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Logical reasoning lesson 22: Venn diagrams · Set 530 · 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 21 children, 8 enjoy drawing, 14 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  2. 2.In a group of 39 children, 19 enjoy drawing, 16 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  3. 3.In a group of 25 children, 12 enjoy drawing, 16 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  4. 4.In a group of 42 children, 12 enjoy drawing, 19 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  5. 5.In a group of 46 children, 18 enjoy drawing, 20 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  6. 6.In a group of 30 grown-ups, 22 drink tea, 9 drink coffee and 3 drink both. How many drink exactly one of the two?
  7. 7.In a group of 36 grown-ups, 21 drink tea, 16 drink coffee and 3 drink both. How many drink at least one of the two?
  8. 8.In a group of 31 children, 7 play chess, 14 play carrom and 2 play both. How many play at least one of the two?
  9. 9.In a group of 43 children, 16 sing Hindi songs, 19 sing English songs and 7 sing both. How many sing neither of the two?
  10. 10.In a group of 38 children, 18 sing Hindi songs, 16 sing English songs and 9 sing both. How many sing only English songs?
  11. 11.In a group of 41 children, 23 like mangoes, 14 like bananas and 7 like both. How many like exactly one of the two?
  12. 12.In a group of 27 children, 15 like mangoes, 16 like bananas and 11 like both. How many like neither of the two?
  13. 13.In a group of 40 children, 7 play cricket, 24 play football and 4 play both. How many play at least one of the two?
  14. 14.In a group of 51 children, 31 play chess, 26 play carrom and 12 play both. How many play only carrom?
  15. 15.In a group of 42 children, 20 enjoy drawing, 27 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  16. 16.In a group of 39 children, 28 sing Hindi songs, 16 sing English songs and 9 sing both. How many sing only English songs?
  17. 17.In a group of 36 children, 20 sing Hindi songs, 16 sing English songs and 5 sing both. How many sing only English songs?
  18. 18.In a group of 40 children, 18 enjoy drawing, 17 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  19. 19.In a group of 29 children, 21 play chess, 6 play carrom and 3 play both. How many play only carrom?
  20. 20.In a group of 35 children, 17 sing Hindi songs, 26 sing English songs and 10 sing both. How many sing neither of the two?
  21. 21.In a group of 53 children, 21 enjoy drawing, 22 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  22. 22.In a group of 34 children, 15 like mangoes, 19 like bananas and 8 like both. How many like exactly one of the two?
  23. 23.In a group of 28 children, 23 like mangoes, 14 like bananas and 10 like both. How many like at least one of the two?
  24. 24.In a group of 28 children, 20 like mangoes, 17 like bananas and 11 like both. How many like only mangoes?
  25. 25.In a group of 35 children, 20 play cricket, 10 play football and 3 play both. How many play only cricket?
  26. 26.In a group of 32 children, 21 play chess, 16 play carrom and 7 play both. How many play only chess?
  27. 27.In a group of 35 children, 11 play cricket, 21 play football and 6 play both. How many play neither of the two?
  28. 28.In a group of 28 children, 21 like mangoes, 18 like bananas and 12 like both. How many like exactly one of the two?
  29. 29.In a group of 37 children, 8 play chess, 17 play carrom and 3 play both. How many play only chess?
  30. 30.In a group of 52 children, 23 like mangoes, 29 like bananas and 11 like both. How many like only bananas?
  31. 31.In a group of 55 children, 29 enjoy drawing, 25 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  32. 32.In a group of 37 children, 20 enjoy drawing, 12 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  33. 33.In a group of 49 children, 26 enjoy drawing, 24 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  34. 34.In a group of 45 children, 14 play cricket, 24 play football and 7 play both. How many play at least one of the two?
  35. 35.In a group of 29 children, 13 play cricket, 10 play football and 2 play both. How many play only cricket?
  36. 36.In a group of 33 children, 16 enjoy drawing, 14 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  37. 37.In a group of 16 children, 12 like mangoes, 7 like bananas and 4 like both. How many like neither of the two?
  38. 38.In a group of 26 children, 11 enjoy drawing, 19 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  39. 39.In a group of 18 grown-ups, 8 drink tea, 7 drink coffee and 4 drink both. How many drink at least one of the two?
  40. 40.In a group of 31 children, 10 play chess, 8 play carrom and 2 play both. How many play only chess?

Answer key

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

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