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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 134 · 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 33 children, 20 play cricket, 9 play football and 3 play both. How many play exactly one of the two?
  2. 2.In a group of 26 children, 16 like mangoes, 21 like bananas and 12 like both. How many like neither of the two?
  3. 3.In a group of 23 children, 16 play cricket, 15 play football and 10 play both. How many play neither of the two?
  4. 4.In a group of 46 children, 24 play chess, 30 play carrom and 11 play both. How many play only chess?
  5. 5.In a group of 30 children, 14 play chess, 12 play carrom and 5 play both. How many play at least one of the two?
  6. 6.In a group of 37 children, 15 play chess, 21 play carrom and 12 play both. How many play only chess?
  7. 7.In a group of 40 children, 21 play chess, 17 play carrom and 6 play both. How many play at least one of the two?
  8. 8.In a group of 32 children, 10 like mangoes, 17 like bananas and 2 like both. How many like only mangoes?
  9. 9.In a group of 31 children, 11 like mangoes, 17 like bananas and 7 like both. How many like at least one of the two?
  10. 10.In a group of 22 grown-ups, 8 drink tea, 9 drink coffee and 2 drink both. How many drink only coffee?
  11. 11.In a group of 29 children, 18 sing Hindi songs, 13 sing English songs and 8 sing both. How many sing only Hindi songs?
  12. 12.In a group of 36 children, 16 play chess, 29 play carrom and 12 play both. How many play exactly one of the two?
  13. 13.In a group of 25 grown-ups, 12 drink tea, 6 drink coffee and 3 drink both. How many drink exactly one of the two?
  14. 14.In a group of 25 children, 13 play chess, 12 play carrom and 3 play both. How many play only carrom?
  15. 15.In a group of 30 children, 20 play chess, 11 play carrom and 8 play both. How many play exactly one of the two?
  16. 16.In a group of 48 children, 25 sing Hindi songs, 26 sing English songs and 8 sing both. How many sing exactly one of the two?
  17. 17.In a group of 56 grown-ups, 29 drink tea, 24 drink coffee and 12 drink both. How many drink neither of the two?
  18. 18.In a group of 37 children, 21 enjoy drawing, 19 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  19. 19.In a group of 46 children, 21 like mangoes, 19 like bananas and 4 like both. How many like exactly one of the two?
  20. 20.In a group of 13 children, 5 play chess, 7 play carrom and 2 play both. How many play exactly one of the two?
  21. 21.In a group of 48 children, 23 sing Hindi songs, 15 sing English songs and 5 sing both. How many sing exactly one of the two?
  22. 22.In a group of 43 children, 17 sing Hindi songs, 20 sing English songs and 5 sing both. How many sing at least one of the two?
  23. 23.In a group of 38 children, 24 like mangoes, 14 like bananas and 4 like both. How many like only mangoes?
  24. 24.In a group of 35 grown-ups, 14 drink tea, 24 drink coffee and 10 drink both. How many drink neither of the two?
  25. 25.In a group of 41 children, 17 play cricket, 14 play football and 2 play both. How many play only football?
  26. 26.In a group of 41 children, 25 enjoy drawing, 17 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  27. 27.In a group of 29 children, 19 sing Hindi songs, 10 sing English songs and 2 sing both. How many sing neither of the two?
  28. 28.In a group of 49 children, 26 like mangoes, 23 like bananas and 6 like both. How many like only mangoes?
  29. 29.In a group of 16 children, 9 play cricket, 7 play football and 4 play both. How many play only football?
  30. 30.In a group of 50 children, 20 enjoy drawing, 25 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  31. 31.In a group of 32 children, 12 play cricket, 10 play football and 5 play both. How many play exactly one of the two?
  32. 32.In a group of 39 children, 24 like mangoes, 16 like bananas and 11 like both. How many like only mangoes?
  33. 33.In a group of 34 children, 18 play chess, 14 play carrom and 10 play both. How many play exactly one of the two?
  34. 34.In a group of 33 children, 11 enjoy drawing, 12 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  35. 35.In a group of 41 children, 21 enjoy drawing, 27 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  36. 36.In a group of 37 grown-ups, 16 drink tea, 20 drink coffee and 2 drink both. How many drink exactly one of the two?
  37. 37.In a group of 23 children, 8 enjoy drawing, 15 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  38. 38.In a group of 37 children, 25 enjoy drawing, 9 enjoy dancing and 5 enjoy both. How many enjoy at least one of the two?
  39. 39.In a group of 19 grown-ups, 12 drink tea, 11 drink coffee and 6 drink both. How many drink at least one of the two?
  40. 40.In a group of 30 children, 20 play cricket, 11 play football and 3 play both. How many play at least one of the two?

Answer key

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

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