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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 366 · 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, 26 sing Hindi songs, 19 sing English songs and 10 sing both. How many sing neither of the two?
  2. 2.In a group of 20 children, 15 like mangoes, 13 like bananas and 9 like both. How many like only mangoes?
  3. 3.In a group of 39 children, 20 like mangoes, 18 like bananas and 2 like both. How many like only bananas?
  4. 4.In a group of 38 children, 20 sing Hindi songs, 17 sing English songs and 3 sing both. How many sing at least one of the two?
  5. 5.In a group of 51 children, 27 like mangoes, 24 like bananas and 10 like both. How many like at least one of the two?
  6. 6.In a group of 26 children, 11 play chess, 9 play carrom and 6 play both. How many play only carrom?
  7. 7.In a group of 38 children, 21 like mangoes, 23 like bananas and 9 like both. How many like at least one of the two?
  8. 8.In a group of 39 children, 22 play chess, 22 play carrom and 11 play both. How many play exactly one of the two?
  9. 9.In a group of 25 children, 14 play cricket, 12 play football and 2 play both. How many play only cricket?
  10. 10.In a group of 29 children, 16 play chess, 18 play carrom and 10 play both. How many play exactly one of the two?
  11. 11.In a group of 17 grown-ups, 11 drink tea, 10 drink coffee and 5 drink both. How many drink only tea?
  12. 12.In a group of 41 children, 25 play cricket, 21 play football and 8 play both. How many play exactly one of the two?
  13. 13.In a group of 48 children, 25 play cricket, 28 play football and 8 play both. How many play only cricket?
  14. 14.In a group of 25 children, 13 enjoy drawing, 18 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  15. 15.In a group of 55 children, 24 play chess, 28 play carrom and 11 play both. How many play exactly one of the two?
  16. 16.In a group of 46 children, 25 sing Hindi songs, 28 sing English songs and 11 sing both. How many sing only Hindi songs?
  17. 17.In a group of 41 children, 8 sing Hindi songs, 21 sing English songs and 3 sing both. How many sing only English songs?
  18. 18.In a group of 19 grown-ups, 11 drink tea, 11 drink coffee and 8 drink both. How many drink only coffee?
  19. 19.In a group of 37 children, 18 enjoy drawing, 15 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  20. 20.In a group of 39 children, 22 enjoy drawing, 13 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  21. 21.In a group of 39 children, 18 play cricket, 25 play football and 5 play both. How many play neither of the two?
  22. 22.In a group of 46 grown-ups, 19 drink tea, 25 drink coffee and 10 drink both. How many drink neither of the two?
  23. 23.In a group of 36 children, 16 like mangoes, 8 like bananas and 2 like both. How many like at least one of the two?
  24. 24.In a group of 46 children, 24 sing Hindi songs, 14 sing English songs and 4 sing both. How many sing at least one of the two?
  25. 25.In a group of 32 children, 20 sing Hindi songs, 15 sing English songs and 4 sing both. How many sing only English songs?
  26. 26.In a group of 59 children, 28 sing Hindi songs, 25 sing English songs and 8 sing both. How many sing only English songs?
  27. 27.In a group of 37 children, 18 sing Hindi songs, 16 sing English songs and 10 sing both. How many sing only English songs?
  28. 28.In a group of 41 children, 16 play chess, 16 play carrom and 3 play both. How many play neither of the two?
  29. 29.In a group of 18 children, 11 like mangoes, 8 like bananas and 2 like both. How many like exactly one of the two?
  30. 30.In a group of 14 children, 9 play cricket, 7 play football and 4 play both. How many play neither of the two?
  31. 31.In a group of 50 children, 30 play cricket, 20 play football and 10 play both. How many play exactly one of the two?
  32. 32.In a group of 25 children, 6 play chess, 8 play carrom and 2 play both. How many play exactly one of the two?
  33. 33.In a group of 21 children, 17 enjoy drawing, 13 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  34. 34.In a group of 42 children, 20 play cricket, 12 play football and 4 play both. How many play at least one of the two?
  35. 35.In a group of 52 grown-ups, 24 drink tea, 25 drink coffee and 10 drink both. How many drink neither of the two?
  36. 36.In a group of 36 children, 8 play cricket, 24 play football and 4 play both. How many play neither of the two?
  37. 37.In a group of 31 children, 10 enjoy drawing, 17 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  38. 38.In a group of 36 children, 13 sing Hindi songs, 18 sing English songs and 7 sing both. How many sing exactly one of the two?
  39. 39.In a group of 47 children, 18 enjoy drawing, 19 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  40. 40.In a group of 49 children, 19 like mangoes, 25 like bananas and 9 like both. How many like only bananas?

Answer key

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

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