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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 352 · 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 30 grown-ups, 15 drink tea, 18 drink coffee and 12 drink both. How many drink at least one of the two?
  2. 2.In a group of 41 children, 16 play cricket, 24 play football and 9 play both. How many play at least one of the two?
  3. 3.In a group of 27 children, 6 like mangoes, 12 like bananas and 2 like both. How many like at least one of the two?
  4. 4.In a group of 26 children, 9 enjoy drawing, 7 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  5. 5.In a group of 30 grown-ups, 13 drink tea, 22 drink coffee and 6 drink both. How many drink neither of the two?
  6. 6.In a group of 38 children, 15 play cricket, 17 play football and 4 play both. How many play exactly one of the two?
  7. 7.In a group of 46 children, 19 sing Hindi songs, 22 sing English songs and 6 sing both. How many sing at least one of the two?
  8. 8.In a group of 45 grown-ups, 22 drink tea, 25 drink coffee and 10 drink both. How many drink only tea?
  9. 9.In a group of 33 children, 14 play cricket, 27 play football and 10 play both. How many play neither of the two?
  10. 10.In a group of 35 children, 10 play chess, 20 play carrom and 7 play both. How many play only carrom?
  11. 11.In a group of 32 children, 9 play cricket, 20 play football and 5 play both. How many play at least one of the two?
  12. 12.In a group of 25 grown-ups, 5 drink tea, 18 drink coffee and 2 drink both. How many drink only tea?
  13. 13.In a group of 39 children, 17 play chess, 17 play carrom and 9 play both. How many play neither of the two?
  14. 14.In a group of 16 children, 7 enjoy drawing, 10 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  15. 15.In a group of 41 children, 25 enjoy drawing, 14 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  16. 16.In a group of 61 children, 30 play cricket, 28 play football and 10 play both. How many play only cricket?
  17. 17.In a group of 43 children, 19 play chess, 25 play carrom and 12 play both. How many play only carrom?
  18. 18.In a group of 33 grown-ups, 21 drink tea, 12 drink coffee and 3 drink both. How many drink at least one of the two?
  19. 19.In a group of 39 children, 17 play chess, 19 play carrom and 8 play both. How many play neither of the two?
  20. 20.In a group of 33 grown-ups, 28 drink tea, 15 drink coffee and 11 drink both. How many drink only coffee?
  21. 21.In a group of 36 children, 14 like mangoes, 23 like bananas and 3 like both. How many like only mangoes?
  22. 22.In a group of 28 children, 9 play chess, 8 play carrom and 2 play both. How many play exactly one of the two?
  23. 23.In a group of 35 children, 20 like mangoes, 17 like bananas and 12 like both. How many like only bananas?
  24. 24.In a group of 40 children, 21 play cricket, 19 play football and 8 play both. How many play exactly one of the two?
  25. 25.In a group of 37 children, 25 sing Hindi songs, 19 sing English songs and 8 sing both. How many sing exactly one of the two?
  26. 26.In a group of 33 children, 10 like mangoes, 18 like bananas and 4 like both. How many like only bananas?
  27. 27.In a group of 32 children, 17 play chess, 17 play carrom and 12 play both. How many play at least one of the two?
  28. 28.In a group of 31 children, 17 play chess, 16 play carrom and 12 play both. How many play only carrom?
  29. 29.In a group of 24 children, 17 sing Hindi songs, 9 sing English songs and 3 sing both. How many sing exactly one of the two?
  30. 30.In a group of 44 children, 22 sing Hindi songs, 26 sing English songs and 11 sing both. How many sing only Hindi songs?
  31. 31.In a group of 37 children, 23 play cricket, 11 play football and 3 play both. How many play only cricket?
  32. 32.In a group of 31 grown-ups, 11 drink tea, 16 drink coffee and 2 drink both. How many drink neither of the two?
  33. 33.In a group of 50 children, 19 sing Hindi songs, 28 sing English songs and 12 sing both. How many sing neither of the two?
  34. 34.In a group of 39 children, 15 enjoy drawing, 32 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  35. 35.In a group of 29 children, 18 sing Hindi songs, 13 sing English songs and 7 sing both. How many sing neither of the two?
  36. 36.In a group of 32 children, 18 sing Hindi songs, 17 sing English songs and 4 sing both. How many sing only English songs?
  37. 37.In a group of 36 children, 21 enjoy drawing, 18 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  38. 38.In a group of 20 children, 12 like mangoes, 6 like bananas and 2 like both. How many like only mangoes?
  39. 39.In a group of 26 children, 15 play cricket, 11 play football and 6 play both. How many play only football?
  40. 40.In a group of 46 children, 21 play chess, 21 play carrom and 9 play both. How many play neither of the two?

Answer key

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

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