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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 668 · 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 40 children, 20 play cricket, 10 play football and 3 play both. How many play exactly one of the two?
  2. 2.In a group of 44 children, 21 enjoy drawing, 26 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  3. 3.In a group of 51 children, 21 enjoy drawing, 19 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  4. 4.In a group of 47 children, 26 play cricket, 19 play football and 12 play both. How many play at least one of the two?
  5. 5.In a group of 26 children, 19 enjoy drawing, 12 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  6. 6.In a group of 36 children, 14 sing Hindi songs, 22 sing English songs and 8 sing both. How many sing only Hindi songs?
  7. 7.In a group of 31 children, 7 play cricket, 12 play football and 2 play both. How many play exactly one of the two?
  8. 8.In a group of 37 children, 19 sing Hindi songs, 17 sing English songs and 3 sing both. How many sing at least one of the two?
  9. 9.In a group of 19 children, 11 enjoy drawing, 12 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  10. 10.In a group of 46 children, 23 like mangoes, 20 like bananas and 6 like both. How many like only mangoes?
  11. 11.In a group of 33 children, 18 like mangoes, 15 like bananas and 5 like both. How many like exactly one of the two?
  12. 12.In a group of 38 children, 14 enjoy drawing, 19 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  13. 13.In a group of 62 children, 29 play chess, 31 play carrom and 12 play both. How many play only carrom?
  14. 14.In a group of 29 children, 10 like mangoes, 12 like bananas and 7 like both. How many like only bananas?
  15. 15.In a group of 45 children, 26 sing Hindi songs, 17 sing English songs and 11 sing both. How many sing only Hindi songs?
  16. 16.In a group of 40 grown-ups, 21 drink tea, 12 drink coffee and 8 drink both. How many drink at least one of the two?
  17. 17.In a group of 45 children, 20 play cricket, 14 play football and 4 play both. How many play neither of the two?
  18. 18.In a group of 28 children, 12 like mangoes, 9 like bananas and 4 like both. How many like exactly one of the two?
  19. 19.In a group of 40 children, 17 like mangoes, 17 like bananas and 2 like both. How many like exactly one of the two?
  20. 20.In a group of 31 children, 18 play cricket, 12 play football and 7 play both. How many play neither of the two?
  21. 21.In a group of 32 children, 15 play chess, 17 play carrom and 10 play both. How many play exactly one of the two?
  22. 22.In a group of 45 grown-ups, 24 drink tea, 17 drink coffee and 8 drink both. How many drink at least one of the two?
  23. 23.In a group of 42 children, 19 enjoy drawing, 24 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  24. 24.In a group of 44 children, 21 play cricket, 24 play football and 8 play both. How many play at least one of the two?
  25. 25.In a group of 49 children, 26 play cricket, 16 play football and 7 play both. How many play only cricket?
  26. 26.In a group of 11 children, 5 sing Hindi songs, 7 sing English songs and 2 sing both. How many sing only Hindi songs?
  27. 27.In a group of 22 children, 10 like mangoes, 14 like bananas and 5 like both. How many like at least one of the two?
  28. 28.In a group of 43 children, 22 enjoy drawing, 27 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  29. 29.In a group of 38 grown-ups, 26 drink tea, 17 drink coffee and 6 drink both. How many drink only tea?
  30. 30.In a group of 27 children, 16 play cricket, 11 play football and 8 play both. How many play only cricket?
  31. 31.In a group of 39 children, 15 enjoy drawing, 27 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  32. 32.In a group of 28 children, 10 like mangoes, 18 like bananas and 2 like both. How many like exactly one of the two?
  33. 33.In a group of 18 children, 12 sing Hindi songs, 5 sing English songs and 2 sing both. How many sing only English songs?
  34. 34.In a group of 37 children, 21 like mangoes, 21 like bananas and 8 like both. How many like at least one of the two?
  35. 35.In a group of 22 grown-ups, 7 drink tea, 6 drink coffee and 3 drink both. How many drink only tea?
  36. 36.In a group of 30 grown-ups, 16 drink tea, 7 drink coffee and 3 drink both. How many drink exactly one of the two?
  37. 37.In a group of 31 children, 20 like mangoes, 11 like bananas and 3 like both. How many like only bananas?
  38. 38.In a group of 33 children, 18 play chess, 18 play carrom and 9 play both. How many play exactly one of the two?
  39. 39.In a group of 52 children, 26 like mangoes, 28 like bananas and 11 like both. How many like at least one of the two?
  40. 40.In a group of 45 children, 22 like mangoes, 24 like bananas and 10 like both. How many like at least one of the two?

Answer key

  1. 24
  2. 19
  3. 15
  4. 33
  5. 22
  6. 6
  7. 15
  8. 33
  9. 15
  10. 17
  11. 23
  12. 13
  13. 19
  14. 5
  15. 15
  16. 25
  17. 15
  18. 13
  19. 30
  20. 8
  21. 12
  22. 33
  23. 36
  24. 37
  25. 19
  26. 3
  27. 19
  28. 3
  29. 20
  30. 8
  31. 19
  32. 24
  33. 3
  34. 34
  35. 4
  36. 17
  37. 8
  38. 18
  39. 43
  40. 36

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