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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 579 · 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 31 grown-ups, 18 drink tea, 14 drink coffee and 4 drink both. How many drink neither of the two?
  2. 2.In a group of 46 grown-ups, 24 drink tea, 15 drink coffee and 8 drink both. How many drink exactly one of the two?
  3. 3.In a group of 27 grown-ups, 16 drink tea, 19 drink coffee and 11 drink both. How many drink only tea?
  4. 4.In a group of 35 grown-ups, 13 drink tea, 19 drink coffee and 4 drink both. How many drink neither of the two?
  5. 5.In a group of 48 children, 28 play cricket, 20 play football and 8 play both. How many play only cricket?
  6. 6.In a group of 40 children, 14 play chess, 20 play carrom and 2 play both. How many play only chess?
  7. 7.In a group of 35 children, 16 enjoy drawing, 16 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  8. 8.In a group of 54 grown-ups, 21 drink tea, 25 drink coffee and 5 drink both. How many drink exactly one of the two?
  9. 9.In a group of 25 grown-ups, 16 drink tea, 10 drink coffee and 3 drink both. How many drink exactly one of the two?
  10. 10.In a group of 38 grown-ups, 12 drink tea, 19 drink coffee and 7 drink both. How many drink only coffee?
  11. 11.In a group of 43 grown-ups, 17 drink tea, 30 drink coffee and 10 drink both. How many drink only coffee?
  12. 12.In a group of 38 children, 23 sing Hindi songs, 26 sing English songs and 12 sing both. How many sing at least one of the two?
  13. 13.In a group of 37 children, 27 like mangoes, 16 like bananas and 12 like both. How many like exactly one of the two?
  14. 14.In a group of 41 children, 26 like mangoes, 24 like bananas and 12 like both. How many like only bananas?
  15. 15.In a group of 41 children, 25 like mangoes, 26 like bananas and 12 like both. How many like exactly one of the two?
  16. 16.In a group of 48 children, 25 sing Hindi songs, 24 sing English songs and 9 sing both. How many sing only English songs?
  17. 17.In a group of 48 children, 26 play chess, 24 play carrom and 11 play both. How many play only carrom?
  18. 18.In a group of 37 children, 11 like mangoes, 20 like bananas and 8 like both. How many like only bananas?
  19. 19.In a group of 34 children, 17 play chess, 19 play carrom and 6 play both. How many play exactly one of the two?
  20. 20.In a group of 40 children, 20 enjoy drawing, 25 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  21. 21.In a group of 32 children, 23 sing Hindi songs, 13 sing English songs and 6 sing both. How many sing only English songs?
  22. 22.In a group of 28 children, 13 sing Hindi songs, 11 sing English songs and 3 sing both. How many sing only English songs?
  23. 23.In a group of 21 children, 14 like mangoes, 12 like bananas and 7 like both. How many like at least one of the two?
  24. 24.In a group of 23 children, 13 enjoy drawing, 13 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  25. 25.In a group of 55 children, 25 play chess, 24 play carrom and 9 play both. How many play at least one of the two?
  26. 26.In a group of 45 children, 12 enjoy drawing, 25 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  27. 27.In a group of 31 children, 10 sing Hindi songs, 10 sing English songs and 4 sing both. How many sing only English songs?
  28. 28.In a group of 58 children, 31 sing Hindi songs, 24 sing English songs and 11 sing both. How many sing neither of the two?
  29. 29.In a group of 34 children, 20 enjoy drawing, 13 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  30. 30.In a group of 30 children, 23 sing Hindi songs, 10 sing English songs and 6 sing both. How many sing neither of the two?
  31. 31.In a group of 33 children, 15 enjoy drawing, 29 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  32. 32.In a group of 43 children, 23 sing Hindi songs, 27 sing English songs and 8 sing both. How many sing neither of the two?
  33. 33.In a group of 36 children, 22 play cricket, 12 play football and 6 play both. How many play exactly one of the two?
  34. 34.In a group of 34 children, 30 sing Hindi songs, 13 sing English songs and 10 sing both. How many sing only English songs?
  35. 35.In a group of 36 children, 10 like mangoes, 15 like bananas and 3 like both. How many like only mangoes?
  36. 36.In a group of 56 children, 22 sing Hindi songs, 27 sing English songs and 8 sing both. How many sing only Hindi songs?
  37. 37.In a group of 45 children, 30 play chess, 18 play carrom and 10 play both. How many play at least one of the two?
  38. 38.In a group of 48 grown-ups, 21 drink tea, 21 drink coffee and 3 drink both. How many drink neither of the two?
  39. 39.In a group of 24 children, 17 like mangoes, 6 like bananas and 3 like both. How many like only bananas?
  40. 40.In a group of 22 children, 12 play chess, 8 play carrom and 3 play both. How many play at least one of the two?

Answer key

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

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