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Logical reasoning lesson 22: Venn diagrams · Set 24 · 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 25 children, 14 like mangoes, 8 like bananas and 4 like both. How many like only bananas?
  2. 2.In a group of 39 children, 14 enjoy drawing, 16 enjoy dancing and 5 enjoy both. How many enjoy at least one of the two?
  3. 3.In a group of 37 grown-ups, 15 drink tea, 19 drink coffee and 9 drink both. How many drink at least one of the two?
  4. 4.In a group of 37 grown-ups, 25 drink tea, 9 drink coffee and 5 drink both. How many drink only tea?
  5. 5.In a group of 32 children, 8 sing Hindi songs, 17 sing English songs and 5 sing both. How many sing neither of the two?
  6. 6.In a group of 41 grown-ups, 21 drink tea, 22 drink coffee and 7 drink both. How many drink exactly one of the two?
  7. 7.In a group of 32 children, 5 like mangoes, 16 like bananas and 2 like both. How many like only mangoes?
  8. 8.In a group of 20 children, 12 play chess, 12 play carrom and 9 play both. How many play exactly one of the two?
  9. 9.In a group of 32 children, 12 play cricket, 8 play football and 2 play both. How many play at least one of the two?
  10. 10.In a group of 36 children, 21 sing Hindi songs, 14 sing English songs and 7 sing both. How many sing only English songs?
  11. 11.In a group of 45 children, 28 enjoy drawing, 25 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  12. 12.In a group of 35 children, 7 sing Hindi songs, 20 sing English songs and 3 sing both. How many sing at least one of the two?
  13. 13.In a group of 40 children, 20 sing Hindi songs, 22 sing English songs and 10 sing both. How many sing neither of the two?
  14. 14.In a group of 23 children, 14 sing Hindi songs, 13 sing English songs and 7 sing both. How many sing only English songs?
  15. 15.In a group of 42 children, 28 play cricket, 18 play football and 8 play both. How many play neither of the two?
  16. 16.In a group of 39 children, 21 enjoy drawing, 14 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  17. 17.In a group of 46 children, 22 play chess, 27 play carrom and 8 play both. How many play at least one of the two?
  18. 18.In a group of 30 grown-ups, 10 drink tea, 21 drink coffee and 2 drink both. How many drink only tea?
  19. 19.In a group of 42 children, 17 play chess, 18 play carrom and 4 play both. How many play at least one of the two?
  20. 20.In a group of 44 children, 21 play cricket, 15 play football and 6 play both. How many play exactly one of the two?
  21. 21.In a group of 25 children, 9 enjoy drawing, 14 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  22. 22.In a group of 32 children, 16 sing Hindi songs, 17 sing English songs and 10 sing both. How many sing neither of the two?
  23. 23.In a group of 27 children, 10 sing Hindi songs, 17 sing English songs and 2 sing both. How many sing neither of the two?
  24. 24.In a group of 43 children, 25 sing Hindi songs, 10 sing English songs and 5 sing both. How many sing only English songs?
  25. 25.In a group of 34 children, 11 play chess, 13 play carrom and 4 play both. How many play only carrom?
  26. 26.In a group of 33 grown-ups, 19 drink tea, 16 drink coffee and 4 drink both. How many drink neither of the two?
  27. 27.In a group of 28 grown-ups, 13 drink tea, 5 drink coffee and 2 drink both. How many drink only coffee?
  28. 28.In a group of 45 children, 14 sing Hindi songs, 29 sing English songs and 10 sing both. How many sing exactly one of the two?
  29. 29.In a group of 45 children, 28 enjoy drawing, 25 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  30. 30.In a group of 34 children, 18 enjoy drawing, 16 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  31. 31.In a group of 46 children, 24 like mangoes, 17 like bananas and 5 like both. How many like exactly one of the two?
  32. 32.In a group of 33 children, 17 play cricket, 5 play football and 2 play both. How many play only cricket?
  33. 33.In a group of 49 children, 24 enjoy drawing, 18 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  34. 34.In a group of 33 children, 22 play cricket, 21 play football and 11 play both. How many play exactly one of the two?
  35. 35.In a group of 42 children, 23 sing Hindi songs, 20 sing English songs and 6 sing both. How many sing at least one of the two?
  36. 36.In a group of 25 grown-ups, 13 drink tea, 18 drink coffee and 9 drink both. How many drink only tea?
  37. 37.In a group of 29 children, 22 play cricket, 10 play football and 4 play both. How many play only football?
  38. 38.In a group of 38 children, 15 enjoy drawing, 23 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  39. 39.In a group of 35 children, 24 play chess, 18 play carrom and 9 play both. How many play only chess?
  40. 40.In a group of 37 children, 18 enjoy drawing, 17 enjoy dancing and 3 enjoy both. How many enjoy only drawing?

Answer key

  1. 4
  2. 25
  3. 25
  4. 20
  5. 12
  6. 29
  7. 3
  8. 6
  9. 18
  10. 7
  11. 41
  12. 24
  13. 8
  14. 6
  15. 4
  16. 27
  17. 41
  18. 8
  19. 31
  20. 24
  21. 4
  22. 9
  23. 2
  24. 5
  25. 9
  26. 2
  27. 3
  28. 23
  29. 1
  30. 8
  31. 31
  32. 15
  33. 26
  34. 21
  35. 37
  36. 4
  37. 6
  38. 14
  39. 15
  40. 15

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