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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 474 · 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 36 children, 10 sing Hindi songs, 17 sing English songs and 3 sing both. How many sing exactly one of the two?
  2. 2.In a group of 24 children, 15 enjoy drawing, 10 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  3. 3.In a group of 55 children, 31 sing Hindi songs, 25 sing English songs and 12 sing both. How many sing only English songs?
  4. 4.In a group of 44 children, 16 play chess, 26 play carrom and 10 play both. How many play only carrom?
  5. 5.In a group of 19 children, 12 play cricket, 10 play football and 5 play both. How many play only football?
  6. 6.In a group of 40 children, 19 sing Hindi songs, 10 sing English songs and 4 sing both. How many sing at least one of the two?
  7. 7.In a group of 26 children, 9 enjoy drawing, 14 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  8. 8.In a group of 26 children, 14 play cricket, 10 play football and 3 play both. How many play neither of the two?
  9. 9.In a group of 41 children, 19 sing Hindi songs, 17 sing English songs and 6 sing both. How many sing at least one of the two?
  10. 10.In a group of 30 children, 15 like mangoes, 16 like bananas and 4 like both. How many like at least one of the two?
  11. 11.In a group of 37 children, 15 enjoy drawing, 20 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  12. 12.In a group of 32 children, 14 play cricket, 22 play football and 5 play both. How many play neither of the two?
  13. 13.In a group of 35 children, 14 like mangoes, 23 like bananas and 7 like both. How many like neither of the two?
  14. 14.In a group of 43 children, 24 enjoy drawing, 19 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  15. 15.In a group of 29 children, 17 sing Hindi songs, 12 sing English songs and 8 sing both. How many sing neither of the two?
  16. 16.In a group of 44 children, 21 play cricket, 19 play football and 7 play both. How many play at least one of the two?
  17. 17.In a group of 52 children, 22 sing Hindi songs, 30 sing English songs and 10 sing both. How many sing neither of the two?
  18. 18.In a group of 26 children, 17 play cricket, 13 play football and 10 play both. How many play at least one of the two?
  19. 19.In a group of 56 children, 29 play cricket, 30 play football and 10 play both. How many play exactly one of the two?
  20. 20.In a group of 35 children, 19 play chess, 17 play carrom and 2 play both. How many play only carrom?
  21. 21.In a group of 26 children, 13 play cricket, 13 play football and 2 play both. How many play only cricket?
  22. 22.In a group of 28 children, 12 play cricket, 11 play football and 3 play both. How many play neither of the two?
  23. 23.In a group of 19 children, 10 play cricket, 9 play football and 2 play both. How many play exactly one of the two?
  24. 24.In a group of 40 grown-ups, 16 drink tea, 23 drink coffee and 9 drink both. How many drink neither of the two?
  25. 25.In a group of 37 children, 14 play chess, 16 play carrom and 5 play both. How many play only chess?
  26. 26.In a group of 36 children, 23 enjoy drawing, 15 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  27. 27.In a group of 43 children, 19 like mangoes, 21 like bananas and 10 like both. How many like neither of the two?
  28. 28.In a group of 46 children, 12 play cricket, 25 play football and 6 play both. How many play neither of the two?
  29. 29.In a group of 44 children, 18 sing Hindi songs, 31 sing English songs and 11 sing both. How many sing at least one of the two?
  30. 30.In a group of 36 grown-ups, 23 drink tea, 14 drink coffee and 11 drink both. How many drink exactly one of the two?
  31. 31.In a group of 30 children, 21 enjoy drawing, 15 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  32. 32.In a group of 54 children, 29 like mangoes, 26 like bananas and 9 like both. How many like only mangoes?
  33. 33.In a group of 23 children, 19 sing Hindi songs, 6 sing English songs and 3 sing both. How many sing neither of the two?
  34. 34.In a group of 32 children, 16 sing Hindi songs, 12 sing English songs and 5 sing both. How many sing at least one of the two?
  35. 35.In a group of 39 children, 9 like mangoes, 22 like bananas and 2 like both. How many like only bananas?
  36. 36.In a group of 34 grown-ups, 18 drink tea, 27 drink coffee and 12 drink both. How many drink at least one of the two?
  37. 37.In a group of 35 grown-ups, 20 drink tea, 9 drink coffee and 6 drink both. How many drink only tea?
  38. 38.In a group of 44 children, 23 play chess, 19 play carrom and 12 play both. How many play neither of the two?
  39. 39.In a group of 42 children, 22 enjoy drawing, 9 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  40. 40.In a group of 39 children, 12 enjoy drawing, 26 enjoy dancing and 8 enjoy both. How many enjoy only drawing?

Answer key

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

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