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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 566 · 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 20 children, 14 play cricket, 15 play football and 10 play both. How many play at least one of the two?
  2. 2.In a group of 33 children, 22 play chess, 16 play carrom and 8 play both. How many play exactly one of the two?
  3. 3.In a group of 52 children, 27 like mangoes, 26 like bananas and 12 like both. How many like at least one of the two?
  4. 4.In a group of 31 children, 16 play chess, 13 play carrom and 3 play both. How many play only chess?
  5. 5.In a group of 45 children, 21 sing Hindi songs, 19 sing English songs and 9 sing both. How many sing exactly one of the two?
  6. 6.In a group of 37 children, 19 sing Hindi songs, 12 sing English songs and 4 sing both. How many sing neither of the two?
  7. 7.In a group of 45 children, 22 sing Hindi songs, 18 sing English songs and 2 sing both. How many sing neither of the two?
  8. 8.In a group of 36 children, 23 sing Hindi songs, 15 sing English songs and 5 sing both. How many sing exactly one of the two?
  9. 9.In a group of 26 children, 11 play cricket, 9 play football and 5 play both. How many play only football?
  10. 10.In a group of 44 children, 23 enjoy drawing, 28 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  11. 11.In a group of 56 children, 30 play chess, 21 play carrom and 10 play both. How many play neither of the two?
  12. 12.In a group of 49 children, 19 like mangoes, 23 like bananas and 3 like both. How many like at least one of the two?
  13. 13.In a group of 21 grown-ups, 12 drink tea, 15 drink coffee and 7 drink both. How many drink neither of the two?
  14. 14.In a group of 38 children, 23 play chess, 15 play carrom and 7 play both. How many play at least one of the two?
  15. 15.In a group of 39 children, 23 sing Hindi songs, 16 sing English songs and 4 sing both. How many sing at least one of the two?
  16. 16.In a group of 29 children, 14 enjoy drawing, 17 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  17. 17.In a group of 48 children, 22 sing Hindi songs, 27 sing English songs and 12 sing both. How many sing neither of the two?
  18. 18.In a group of 42 children, 23 enjoy drawing, 8 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  19. 19.In a group of 34 children, 20 like mangoes, 12 like bananas and 2 like both. How many like only mangoes?
  20. 20.In a group of 42 grown-ups, 21 drink tea, 23 drink coffee and 5 drink both. How many drink only coffee?
  21. 21.In a group of 30 children, 15 play chess, 22 play carrom and 12 play both. How many play only carrom?
  22. 22.In a group of 26 children, 19 enjoy drawing, 10 enjoy dancing and 5 enjoy both. How many enjoy at least one of the two?
  23. 23.In a group of 34 children, 12 like mangoes, 21 like bananas and 9 like both. How many like only mangoes?
  24. 24.In a group of 39 children, 13 sing Hindi songs, 17 sing English songs and 2 sing both. How many sing only English songs?
  25. 25.In a group of 32 children, 15 play chess, 16 play carrom and 4 play both. How many play only chess?
  26. 26.In a group of 54 children, 31 like mangoes, 28 like bananas and 12 like both. How many like only bananas?
  27. 27.In a group of 37 children, 21 play cricket, 21 play football and 11 play both. How many play exactly one of the two?
  28. 28.In a group of 36 children, 16 like mangoes, 28 like bananas and 11 like both. How many like only mangoes?
  29. 29.In a group of 28 children, 13 sing Hindi songs, 21 sing English songs and 8 sing both. How many sing only English songs?
  30. 30.In a group of 39 children, 21 play chess, 13 play carrom and 4 play both. How many play only carrom?
  31. 31.In a group of 28 children, 15 enjoy drawing, 19 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  32. 32.In a group of 24 children, 14 enjoy drawing, 7 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  33. 33.In a group of 56 grown-ups, 29 drink tea, 30 drink coffee and 10 drink both. How many drink at least one of the two?
  34. 34.In a group of 26 children, 9 like mangoes, 8 like bananas and 4 like both. How many like only bananas?
  35. 35.In a group of 45 grown-ups, 17 drink tea, 27 drink coffee and 11 drink both. How many drink only tea?
  36. 36.In a group of 30 children, 16 play chess, 14 play carrom and 7 play both. How many play neither of the two?
  37. 37.In a group of 30 children, 24 sing Hindi songs, 16 sing English songs and 11 sing both. How many sing at least one of the two?
  38. 38.In a group of 24 children, 16 sing Hindi songs, 12 sing English songs and 6 sing both. How many sing only Hindi songs?
  39. 39.In a group of 46 children, 27 play cricket, 20 play football and 9 play both. How many play neither of the two?
  40. 40.In a group of 47 children, 16 sing Hindi songs, 23 sing English songs and 6 sing both. How many sing only Hindi songs?

Answer key

  1. 19
  2. 22
  3. 41
  4. 13
  5. 22
  6. 10
  7. 7
  8. 28
  9. 4
  10. 33
  11. 15
  12. 39
  13. 1
  14. 31
  15. 35
  16. 6
  17. 11
  18. 19
  19. 18
  20. 18
  21. 10
  22. 24
  23. 3
  24. 15
  25. 11
  26. 16
  27. 20
  28. 5
  29. 13
  30. 9
  31. 27
  32. 6
  33. 49
  34. 4
  35. 6
  36. 7
  37. 29
  38. 10
  39. 8
  40. 10

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