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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 654 · 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 children, 18 like mangoes, 18 like bananas and 12 like both. How many like exactly one of the two?
  2. 2.In a group of 46 children, 30 play chess, 17 play carrom and 12 play both. How many play only chess?
  3. 3.In a group of 30 children, 13 enjoy drawing, 13 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  4. 4.In a group of 45 children, 19 like mangoes, 23 like bananas and 6 like both. How many like only bananas?
  5. 5.In a group of 53 children, 19 like mangoes, 24 like bananas and 5 like both. How many like only mangoes?
  6. 6.In a group of 34 children, 23 enjoy drawing, 13 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  7. 7.In a group of 20 grown-ups, 15 drink tea, 10 drink coffee and 6 drink both. How many drink only coffee?
  8. 8.In a group of 39 children, 22 sing Hindi songs, 17 sing English songs and 2 sing both. How many sing at least one of the two?
  9. 9.In a group of 46 grown-ups, 22 drink tea, 15 drink coffee and 4 drink both. How many drink only coffee?
  10. 10.In a group of 42 grown-ups, 28 drink tea, 16 drink coffee and 10 drink both. How many drink only coffee?
  11. 11.In a group of 32 children, 15 sing Hindi songs, 9 sing English songs and 2 sing both. How many sing only English songs?
  12. 12.In a group of 21 grown-ups, 11 drink tea, 7 drink coffee and 4 drink both. How many drink neither of the two?
  13. 13.In a group of 24 children, 7 like mangoes, 5 like bananas and 2 like both. How many like only bananas?
  14. 14.In a group of 30 children, 10 like mangoes, 11 like bananas and 5 like both. How many like only mangoes?
  15. 15.In a group of 20 children, 7 play cricket, 9 play football and 4 play both. How many play exactly one of the two?
  16. 16.In a group of 37 children, 29 enjoy drawing, 14 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  17. 17.In a group of 46 children, 22 enjoy drawing, 13 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  18. 18.In a group of 22 children, 10 sing Hindi songs, 13 sing English songs and 3 sing both. How many sing neither of the two?
  19. 19.In a group of 36 children, 24 play chess, 12 play carrom and 9 play both. How many play only chess?
  20. 20.In a group of 41 children, 14 sing Hindi songs, 19 sing English songs and 5 sing both. How many sing neither of the two?
  21. 21.In a group of 26 children, 10 enjoy drawing, 13 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  22. 22.In a group of 18 children, 6 like mangoes, 14 like bananas and 3 like both. How many like at least one of the two?
  23. 23.In a group of 43 children, 20 play chess, 15 play carrom and 5 play both. How many play at least one of the two?
  24. 24.In a group of 27 children, 5 enjoy drawing, 13 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  25. 25.In a group of 20 grown-ups, 15 drink tea, 7 drink coffee and 3 drink both. How many drink only coffee?
  26. 26.In a group of 39 children, 24 play chess, 16 play carrom and 6 play both. How many play only carrom?
  27. 27.In a group of 37 children, 13 like mangoes, 23 like bananas and 7 like both. How many like only mangoes?
  28. 28.In a group of 29 grown-ups, 24 drink tea, 10 drink coffee and 6 drink both. How many drink neither of the two?
  29. 29.In a group of 27 children, 9 sing Hindi songs, 21 sing English songs and 5 sing both. How many sing only Hindi songs?
  30. 30.In a group of 36 grown-ups, 19 drink tea, 18 drink coffee and 6 drink both. How many drink only tea?
  31. 31.In a group of 42 children, 23 like mangoes, 12 like bananas and 3 like both. How many like at least one of the two?
  32. 32.In a group of 52 children, 24 play cricket, 22 play football and 4 play both. How many play only cricket?
  33. 33.In a group of 18 children, 5 play cricket, 12 play football and 2 play both. How many play exactly one of the two?
  34. 34.In a group of 37 grown-ups, 23 drink tea, 15 drink coffee and 9 drink both. How many drink only tea?
  35. 35.In a group of 42 grown-ups, 16 drink tea, 26 drink coffee and 10 drink both. How many drink only coffee?
  36. 36.In a group of 46 children, 28 like mangoes, 20 like bananas and 10 like both. How many like at least one of the two?
  37. 37.In a group of 35 children, 14 play chess, 11 play carrom and 4 play both. How many play at least one of the two?
  38. 38.In a group of 44 children, 21 play chess, 27 play carrom and 10 play both. How many play at least one of the two?
  39. 39.In a group of 37 children, 17 sing Hindi songs, 23 sing English songs and 5 sing both. How many sing only Hindi songs?
  40. 40.In a group of 42 children, 25 enjoy drawing, 15 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?

Answer key

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

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