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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 505 · 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 48 children, 19 like mangoes, 27 like bananas and 10 like both. How many like exactly one of the two?
  2. 2.In a group of 36 children, 17 play cricket, 21 play football and 5 play both. How many play only cricket?
  3. 3.In a group of 35 children, 22 enjoy drawing, 6 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  4. 4.In a group of 42 children, 14 play cricket, 24 play football and 6 play both. How many play only cricket?
  5. 5.In a group of 29 children, 10 sing Hindi songs, 13 sing English songs and 4 sing both. How many sing exactly one of the two?
  6. 6.In a group of 45 children, 25 sing Hindi songs, 24 sing English songs and 9 sing both. How many sing only Hindi songs?
  7. 7.In a group of 35 grown-ups, 12 drink tea, 19 drink coffee and 6 drink both. How many drink only coffee?
  8. 8.In a group of 31 children, 20 play cricket, 15 play football and 8 play both. How many play at least one of the two?
  9. 9.In a group of 49 children, 23 sing Hindi songs, 22 sing English songs and 6 sing both. How many sing neither of the two?
  10. 10.In a group of 32 children, 15 sing Hindi songs, 18 sing English songs and 12 sing both. How many sing neither of the two?
  11. 11.In a group of 35 grown-ups, 13 drink tea, 18 drink coffee and 4 drink both. How many drink at least one of the two?
  12. 12.In a group of 33 children, 21 play chess, 11 play carrom and 2 play both. How many play only chess?
  13. 13.In a group of 36 children, 19 sing Hindi songs, 19 sing English songs and 10 sing both. How many sing only English songs?
  14. 14.In a group of 48 children, 24 play chess, 27 play carrom and 7 play both. How many play only carrom?
  15. 15.In a group of 32 children, 15 enjoy drawing, 21 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  16. 16.In a group of 43 grown-ups, 21 drink tea, 19 drink coffee and 6 drink both. How many drink at least one of the two?
  17. 17.In a group of 48 children, 18 play cricket, 29 play football and 11 play both. How many play exactly one of the two?
  18. 18.In a group of 27 children, 20 enjoy drawing, 13 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  19. 19.In a group of 48 children, 17 play chess, 29 play carrom and 11 play both. How many play neither of the two?
  20. 20.In a group of 35 children, 12 play chess, 24 play carrom and 8 play both. How many play at least one of the two?
  21. 21.In a group of 42 children, 19 play cricket, 25 play football and 11 play both. How many play only football?
  22. 22.In a group of 45 children, 21 like mangoes, 22 like bananas and 9 like both. How many like neither of the two?
  23. 23.In a group of 61 children, 29 like mangoes, 31 like bananas and 11 like both. How many like only bananas?
  24. 24.In a group of 35 children, 18 enjoy drawing, 13 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  25. 25.In a group of 58 children, 28 sing Hindi songs, 30 sing English songs and 10 sing both. How many sing at least one of the two?
  26. 26.In a group of 26 children, 18 sing Hindi songs, 14 sing English songs and 10 sing both. How many sing only Hindi songs?
  27. 27.In a group of 37 children, 25 play cricket, 20 play football and 11 play both. How many play only football?
  28. 28.In a group of 28 children, 17 like mangoes, 10 like bananas and 4 like both. How many like neither of the two?
  29. 29.In a group of 33 grown-ups, 25 drink tea, 12 drink coffee and 6 drink both. How many drink only tea?
  30. 30.In a group of 24 children, 13 sing Hindi songs, 16 sing English songs and 7 sing both. How many sing only Hindi songs?
  31. 31.In a group of 37 children, 12 play cricket, 18 play football and 4 play both. How many play only cricket?
  32. 32.In a group of 36 children, 16 play cricket, 29 play football and 11 play both. How many play only cricket?
  33. 33.In a group of 35 children, 17 play chess, 16 play carrom and 10 play both. How many play neither of the two?
  34. 34.In a group of 20 children, 13 play cricket, 7 play football and 3 play both. How many play neither of the two?
  35. 35.In a group of 45 children, 18 play chess, 20 play carrom and 3 play both. How many play exactly one of the two?
  36. 36.In a group of 43 children, 16 sing Hindi songs, 24 sing English songs and 7 sing both. How many sing only Hindi songs?
  37. 37.In a group of 44 children, 25 enjoy drawing, 13 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  38. 38.In a group of 36 children, 13 like mangoes, 23 like bananas and 3 like both. How many like only bananas?
  39. 39.In a group of 47 children, 26 sing Hindi songs, 20 sing English songs and 10 sing both. How many sing only Hindi songs?
  40. 40.In a group of 31 children, 15 play cricket, 16 play football and 3 play both. How many play only cricket?

Answer key

  1. 26
  2. 12
  3. 22
  4. 8
  5. 15
  6. 16
  7. 13
  8. 27
  9. 10
  10. 11
  11. 27
  12. 19
  13. 9
  14. 20
  15. 28
  16. 34
  17. 25
  18. 3
  19. 13
  20. 28
  21. 14
  22. 11
  23. 20
  24. 15
  25. 48
  26. 8
  27. 9
  28. 5
  29. 19
  30. 6
  31. 8
  32. 5
  33. 12
  34. 3
  35. 32
  36. 9
  37. 18
  38. 20
  39. 16
  40. 12

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