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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 319 · 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 49 children, 26 sing Hindi songs, 23 sing English songs and 9 sing both. How many sing exactly one of the two?
  2. 2.In a group of 48 children, 27 sing Hindi songs, 25 sing English songs and 9 sing both. How many sing only Hindi songs?
  3. 3.In a group of 30 children, 24 play chess, 14 play carrom and 9 play both. How many play only chess?
  4. 4.In a group of 56 children, 27 play cricket, 28 play football and 10 play both. How many play neither of the two?
  5. 5.In a group of 22 children, 11 play cricket, 16 play football and 7 play both. How many play neither of the two?
  6. 6.In a group of 43 children, 21 play cricket, 13 play football and 2 play both. How many play only cricket?
  7. 7.In a group of 42 children, 17 play cricket, 22 play football and 11 play both. How many play only cricket?
  8. 8.In a group of 39 children, 13 enjoy drawing, 21 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  9. 9.In a group of 27 grown-ups, 13 drink tea, 21 drink coffee and 9 drink both. How many drink only coffee?
  10. 10.In a group of 35 grown-ups, 18 drink tea, 8 drink coffee and 5 drink both. How many drink only coffee?
  11. 11.In a group of 29 children, 16 enjoy drawing, 15 enjoy dancing and 5 enjoy both. How many enjoy at least one of the two?
  12. 12.In a group of 29 children, 15 like mangoes, 17 like bananas and 7 like both. How many like neither of the two?
  13. 13.In a group of 27 grown-ups, 21 drink tea, 6 drink coffee and 3 drink both. How many drink only coffee?
  14. 14.In a group of 16 children, 5 play cricket, 10 play football and 2 play both. How many play exactly one of the two?
  15. 15.In a group of 42 grown-ups, 11 drink tea, 20 drink coffee and 3 drink both. How many drink at least one of the two?
  16. 16.In a group of 52 grown-ups, 22 drink tea, 18 drink coffee and 2 drink both. How many drink at least one of the two?
  17. 17.In a group of 34 children, 17 play cricket, 14 play football and 10 play both. How many play exactly one of the two?
  18. 18.In a group of 36 children, 22 like mangoes, 21 like bananas and 9 like both. How many like only mangoes?
  19. 19.In a group of 29 children, 9 enjoy drawing, 16 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  20. 20.In a group of 19 children, 14 enjoy drawing, 10 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  21. 21.In a group of 42 grown-ups, 20 drink tea, 17 drink coffee and 10 drink both. How many drink at least one of the two?
  22. 22.In a group of 51 children, 20 sing Hindi songs, 24 sing English songs and 6 sing both. How many sing only English songs?
  23. 23.In a group of 45 children, 26 like mangoes, 11 like bananas and 6 like both. How many like neither of the two?
  24. 24.In a group of 24 children, 10 enjoy drawing, 11 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  25. 25.In a group of 25 children, 14 enjoy drawing, 11 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  26. 26.In a group of 48 children, 21 enjoy drawing, 27 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  27. 27.In a group of 43 children, 26 enjoy drawing, 13 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?
  28. 28.In a group of 47 grown-ups, 27 drink tea, 21 drink coffee and 11 drink both. How many drink at least one of the two?
  29. 29.In a group of 48 grown-ups, 21 drink tea, 16 drink coffee and 3 drink both. How many drink only tea?
  30. 30.In a group of 31 children, 26 sing Hindi songs, 13 sing English songs and 10 sing both. How many sing only Hindi songs?
  31. 31.In a group of 36 children, 8 play chess, 22 play carrom and 5 play both. How many play neither of the two?
  32. 32.In a group of 34 children, 9 sing Hindi songs, 20 sing English songs and 6 sing both. How many sing at least one of the two?
  33. 33.In a group of 37 grown-ups, 17 drink tea, 18 drink coffee and 3 drink both. How many drink at least one of the two?
  34. 34.In a group of 48 children, 18 like mangoes, 29 like bananas and 12 like both. How many like only mangoes?
  35. 35.In a group of 43 children, 23 like mangoes, 18 like bananas and 9 like both. How many like neither of the two?
  36. 36.In a group of 36 children, 22 enjoy drawing, 14 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  37. 37.In a group of 23 grown-ups, 11 drink tea, 9 drink coffee and 3 drink both. How many drink neither of the two?
  38. 38.In a group of 42 children, 17 play chess, 25 play carrom and 10 play both. How many play at least one of the two?
  39. 39.In a group of 16 children, 10 play cricket, 12 play football and 7 play both. How many play exactly one of the two?
  40. 40.In a group of 41 children, 15 like mangoes, 21 like bananas and 4 like both. How many like exactly one of the two?

Answer key

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

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