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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 127 · 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 26 children, 14 enjoy drawing, 13 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  2. 2.In a group of 56 children, 27 play cricket, 25 play football and 10 play both. How many play neither of the two?
  3. 3.In a group of 49 children, 22 enjoy drawing, 22 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  4. 4.In a group of 41 children, 20 enjoy drawing, 18 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  5. 5.In a group of 49 children, 25 sing Hindi songs, 25 sing English songs and 5 sing both. How many sing exactly one of the two?
  6. 6.In a group of 37 children, 15 play cricket, 22 play football and 6 play both. How many play at least one of the two?
  7. 7.In a group of 26 children, 15 play cricket, 11 play football and 4 play both. How many play only cricket?
  8. 8.In a group of 43 children, 22 like mangoes, 13 like bananas and 3 like both. How many like only bananas?
  9. 9.In a group of 35 children, 22 enjoy drawing, 15 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  10. 10.In a group of 34 children, 25 play chess, 13 play carrom and 6 play both. How many play neither of the two?
  11. 11.In a group of 37 children, 19 play cricket, 12 play football and 4 play both. How many play only cricket?
  12. 12.In a group of 35 children, 12 play chess, 23 play carrom and 7 play both. How many play exactly one of the two?
  13. 13.In a group of 16 children, 9 play chess, 6 play carrom and 2 play both. How many play at least one of the two?
  14. 14.In a group of 39 children, 14 play cricket, 15 play football and 3 play both. How many play only football?
  15. 15.In a group of 24 children, 7 like mangoes, 6 like bananas and 2 like both. How many like only mangoes?
  16. 16.In a group of 37 children, 21 like mangoes, 15 like bananas and 10 like both. How many like neither of the two?
  17. 17.In a group of 38 children, 9 sing Hindi songs, 25 sing English songs and 5 sing both. How many sing neither of the two?
  18. 18.In a group of 35 children, 13 play cricket, 21 play football and 10 play both. How many play neither of the two?
  19. 19.In a group of 49 children, 24 play cricket, 26 play football and 11 play both. How many play only football?
  20. 20.In a group of 46 children, 13 sing Hindi songs, 23 sing English songs and 4 sing both. How many sing exactly one of the two?
  21. 21.In a group of 47 grown-ups, 29 drink tea, 27 drink coffee and 11 drink both. How many drink only tea?
  22. 22.In a group of 37 children, 22 play chess, 10 play carrom and 6 play both. How many play only chess?
  23. 23.In a group of 23 children, 15 play cricket, 12 play football and 5 play both. How many play only football?
  24. 24.In a group of 41 children, 22 play chess, 19 play carrom and 3 play both. How many play at least one of the two?
  25. 25.In a group of 46 children, 28 play chess, 22 play carrom and 8 play both. How many play only chess?
  26. 26.In a group of 42 grown-ups, 19 drink tea, 15 drink coffee and 6 drink both. How many drink at least one of the two?
  27. 27.In a group of 28 children, 19 enjoy drawing, 10 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  28. 28.In a group of 41 children, 17 like mangoes, 20 like bananas and 9 like both. How many like exactly one of the two?
  29. 29.In a group of 39 children, 9 play cricket, 21 play football and 3 play both. How many play neither of the two?
  30. 30.In a group of 20 children, 12 sing Hindi songs, 11 sing English songs and 5 sing both. How many sing only English songs?
  31. 31.In a group of 29 children, 17 sing Hindi songs, 14 sing English songs and 11 sing both. How many sing at least one of the two?
  32. 32.In a group of 28 children, 16 enjoy drawing, 16 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  33. 33.In a group of 23 children, 8 play cricket, 15 play football and 3 play both. How many play neither of the two?
  34. 34.In a group of 36 children, 24 sing Hindi songs, 17 sing English songs and 11 sing both. How many sing only English songs?
  35. 35.In a group of 38 children, 22 enjoy drawing, 12 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  36. 36.In a group of 41 children, 16 enjoy drawing, 16 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  37. 37.In a group of 36 children, 11 like mangoes, 18 like bananas and 4 like both. How many like only bananas?
  38. 38.In a group of 50 children, 21 play cricket, 25 play football and 5 play both. How many play only football?
  39. 39.In a group of 25 grown-ups, 7 drink tea, 8 drink coffee and 2 drink both. How many drink only coffee?
  40. 40.In a group of 30 children, 12 play cricket, 20 play football and 5 play both. How many play exactly one of the two?

Answer key

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

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