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Logical reasoning lesson 22: Venn diagrams · Set 354 · 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 32 children, 13 play cricket, 22 play football and 6 play both. How many play at least one of the two?
  2. 2.In a group of 28 children, 14 play cricket, 16 play football and 7 play both. How many play neither of the two?
  3. 3.In a group of 34 children, 9 enjoy drawing, 12 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  4. 4.In a group of 55 children, 23 sing Hindi songs, 24 sing English songs and 5 sing both. How many sing only Hindi songs?
  5. 5.In a group of 45 children, 23 like mangoes, 19 like bananas and 5 like both. How many like at least one of the two?
  6. 6.In a group of 49 children, 22 play cricket, 24 play football and 10 play both. How many play only football?
  7. 7.In a group of 46 children, 24 enjoy drawing, 19 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  8. 8.In a group of 34 grown-ups, 13 drink tea, 22 drink coffee and 10 drink both. How many drink neither of the two?
  9. 9.In a group of 31 children, 16 play cricket, 11 play football and 5 play both. How many play exactly one of the two?
  10. 10.In a group of 23 children, 14 enjoy drawing, 8 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  11. 11.In a group of 37 grown-ups, 27 drink tea, 16 drink coffee and 9 drink both. How many drink neither of the two?
  12. 12.In a group of 36 children, 13 sing Hindi songs, 16 sing English songs and 4 sing both. How many sing only English songs?
  13. 13.In a group of 25 children, 8 enjoy drawing, 15 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  14. 14.In a group of 34 children, 18 sing Hindi songs, 13 sing English songs and 9 sing both. How many sing exactly one of the two?
  15. 15.In a group of 51 children, 25 sing Hindi songs, 21 sing English songs and 9 sing both. How many sing exactly one of the two?
  16. 16.In a group of 35 children, 18 play chess, 13 play carrom and 4 play both. How many play at least one of the two?
  17. 17.In a group of 22 children, 17 play chess, 7 play carrom and 4 play both. How many play neither of the two?
  18. 18.In a group of 29 children, 19 enjoy drawing, 16 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  19. 19.In a group of 42 children, 23 play chess, 12 play carrom and 7 play both. How many play at least one of the two?
  20. 20.In a group of 32 children, 12 play chess, 13 play carrom and 6 play both. How many play neither of the two?
  21. 21.In a group of 49 children, 17 play cricket, 21 play football and 3 play both. How many play only cricket?
  22. 22.In a group of 33 children, 13 play cricket, 17 play football and 7 play both. How many play neither of the two?
  23. 23.In a group of 35 children, 14 sing Hindi songs, 24 sing English songs and 7 sing both. How many sing neither of the two?
  24. 24.In a group of 47 grown-ups, 28 drink tea, 23 drink coffee and 10 drink both. How many drink exactly one of the two?
  25. 25.In a group of 41 children, 32 play cricket, 18 play football and 12 play both. How many play only cricket?
  26. 26.In a group of 47 children, 23 play cricket, 13 play football and 3 play both. How many play at least one of the two?
  27. 27.In a group of 29 grown-ups, 11 drink tea, 10 drink coffee and 7 drink both. How many drink neither of the two?
  28. 28.In a group of 52 grown-ups, 24 drink tea, 23 drink coffee and 4 drink both. How many drink at least one of the two?
  29. 29.In a group of 23 children, 17 like mangoes, 14 like bananas and 11 like both. How many like only bananas?
  30. 30.In a group of 44 children, 20 like mangoes, 28 like bananas and 11 like both. How many like only mangoes?
  31. 31.In a group of 56 grown-ups, 24 drink tea, 27 drink coffee and 10 drink both. How many drink at least one of the two?
  32. 32.In a group of 44 children, 24 enjoy drawing, 17 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  33. 33.In a group of 28 children, 15 sing Hindi songs, 12 sing English songs and 6 sing both. How many sing neither of the two?
  34. 34.In a group of 25 children, 12 sing Hindi songs, 15 sing English songs and 4 sing both. How many sing only English songs?
  35. 35.In a group of 52 children, 23 enjoy drawing, 28 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  36. 36.In a group of 29 children, 11 play chess, 22 play carrom and 8 play both. How many play neither of the two?
  37. 37.In a group of 37 children, 18 play chess, 26 play carrom and 9 play both. How many play neither of the two?
  38. 38.In a group of 44 children, 28 like mangoes, 24 like bananas and 12 like both. How many like only bananas?
  39. 39.In a group of 37 children, 14 enjoy drawing, 22 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  40. 40.In a group of 34 children, 21 play chess, 18 play carrom and 11 play both. How many play neither of the two?

Answer key

  1. 29
  2. 5
  3. 10
  4. 18
  5. 37
  6. 14
  7. 14
  8. 9
  9. 17
  10. 14
  11. 3
  12. 12
  13. 3
  14. 13
  15. 28
  16. 27
  17. 2
  18. 11
  19. 28
  20. 13
  21. 14
  22. 10
  23. 4
  24. 31
  25. 20
  26. 33
  27. 15
  28. 43
  29. 3
  30. 9
  31. 41
  32. 12
  33. 7
  34. 11
  35. 43
  36. 4
  37. 2
  38. 12
  39. 7
  40. 6

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