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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 610 · 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 44 children, 27 sing Hindi songs, 21 sing English songs and 8 sing both. How many sing at least one of the two?
  2. 2.In a group of 28 children, 18 play chess, 13 play carrom and 5 play both. How many play exactly one of the two?
  3. 3.In a group of 37 children, 14 enjoy drawing, 22 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  4. 4.In a group of 33 children, 29 sing Hindi songs, 12 sing English songs and 9 sing both. How many sing only English songs?
  5. 5.In a group of 58 grown-ups, 29 drink tea, 23 drink coffee and 9 drink both. How many drink neither of the two?
  6. 6.In a group of 30 children, 15 play cricket, 16 play football and 7 play both. How many play neither of the two?
  7. 7.In a group of 24 children, 13 enjoy drawing, 7 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  8. 8.In a group of 38 children, 22 like mangoes, 16 like bananas and 4 like both. How many like only bananas?
  9. 9.In a group of 50 children, 21 like mangoes, 22 like bananas and 5 like both. How many like only mangoes?
  10. 10.In a group of 26 children, 17 play cricket, 15 play football and 8 play both. How many play exactly one of the two?
  11. 11.In a group of 38 children, 19 sing Hindi songs, 15 sing English songs and 10 sing both. How many sing at least one of the two?
  12. 12.In a group of 33 children, 26 play cricket, 15 play football and 9 play both. How many play only cricket?
  13. 13.In a group of 53 children, 24 play chess, 24 play carrom and 6 play both. How many play only carrom?
  14. 14.In a group of 26 children, 16 enjoy drawing, 13 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  15. 15.In a group of 50 children, 29 play cricket, 17 play football and 11 play both. How many play only cricket?
  16. 16.In a group of 25 children, 6 sing Hindi songs, 6 sing English songs and 2 sing both. How many sing neither of the two?
  17. 17.In a group of 39 children, 9 play cricket, 18 play football and 3 play both. How many play only football?
  18. 18.In a group of 41 grown-ups, 21 drink tea, 22 drink coffee and 3 drink both. How many drink exactly one of the two?
  19. 19.In a group of 29 grown-ups, 15 drink tea, 16 drink coffee and 6 drink both. How many drink exactly one of the two?
  20. 20.In a group of 26 children, 14 like mangoes, 16 like bananas and 5 like both. How many like only mangoes?
  21. 21.In a group of 40 children, 15 like mangoes, 22 like bananas and 12 like both. How many like only mangoes?
  22. 22.In a group of 39 grown-ups, 7 drink tea, 21 drink coffee and 3 drink both. How many drink only coffee?
  23. 23.In a group of 43 grown-ups, 26 drink tea, 15 drink coffee and 7 drink both. How many drink neither of the two?
  24. 24.In a group of 34 children, 22 play chess, 5 play carrom and 2 play both. How many play exactly one of the two?
  25. 25.In a group of 41 children, 25 like mangoes, 25 like bananas and 12 like both. How many like only bananas?
  26. 26.In a group of 45 children, 23 like mangoes, 16 like bananas and 6 like both. How many like only mangoes?
  27. 27.In a group of 41 children, 17 sing Hindi songs, 23 sing English songs and 7 sing both. How many sing neither of the two?
  28. 28.In a group of 52 children, 24 sing Hindi songs, 17 sing English songs and 4 sing both. How many sing neither of the two?
  29. 29.In a group of 26 children, 12 play chess, 19 play carrom and 7 play both. How many play only chess?
  30. 30.In a group of 44 children, 20 play chess, 18 play carrom and 7 play both. How many play only chess?
  31. 31.In a group of 24 children, 10 play chess, 18 play carrom and 7 play both. How many play at least one of the two?
  32. 32.In a group of 31 grown-ups, 16 drink tea, 14 drink coffee and 10 drink both. How many drink neither of the two?
  33. 33.In a group of 25 children, 19 play chess, 5 play carrom and 2 play both. How many play exactly one of the two?
  34. 34.In a group of 40 grown-ups, 21 drink tea, 24 drink coffee and 10 drink both. How many drink only coffee?
  35. 35.In a group of 49 children, 27 enjoy drawing, 20 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  36. 36.In a group of 42 children, 13 enjoy drawing, 19 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  37. 37.In a group of 38 children, 10 enjoy drawing, 22 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  38. 38.In a group of 40 children, 12 play chess, 20 play carrom and 7 play both. How many play neither of the two?
  39. 39.In a group of 32 children, 21 sing Hindi songs, 21 sing English songs and 12 sing both. How many sing only Hindi songs?
  40. 40.In a group of 31 children, 13 enjoy drawing, 19 enjoy dancing and 3 enjoy both. How many enjoy only dancing?

Answer key

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

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