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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 73 · 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 55 children, 26 play cricket, 26 play football and 7 play both. How many play at least one of the two?
  2. 2.In a group of 51 children, 26 sing Hindi songs, 23 sing English songs and 12 sing both. How many sing at least one of the two?
  3. 3.In a group of 26 children, 9 enjoy drawing, 12 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  4. 4.In a group of 30 children, 20 play cricket, 11 play football and 2 play both. How many play only cricket?
  5. 5.In a group of 36 children, 15 play cricket, 20 play football and 11 play both. How many play only football?
  6. 6.In a group of 41 children, 25 play chess, 11 play carrom and 7 play both. How many play at least one of the two?
  7. 7.In a group of 38 children, 18 like mangoes, 17 like bananas and 11 like both. How many like only mangoes?
  8. 8.In a group of 35 children, 15 play cricket, 19 play football and 6 play both. How many play only cricket?
  9. 9.In a group of 34 children, 13 sing Hindi songs, 20 sing English songs and 6 sing both. How many sing only Hindi songs?
  10. 10.In a group of 47 children, 22 like mangoes, 19 like bananas and 3 like both. How many like neither of the two?
  11. 11.In a group of 9 children, 5 play chess, 5 play carrom and 2 play both. How many play exactly one of the two?
  12. 12.In a group of 35 children, 15 like mangoes, 13 like bananas and 3 like both. How many like exactly one of the two?
  13. 13.In a group of 36 children, 22 play cricket, 8 play football and 5 play both. How many play exactly one of the two?
  14. 14.In a group of 35 children, 24 play cricket, 7 play football and 4 play both. How many play exactly one of the two?
  15. 15.In a group of 38 children, 13 enjoy drawing, 19 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  16. 16.In a group of 42 children, 24 enjoy drawing, 11 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  17. 17.In a group of 52 children, 21 like mangoes, 21 like bananas and 4 like both. How many like only bananas?
  18. 18.In a group of 44 grown-ups, 23 drink tea, 30 drink coffee and 10 drink both. How many drink at least one of the two?
  19. 19.In a group of 32 children, 22 play cricket, 8 play football and 3 play both. How many play neither of the two?
  20. 20.In a group of 30 children, 23 play chess, 9 play carrom and 3 play both. How many play exactly one of the two?
  21. 21.In a group of 60 children, 29 enjoy drawing, 28 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  22. 22.In a group of 40 children, 22 sing Hindi songs, 9 sing English songs and 2 sing both. How many sing neither of the two?
  23. 23.In a group of 26 children, 19 enjoy drawing, 14 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  24. 24.In a group of 22 children, 16 sing Hindi songs, 8 sing English songs and 4 sing both. How many sing only Hindi songs?
  25. 25.In a group of 31 children, 23 enjoy drawing, 11 enjoy dancing and 5 enjoy both. How many enjoy at least one of the two?
  26. 26.In a group of 36 children, 18 play cricket, 15 play football and 10 play both. How many play only cricket?
  27. 27.In a group of 25 children, 8 enjoy drawing, 9 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  28. 28.In a group of 32 children, 21 play chess, 17 play carrom and 9 play both. How many play exactly one of the two?
  29. 29.In a group of 28 children, 20 play cricket, 13 play football and 7 play both. How many play only cricket?
  30. 30.In a group of 48 children, 25 like mangoes, 21 like bananas and 10 like both. How many like only mangoes?
  31. 31.In a group of 31 children, 24 play cricket, 13 play football and 7 play both. How many play exactly one of the two?
  32. 32.In a group of 37 grown-ups, 14 drink tea, 17 drink coffee and 9 drink both. How many drink only tea?
  33. 33.In a group of 42 children, 22 play chess, 16 play carrom and 2 play both. How many play only chess?
  34. 34.In a group of 47 children, 23 play cricket, 20 play football and 5 play both. How many play only cricket?
  35. 35.In a group of 31 grown-ups, 13 drink tea, 21 drink coffee and 7 drink both. How many drink only coffee?
  36. 36.In a group of 52 children, 26 play cricket, 28 play football and 8 play both. How many play at least one of the two?
  37. 37.In a group of 38 children, 15 play chess, 26 play carrom and 11 play both. How many play only chess?
  38. 38.In a group of 36 grown-ups, 20 drink tea, 14 drink coffee and 2 drink both. How many drink exactly one of the two?
  39. 39.In a group of 43 children, 21 play chess, 25 play carrom and 7 play both. How many play neither of the two?
  40. 40.In a group of 51 children, 28 sing Hindi songs, 28 sing English songs and 8 sing both. How many sing only English songs?

Answer key

  1. 45
  2. 37
  3. 10
  4. 18
  5. 9
  6. 29
  7. 7
  8. 9
  9. 7
  10. 9
  11. 6
  12. 22
  13. 20
  14. 23
  15. 7
  16. 7
  17. 17
  18. 43
  19. 5
  20. 26
  21. 16
  22. 11
  23. 4
  24. 12
  25. 29
  26. 8
  27. 6
  28. 20
  29. 13
  30. 15
  31. 23
  32. 5
  33. 20
  34. 18
  35. 14
  36. 46
  37. 4
  38. 30
  39. 4
  40. 20

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