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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 402 · 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 32 children, 17 play cricket, 19 play football and 7 play both. How many play at least one of the two?
  2. 2.In a group of 32 children, 14 sing Hindi songs, 20 sing English songs and 10 sing both. How many sing neither of the two?
  3. 3.In a group of 18 children, 10 enjoy drawing, 12 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  4. 4.In a group of 30 children, 13 play chess, 18 play carrom and 7 play both. How many play neither of the two?
  5. 5.In a group of 41 grown-ups, 11 drink tea, 21 drink coffee and 6 drink both. How many drink exactly one of the two?
  6. 6.In a group of 49 children, 25 play cricket, 23 play football and 12 play both. How many play only football?
  7. 7.In a group of 31 children, 20 enjoy drawing, 14 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  8. 8.In a group of 49 children, 25 play cricket, 17 play football and 6 play both. How many play exactly one of the two?
  9. 9.In a group of 38 children, 12 sing Hindi songs, 15 sing English songs and 3 sing both. How many sing only English songs?
  10. 10.In a group of 37 grown-ups, 18 drink tea, 22 drink coffee and 4 drink both. How many drink neither of the two?
  11. 11.In a group of 32 children, 22 enjoy drawing, 8 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  12. 12.In a group of 39 children, 20 play cricket, 23 play football and 12 play both. How many play only cricket?
  13. 13.In a group of 41 children, 28 play cricket, 20 play football and 8 play both. How many play at least one of the two?
  14. 14.In a group of 45 children, 26 like mangoes, 20 like bananas and 10 like both. How many like neither of the two?
  15. 15.In a group of 43 children, 24 enjoy drawing, 8 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  16. 16.In a group of 34 grown-ups, 24 drink tea, 14 drink coffee and 7 drink both. How many drink neither of the two?
  17. 17.In a group of 41 children, 20 play cricket, 25 play football and 5 play both. How many play only football?
  18. 18.In a group of 43 grown-ups, 23 drink tea, 16 drink coffee and 7 drink both. How many drink at least one of the two?
  19. 19.In a group of 37 children, 15 like mangoes, 18 like bananas and 10 like both. How many like neither of the two?
  20. 20.In a group of 34 children, 17 enjoy drawing, 8 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  21. 21.In a group of 30 children, 15 sing Hindi songs, 11 sing English songs and 3 sing both. How many sing at least one of the two?
  22. 22.In a group of 32 children, 6 sing Hindi songs, 17 sing English songs and 3 sing both. How many sing only Hindi songs?
  23. 23.In a group of 41 children, 20 enjoy drawing, 29 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  24. 24.In a group of 44 children, 27 play cricket, 19 play football and 11 play both. How many play neither of the two?
  25. 25.In a group of 55 children, 24 enjoy drawing, 26 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  26. 26.In a group of 52 children, 28 sing Hindi songs, 23 sing English songs and 10 sing both. How many sing only Hindi songs?
  27. 27.In a group of 41 children, 22 enjoy drawing, 23 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  28. 28.In a group of 25 grown-ups, 10 drink tea, 14 drink coffee and 4 drink both. How many drink exactly one of the two?
  29. 29.In a group of 29 children, 14 sing Hindi songs, 16 sing English songs and 11 sing both. How many sing only English songs?
  30. 30.In a group of 52 children, 20 enjoy drawing, 31 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  31. 31.In a group of 45 children, 13 like mangoes, 23 like bananas and 5 like both. How many like only mangoes?
  32. 32.In a group of 45 children, 17 play cricket, 20 play football and 2 play both. How many play at least one of the two?
  33. 33.In a group of 35 children, 14 play cricket, 9 play football and 3 play both. How many play exactly one of the two?
  34. 34.In a group of 57 children, 29 play cricket, 32 play football and 12 play both. How many play at least one of the two?
  35. 35.In a group of 43 children, 22 sing Hindi songs, 9 sing English songs and 3 sing both. How many sing exactly one of the two?
  36. 36.In a group of 45 children, 29 enjoy drawing, 21 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  37. 37.In a group of 29 children, 13 sing Hindi songs, 7 sing English songs and 3 sing both. How many sing exactly one of the two?
  38. 38.In a group of 40 children, 14 like mangoes, 27 like bananas and 7 like both. How many like exactly one of the two?
  39. 39.In a group of 32 grown-ups, 11 drink tea, 15 drink coffee and 4 drink both. How many drink neither of the two?
  40. 40.In a group of 29 children, 19 play chess, 15 play carrom and 6 play both. How many play neither of the two?

Answer key

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

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