 enjoy drawing, 15 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  14. 14.In a group of 35 children, 9 play cricket, 20 play football and 2 play both. How many play only cricket?
  15. 15.In a group of 44 children, 25 sing Hindi songs, 17 sing English songs and 10 sing both. How many sing only English songs?
  16. 16.In a group of 43 grown-ups, 26 drink tea, 12 drink coffee and 7 drink both. How many drink at least one of the two?
  17. 17.In a group of 25 children, 10 sing Hindi songs, 15 sing English songs and 7 sing both. How many sing neither of the two?
  18. 18.In a group of 36 children, 17 enjoy drawing, 10 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  19. 19.In a group of 20 children, 12 enjoy drawing, 15 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  20. 20.In a group of 29 children, 10 play chess, 17 play carrom and 2 play both. How many play neither of the two?
  21. 21.In a group of 40 children, 10 play chess, 21 play carrom and 3 play both. How many play at least one of the two?
  22. 22.In a group of 39 children, 32 like mangoes, 18 like bananas and 12 like both. How many like only bananas?
  23. 23.In a group of 32 children, 5 play chess, 14 play carrom and 2 play both. How many play only carrom?
  24. 24.In a group of 19 children, 14 enjoy drawing, 13 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  25. 25.In a group of 42 children, 16 play chess, 17 play carrom and 2 play both. How many play only chess?
  26. 26.In a group of 48 children, 25 enjoy drawing, 19 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  27. 27.In a group of 31 children, 17 sing Hindi songs, 8 sing English songs and 4 sing both. How many sing neither of the two?
  28. 28.In a group of 14 children, 6 enjoy drawing, 9 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  29. 29.In a group of 39 children, 18 play chess, 21 play carrom and 2 play both. How many play at least one of the two?
  30. 30.In a group of 43 grown-ups, 21 drink tea, 19 drink coffee and 2 drink both. How many drink only tea?
  31. 31.In a group of 31 children, 18 play cricket, 16 play football and 9 play both. How many play only cricket?
  32. 32.In a group of 48 children, 17 like mangoes, 30 like bananas and 12 like both. How many like only mangoes?
  33. 33.In a group of 36 children, 18 play chess, 7 play carrom and 3 play both. How many play only carrom?
  34. 34.In a group of 45 children, 19 sing Hindi songs, 21 sing English songs and 7 sing both. How many sing only English songs?
  35. 35.In a group of 42 children, 23 sing Hindi songs, 24 sing English songs and 6 sing both. How many sing only English songs?
  36. 36.In a group of 59 children, 27 play cricket, 29 play football and 12 play both. How many play only football?
  37. 37.In a group of 35 children, 21 enjoy drawing, 21 enjoy dancing and 10 enjoy both. How many enjoy at least one of the two?
  38. 38.In a group of 40 grown-ups, 20 drink tea, 21 drink coffee and 3 drink both. How many drink neither of the two?
  39. 39.In a group of 41 children, 27 like mangoes, 11 like bananas and 7 like both. How many like exactly one of the two?
  40. 40.In a group of 34 children, 22 play chess, 17 play carrom and 11 play both. How many play neither of the two?

Answer key

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

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