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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 489 · 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 39 children, 25 play cricket, 16 play football and 12 play both. How many play only football?
  2. 2.In a group of 38 children, 19 play cricket, 20 play football and 9 play both. How many play exactly one of the two?
  3. 3.In a group of 21 children, 12 play chess, 8 play carrom and 2 play both. How many play only carrom?
  4. 4.In a group of 36 children, 24 enjoy drawing, 14 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  5. 5.In a group of 52 children, 27 play chess, 21 play carrom and 8 play both. How many play at least one of the two?
  6. 6.In a group of 27 children, 15 sing Hindi songs, 15 sing English songs and 4 sing both. How many sing exactly one of the two?
  7. 7.In a group of 23 grown-ups, 7 drink tea, 8 drink coffee and 3 drink both. How many drink neither of the two?
  8. 8.In a group of 45 children, 21 sing Hindi songs, 23 sing English songs and 3 sing both. How many sing at least one of the two?
  9. 9.In a group of 46 children, 27 like mangoes, 24 like bananas and 9 like both. How many like at least one of the two?
  10. 10.In a group of 54 children, 31 play chess, 25 play carrom and 11 play both. How many play at least one of the two?
  11. 11.In a group of 50 children, 15 sing Hindi songs, 23 sing English songs and 3 sing both. How many sing only English songs?
  12. 12.In a group of 48 children, 26 sing Hindi songs, 24 sing English songs and 7 sing both. How many sing neither of the two?
  13. 13.In a group of 44 children, 19 play cricket, 24 play football and 7 play both. How many play at least one of the two?
  14. 14.In a group of 60 children, 27 play chess, 30 play carrom and 12 play both. How many play exactly one of the two?
  15. 15.In a group of 24 grown-ups, 11 drink tea, 16 drink coffee and 8 drink both. How many drink at least one of the two?
  16. 16.In a group of 24 children, 10 play chess, 13 play carrom and 7 play both. How many play only chess?
  17. 17.In a group of 28 children, 10 play cricket, 13 play football and 6 play both. How many play only football?
  18. 18.In a group of 48 children, 21 play chess, 24 play carrom and 8 play both. How many play only chess?
  19. 19.In a group of 40 children, 13 like mangoes, 26 like bananas and 6 like both. How many like only bananas?
  20. 20.In a group of 50 children, 24 play cricket, 23 play football and 11 play both. How many play exactly one of the two?
  21. 21.In a group of 33 children, 12 play chess, 22 play carrom and 8 play both. How many play neither of the two?
  22. 22.In a group of 38 children, 16 sing Hindi songs, 25 sing English songs and 7 sing both. How many sing at least one of the two?
  23. 23.In a group of 36 children, 18 like mangoes, 28 like bananas and 12 like both. How many like exactly one of the two?
  24. 24.In a group of 40 children, 22 play cricket, 25 play football and 11 play both. How many play neither of the two?
  25. 25.In a group of 39 children, 16 sing Hindi songs, 17 sing English songs and 7 sing both. How many sing exactly one of the two?
  26. 26.In a group of 39 children, 21 enjoy drawing, 16 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  27. 27.In a group of 24 children, 8 like mangoes, 9 like bananas and 3 like both. How many like only mangoes?
  28. 28.In a group of 36 children, 14 play cricket, 24 play football and 9 play both. How many play only football?
  29. 29.In a group of 26 children, 10 like mangoes, 14 like bananas and 3 like both. How many like only bananas?
  30. 30.In a group of 51 children, 17 sing Hindi songs, 30 sing English songs and 11 sing both. How many sing only English songs?
  31. 31.In a group of 43 children, 27 play chess, 22 play carrom and 7 play both. How many play only carrom?
  32. 32.In a group of 31 children, 17 like mangoes, 13 like bananas and 10 like both. How many like exactly one of the two?
  33. 33.In a group of 37 children, 15 like mangoes, 12 like bananas and 4 like both. How many like only bananas?
  34. 34.In a group of 25 children, 7 like mangoes, 9 like bananas and 2 like both. How many like exactly one of the two?
  35. 35.In a group of 35 children, 10 enjoy drawing, 18 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  36. 36.In a group of 27 children, 12 sing Hindi songs, 6 sing English songs and 2 sing both. How many sing only English songs?
  37. 37.In a group of 42 grown-ups, 16 drink tea, 21 drink coffee and 3 drink both. How many drink at least one of the two?
  38. 38.In a group of 38 children, 12 sing Hindi songs, 24 sing English songs and 8 sing both. How many sing only Hindi songs?
  39. 39.In a group of 37 children, 16 play cricket, 13 play football and 5 play both. How many play at least one of the two?
  40. 40.In a group of 22 grown-ups, 10 drink tea, 12 drink coffee and 7 drink both. How many drink only coffee?

Answer key

  1. 4
  2. 21
  3. 6
  4. 9
  5. 40
  6. 22
  7. 11
  8. 41
  9. 42
  10. 45
  11. 20
  12. 5
  13. 36
  14. 33
  15. 19
  16. 3
  17. 7
  18. 13
  19. 20
  20. 25
  21. 7
  22. 34
  23. 22
  24. 4
  25. 19
  26. 21
  27. 5
  28. 15
  29. 11
  30. 19
  31. 15
  32. 10
  33. 8
  34. 12
  35. 7
  36. 4
  37. 34
  38. 4
  39. 24
  40. 5

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