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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 274 · 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 35 children, 15 play chess, 22 play carrom and 6 play both. How many play at least one of the two?
  2. 2.In a group of 32 grown-ups, 13 drink tea, 8 drink coffee and 2 drink both. How many drink at least one of the two?
  3. 3.In a group of 45 grown-ups, 22 drink tea, 25 drink coffee and 7 drink both. How many drink exactly one of the two?
  4. 4.In a group of 28 children, 7 play chess, 23 play carrom and 3 play both. How many play only carrom?
  5. 5.In a group of 34 children, 14 play chess, 16 play carrom and 2 play both. How many play only chess?
  6. 6.In a group of 32 children, 22 play cricket, 14 play football and 10 play both. How many play only cricket?
  7. 7.In a group of 18 children, 5 enjoy drawing, 12 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  8. 8.In a group of 31 children, 18 sing Hindi songs, 12 sing English songs and 2 sing both. How many sing neither of the two?
  9. 9.In a group of 31 children, 27 play chess, 15 play carrom and 12 play both. How many play at least one of the two?
  10. 10.In a group of 41 children, 19 play cricket, 18 play football and 8 play both. How many play only cricket?
  11. 11.In a group of 20 children, 5 like mangoes, 13 like bananas and 2 like both. How many like only bananas?
  12. 12.In a group of 46 children, 29 like mangoes, 18 like bananas and 11 like both. How many like only mangoes?
  13. 13.In a group of 41 children, 21 enjoy drawing, 22 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  14. 14.In a group of 30 children, 13 play cricket, 9 play football and 4 play both. How many play exactly one of the two?
  15. 15.In a group of 43 children, 26 enjoy drawing, 13 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  16. 16.In a group of 42 children, 9 play cricket, 20 play football and 2 play both. How many play exactly one of the two?
  17. 17.In a group of 33 children, 28 like mangoes, 14 like bananas and 10 like both. How many like only mangoes?
  18. 18.In a group of 22 grown-ups, 10 drink tea, 9 drink coffee and 6 drink both. How many drink exactly one of the two?
  19. 19.In a group of 52 grown-ups, 26 drink tea, 24 drink coffee and 7 drink both. How many drink neither of the two?
  20. 20.In a group of 55 children, 23 enjoy drawing, 28 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  21. 21.In a group of 35 children, 29 sing Hindi songs, 14 sing English songs and 10 sing both. How many sing exactly one of the two?
  22. 22.In a group of 20 children, 7 play chess, 13 play carrom and 4 play both. How many play at least one of the two?
  23. 23.In a group of 43 children, 20 play cricket, 30 play football and 10 play both. How many play at least one of the two?
  24. 24.In a group of 27 children, 10 like mangoes, 12 like bananas and 3 like both. How many like only bananas?
  25. 25.In a group of 43 children, 25 sing Hindi songs, 23 sing English songs and 12 sing both. How many sing only Hindi songs?
  26. 26.In a group of 44 children, 26 like mangoes, 21 like bananas and 12 like both. How many like neither of the two?
  27. 27.In a group of 41 children, 15 enjoy drawing, 22 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  28. 28.In a group of 37 children, 17 play cricket, 22 play football and 7 play both. How many play only cricket?
  29. 29.In a group of 36 children, 17 play cricket, 16 play football and 12 play both. How many play at least one of the two?
  30. 30.In a group of 37 children, 18 sing Hindi songs, 26 sing English songs and 12 sing both. How many sing neither of the two?
  31. 31.In a group of 31 children, 17 play cricket, 22 play football and 10 play both. How many play at least one of the two?
  32. 32.In a group of 54 children, 26 like mangoes, 21 like bananas and 6 like both. How many like at least one of the two?
  33. 33.In a group of 32 children, 21 play chess, 11 play carrom and 7 play both. How many play neither of the two?
  34. 34.In a group of 27 children, 14 enjoy drawing, 14 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  35. 35.In a group of 37 children, 14 play cricket, 17 play football and 3 play both. How many play at least one of the two?
  36. 36.In a group of 26 children, 13 sing Hindi songs, 13 sing English songs and 4 sing both. How many sing only Hindi songs?
  37. 37.In a group of 29 children, 5 play chess, 21 play carrom and 2 play both. How many play only chess?
  38. 38.In a group of 33 children, 16 play chess, 8 play carrom and 4 play both. How many play only chess?
  39. 39.In a group of 34 grown-ups, 10 drink tea, 15 drink coffee and 4 drink both. How many drink exactly one of the two?
  40. 40.In a group of 43 grown-ups, 26 drink tea, 21 drink coffee and 7 drink both. How many drink exactly one of the two?

Answer key

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

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