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Logical reasoning lesson 22: Venn diagrams · Set 329 · 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 41 children, 20 like mangoes, 19 like bananas and 8 like both. How many like only bananas?
  2. 2.In a group of 50 children, 19 like mangoes, 23 like bananas and 5 like both. How many like only bananas?
  3. 3.In a group of 37 children, 27 play chess, 14 play carrom and 7 play both. How many play neither of the two?
  4. 4.In a group of 28 children, 8 enjoy drawing, 12 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  5. 5.In a group of 35 children, 12 enjoy drawing, 23 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  6. 6.In a group of 28 children, 14 sing Hindi songs, 14 sing English songs and 8 sing both. How many sing at least one of the two?
  7. 7.In a group of 39 children, 16 sing Hindi songs, 23 sing English songs and 4 sing both. How many sing only English songs?
  8. 8.In a group of 32 children, 18 sing Hindi songs, 11 sing English songs and 7 sing both. How many sing neither of the two?
  9. 9.In a group of 42 children, 18 sing Hindi songs, 25 sing English songs and 8 sing both. How many sing neither of the two?
  10. 10.In a group of 36 children, 24 sing Hindi songs, 15 sing English songs and 5 sing both. How many sing exactly one of the two?
  11. 11.In a group of 37 grown-ups, 16 drink tea, 20 drink coffee and 3 drink both. How many drink neither of the two?
  12. 12.In a group of 20 children, 12 enjoy drawing, 7 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  13. 13.In a group of 17 children, 10 like mangoes, 11 like bananas and 5 like both. How many like at least one of the two?
  14. 14.In a group of 39 children, 25 enjoy drawing, 23 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  15. 15.In a group of 41 children, 21 play chess, 20 play carrom and 10 play both. How many play only carrom?
  16. 16.In a group of 23 children, 6 play chess, 15 play carrom and 2 play both. How many play only chess?
  17. 17.In a group of 50 grown-ups, 24 drink tea, 26 drink coffee and 12 drink both. How many drink only tea?
  18. 18.In a group of 29 grown-ups, 23 drink tea, 13 drink coffee and 8 drink both. How many drink exactly one of the two?
  19. 19.In a group of 42 children, 21 sing Hindi songs, 15 sing English songs and 5 sing both. How many sing only English songs?
  20. 20.In a group of 33 children, 20 enjoy drawing, 16 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  21. 21.In a group of 32 children, 15 sing Hindi songs, 19 sing English songs and 7 sing both. How many sing only English songs?
  22. 22.In a group of 32 children, 23 play cricket, 12 play football and 5 play both. How many play at least one of the two?
  23. 23.In a group of 44 children, 20 sing Hindi songs, 28 sing English songs and 9 sing both. How many sing neither of the two?
  24. 24.In a group of 29 children, 16 play cricket, 9 play football and 3 play both. How many play only cricket?
  25. 25.In a group of 41 children, 16 play cricket, 22 play football and 3 play both. How many play only football?
  26. 26.In a group of 36 children, 25 play cricket, 10 play football and 5 play both. How many play neither of the two?
  27. 27.In a group of 29 children, 14 enjoy drawing, 15 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  28. 28.In a group of 25 children, 18 sing Hindi songs, 17 sing English songs and 12 sing both. How many sing only Hindi songs?
  29. 29.In a group of 32 children, 18 sing Hindi songs, 7 sing English songs and 2 sing both. How many sing neither of the two?
  30. 30.In a group of 50 children, 29 like mangoes, 20 like bananas and 12 like both. How many like only bananas?
  31. 31.In a group of 52 children, 30 like mangoes, 29 like bananas and 10 like both. How many like only mangoes?
  32. 32.In a group of 32 children, 12 enjoy drawing, 22 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  33. 33.In a group of 37 children, 10 play cricket, 21 play football and 5 play both. How many play only football?
  34. 34.In a group of 40 children, 19 like mangoes, 19 like bananas and 3 like both. How many like only bananas?
  35. 35.In a group of 30 children, 13 sing Hindi songs, 21 sing English songs and 10 sing both. How many sing at least one of the two?
  36. 36.In a group of 45 children, 25 play chess, 13 play carrom and 6 play both. How many play neither of the two?
  37. 37.In a group of 39 children, 19 play cricket, 23 play football and 6 play both. How many play only football?
  38. 38.In a group of 46 children, 24 enjoy drawing, 23 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  39. 39.In a group of 29 children, 19 play chess, 12 play carrom and 8 play both. How many play only chess?
  40. 40.In a group of 39 children, 21 sing Hindi songs, 17 sing English songs and 2 sing both. How many sing at least one of the two?

Answer key

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

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