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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 355 · 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 60 children, 28 like mangoes, 26 like bananas and 8 like both. How many like only mangoes?
  2. 2.In a group of 26 children, 10 like mangoes, 16 like bananas and 6 like both. How many like neither of the two?
  3. 3.In a group of 25 children, 11 sing Hindi songs, 10 sing English songs and 2 sing both. How many sing at least one of the two?
  4. 4.In a group of 44 children, 17 enjoy drawing, 27 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  5. 5.In a group of 21 children, 12 sing Hindi songs, 11 sing English songs and 5 sing both. How many sing neither of the two?
  6. 6.In a group of 37 children, 19 play cricket, 18 play football and 11 play both. How many play at least one of the two?
  7. 7.In a group of 47 children, 25 play cricket, 30 play football and 10 play both. How many play neither of the two?
  8. 8.In a group of 48 children, 23 enjoy drawing, 21 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  9. 9.In a group of 34 children, 22 play cricket, 20 play football and 12 play both. How many play only football?
  10. 10.In a group of 31 children, 17 like mangoes, 7 like bananas and 2 like both. How many like neither of the two?
  11. 11.In a group of 49 grown-ups, 27 drink tea, 31 drink coffee and 11 drink both. How many drink only coffee?
  12. 12.In a group of 30 grown-ups, 11 drink tea, 15 drink coffee and 8 drink both. How many drink only tea?
  13. 13.In a group of 36 children, 19 play chess, 18 play carrom and 10 play both. How many play at least one of the two?
  14. 14.In a group of 38 grown-ups, 19 drink tea, 12 drink coffee and 8 drink both. How many drink only tea?
  15. 15.In a group of 60 children, 30 like mangoes, 27 like bananas and 12 like both. How many like exactly one of the two?
  16. 16.In a group of 46 children, 28 play chess, 16 play carrom and 12 play both. How many play only chess?
  17. 17.In a group of 36 children, 25 play cricket, 20 play football and 11 play both. How many play neither of the two?
  18. 18.In a group of 21 children, 8 play cricket, 7 play football and 4 play both. How many play only cricket?
  19. 19.In a group of 45 children, 29 enjoy drawing, 24 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  20. 20.In a group of 43 children, 18 like mangoes, 22 like bananas and 6 like both. How many like neither of the two?
  21. 21.In a group of 30 grown-ups, 13 drink tea, 15 drink coffee and 8 drink both. How many drink only tea?
  22. 22.In a group of 58 children, 27 play chess, 26 play carrom and 9 play both. How many play exactly one of the two?
  23. 23.In a group of 45 children, 20 sing Hindi songs, 27 sing English songs and 10 sing both. How many sing at least one of the two?
  24. 24.In a group of 38 children, 16 like mangoes, 19 like bananas and 7 like both. How many like at least one of the two?
  25. 25.In a group of 39 children, 18 play cricket, 23 play football and 12 play both. How many play at least one of the two?
  26. 26.In a group of 16 children, 9 enjoy drawing, 12 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?
  27. 27.In a group of 33 grown-ups, 20 drink tea, 15 drink coffee and 9 drink both. How many drink only tea?
  28. 28.In a group of 26 children, 12 like mangoes, 11 like bananas and 5 like both. How many like only bananas?
  29. 29.In a group of 22 children, 9 sing Hindi songs, 9 sing English songs and 6 sing both. How many sing exactly one of the two?
  30. 30.In a group of 48 children, 29 like mangoes, 30 like bananas and 12 like both. How many like only mangoes?
  31. 31.In a group of 23 children, 14 like mangoes, 18 like bananas and 11 like both. How many like only mangoes?
  32. 32.In a group of 50 children, 16 enjoy drawing, 30 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  33. 33.In a group of 51 children, 24 play cricket, 21 play football and 5 play both. How many play only cricket?
  34. 34.In a group of 61 children, 27 play cricket, 28 play football and 9 play both. How many play only cricket?
  35. 35.In a group of 36 children, 26 play cricket, 10 play football and 7 play both. How many play exactly one of the two?
  36. 36.In a group of 25 children, 14 play cricket, 14 play football and 7 play both. How many play exactly one of the two?
  37. 37.In a group of 33 children, 16 like mangoes, 18 like bananas and 2 like both. How many like only bananas?
  38. 38.In a group of 27 children, 16 play chess, 20 play carrom and 10 play both. How many play neither of the two?
  39. 39.In a group of 38 children, 21 play cricket, 12 play football and 6 play both. How many play exactly one of the two?
  40. 40.In a group of 42 children, 16 play cricket, 17 play football and 5 play both. How many play only football?

Answer key

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

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