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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 529 · 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 38 children, 11 play cricket, 23 play football and 8 play both. How many play only cricket?
  2. 2.In a group of 36 children, 13 sing Hindi songs, 16 sing English songs and 3 sing both. How many sing only English songs?
  3. 3.In a group of 35 children, 7 play cricket, 18 play football and 3 play both. How many play neither of the two?
  4. 4.In a group of 37 children, 20 like mangoes, 21 like bananas and 9 like both. How many like only bananas?
  5. 5.In a group of 36 children, 16 play cricket, 10 play football and 3 play both. How many play at least one of the two?
  6. 6.In a group of 39 children, 13 play chess, 21 play carrom and 5 play both. How many play only carrom?
  7. 7.In a group of 30 children, 19 play cricket, 15 play football and 5 play both. How many play exactly one of the two?
  8. 8.In a group of 53 children, 24 play chess, 23 play carrom and 6 play both. How many play at least one of the two?
  9. 9.In a group of 20 children, 12 sing Hindi songs, 9 sing English songs and 5 sing both. How many sing at least one of the two?
  10. 10.In a group of 42 children, 18 enjoy drawing, 25 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  11. 11.In a group of 27 children, 16 play cricket, 12 play football and 8 play both. How many play exactly one of the two?
  12. 12.In a group of 30 grown-ups, 13 drink tea, 14 drink coffee and 5 drink both. How many drink exactly one of the two?
  13. 13.In a group of 28 children, 18 play chess, 9 play carrom and 4 play both. How many play only carrom?
  14. 14.In a group of 30 grown-ups, 14 drink tea, 14 drink coffee and 4 drink both. How many drink at least one of the two?
  15. 15.In a group of 33 children, 10 sing Hindi songs, 25 sing English songs and 6 sing both. How many sing only Hindi songs?
  16. 16.In a group of 55 children, 26 sing Hindi songs, 27 sing English songs and 12 sing both. How many sing only Hindi songs?
  17. 17.In a group of 54 children, 20 play cricket, 22 play football and 3 play both. How many play at least one of the two?
  18. 18.In a group of 49 children, 31 enjoy drawing, 28 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  19. 19.In a group of 49 children, 23 like mangoes, 16 like bananas and 4 like both. How many like neither of the two?
  20. 20.In a group of 48 children, 31 sing Hindi songs, 22 sing English songs and 12 sing both. How many sing only Hindi songs?
  21. 21.In a group of 34 children, 19 sing Hindi songs, 14 sing English songs and 10 sing both. How many sing neither of the two?
  22. 22.In a group of 34 children, 14 sing Hindi songs, 25 sing English songs and 11 sing both. How many sing only Hindi songs?
  23. 23.In a group of 30 children, 17 enjoy drawing, 16 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  24. 24.In a group of 34 children, 7 enjoy drawing, 16 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  25. 25.In a group of 33 children, 19 play chess, 20 play carrom and 10 play both. How many play at least one of the two?
  26. 26.In a group of 22 children, 8 play chess, 14 play carrom and 2 play both. How many play at least one of the two?
  27. 27.In a group of 51 children, 26 play chess, 24 play carrom and 7 play both. How many play only chess?
  28. 28.In a group of 43 children, 22 sing Hindi songs, 19 sing English songs and 3 sing both. How many sing neither of the two?
  29. 29.In a group of 45 children, 13 enjoy drawing, 20 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  30. 30.In a group of 53 children, 23 play chess, 26 play carrom and 8 play both. How many play at least one of the two?
  31. 31.In a group of 44 children, 25 play chess, 27 play carrom and 10 play both. How many play exactly one of the two?
  32. 32.In a group of 48 children, 26 like mangoes, 29 like bananas and 10 like both. How many like only bananas?
  33. 33.In a group of 23 children, 14 play cricket, 8 play football and 3 play both. How many play neither of the two?
  34. 34.In a group of 33 children, 14 sing Hindi songs, 19 sing English songs and 9 sing both. How many sing at least one of the two?
  35. 35.In a group of 58 grown-ups, 29 drink tea, 26 drink coffee and 11 drink both. How many drink only coffee?
  36. 36.In a group of 45 children, 25 sing Hindi songs, 31 sing English songs and 12 sing both. How many sing only English songs?
  37. 37.In a group of 35 children, 18 like mangoes, 22 like bananas and 12 like both. How many like exactly one of the two?
  38. 38.In a group of 58 children, 24 enjoy drawing, 27 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  39. 39.In a group of 25 children, 12 play chess, 15 play carrom and 9 play both. How many play only chess?
  40. 40.In a group of 40 children, 21 play chess, 19 play carrom and 6 play both. How many play at least one of the two?

Answer key

  1. 3
  2. 13
  3. 13
  4. 12
  5. 23
  6. 16
  7. 24
  8. 41
  9. 16
  10. 27
  11. 12
  12. 17
  13. 5
  14. 24
  15. 4
  16. 14
  17. 39
  18. 1
  19. 14
  20. 19
  21. 11
  22. 3
  23. 21
  24. 3
  25. 29
  26. 20
  27. 19
  28. 5
  29. 14
  30. 41
  31. 32
  32. 19
  33. 4
  34. 24
  35. 15
  36. 19
  37. 16
  38. 17
  39. 3
  40. 34

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