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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 658 · 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 50 children, 27 sing Hindi songs, 28 sing English songs and 8 sing both. How many sing only English songs?
  2. 2.In a group of 39 children, 23 play chess, 14 play carrom and 3 play both. How many play neither of the two?
  3. 3.In a group of 38 children, 24 sing Hindi songs, 19 sing English songs and 7 sing both. How many sing exactly one of the two?
  4. 4.In a group of 32 children, 23 play cricket, 17 play football and 10 play both. How many play neither of the two?
  5. 5.In a group of 26 children, 10 like mangoes, 15 like bananas and 3 like both. How many like neither of the two?
  6. 6.In a group of 25 grown-ups, 12 drink tea, 9 drink coffee and 5 drink both. How many drink only tea?
  7. 7.In a group of 37 children, 25 play cricket, 22 play football and 11 play both. How many play only football?
  8. 8.In a group of 29 children, 17 play cricket, 6 play football and 2 play both. How many play only football?
  9. 9.In a group of 35 children, 20 play chess, 18 play carrom and 12 play both. How many play neither of the two?
  10. 10.In a group of 15 grown-ups, 7 drink tea, 6 drink coffee and 2 drink both. How many drink only tea?
  11. 11.In a group of 39 grown-ups, 22 drink tea, 22 drink coffee and 8 drink both. How many drink at least one of the two?
  12. 12.In a group of 26 grown-ups, 8 drink tea, 15 drink coffee and 2 drink both. How many drink at least one of the two?
  13. 13.In a group of 40 children, 19 enjoy drawing, 26 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  14. 14.In a group of 41 grown-ups, 20 drink tea, 18 drink coffee and 9 drink both. How many drink exactly one of the two?
  15. 15.In a group of 27 children, 12 play cricket, 19 play football and 7 play both. How many play only cricket?
  16. 16.In a group of 39 children, 15 play cricket, 18 play football and 4 play both. How many play only football?
  17. 17.In a group of 47 children, 26 sing Hindi songs, 16 sing English songs and 6 sing both. How many sing at least one of the two?
  18. 18.In a group of 46 grown-ups, 21 drink tea, 24 drink coffee and 6 drink both. How many drink neither of the two?
  19. 19.In a group of 36 grown-ups, 22 drink tea, 8 drink coffee and 2 drink both. How many drink neither of the two?
  20. 20.In a group of 27 children, 17 play cricket, 12 play football and 5 play both. How many play at least one of the two?
  21. 21.In a group of 37 children, 22 like mangoes, 7 like bananas and 2 like both. How many like only mangoes?
  22. 22.In a group of 33 children, 23 sing Hindi songs, 20 sing English songs and 12 sing both. How many sing only Hindi songs?
  23. 23.In a group of 53 children, 24 play cricket, 20 play football and 6 play both. How many play only football?
  24. 24.In a group of 36 children, 13 enjoy drawing, 22 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  25. 25.In a group of 51 children, 24 play cricket, 24 play football and 4 play both. How many play exactly one of the two?
  26. 26.In a group of 29 children, 20 play chess, 6 play carrom and 2 play both. How many play at least one of the two?
  27. 27.In a group of 45 grown-ups, 22 drink tea, 21 drink coffee and 12 drink both. How many drink exactly one of the two?
  28. 28.In a group of 34 children, 22 enjoy drawing, 13 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  29. 29.In a group of 26 children, 7 enjoy drawing, 16 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  30. 30.In a group of 44 grown-ups, 21 drink tea, 24 drink coffee and 4 drink both. How many drink exactly one of the two?
  31. 31.In a group of 22 children, 16 enjoy drawing, 9 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?
  32. 32.In a group of 61 children, 28 sing Hindi songs, 32 sing English songs and 12 sing both. How many sing at least one of the two?
  33. 33.In a group of 32 children, 21 sing Hindi songs, 11 sing English songs and 7 sing both. How many sing neither of the two?
  34. 34.In a group of 36 children, 29 enjoy drawing, 13 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  35. 35.In a group of 40 children, 19 sing Hindi songs, 16 sing English songs and 2 sing both. How many sing only Hindi songs?
  36. 36.In a group of 37 children, 24 play chess, 15 play carrom and 10 play both. How many play only chess?
  37. 37.In a group of 19 children, 11 enjoy drawing, 11 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  38. 38.In a group of 49 children, 20 sing Hindi songs, 24 sing English songs and 10 sing both. How many sing only Hindi songs?
  39. 39.In a group of 36 children, 16 play chess, 25 play carrom and 9 play both. How many play at least one of the two?
  40. 40.In a group of 49 children, 28 play cricket, 15 play football and 9 play both. How many play neither of the two?

Answer key

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

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