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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 83 · 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 44 children, 26 sing Hindi songs, 12 sing English songs and 6 sing both. How many sing only Hindi songs?
  2. 2.In a group of 30 children, 26 play cricket, 15 play football and 12 play both. How many play exactly one of the two?
  3. 3.In a group of 45 children, 19 play cricket, 25 play football and 9 play both. How many play exactly one of the two?
  4. 4.In a group of 47 children, 23 sing Hindi songs, 26 sing English songs and 6 sing both. How many sing only English songs?
  5. 5.In a group of 34 children, 19 play cricket, 13 play football and 9 play both. How many play neither of the two?
  6. 6.In a group of 42 children, 18 sing Hindi songs, 22 sing English songs and 6 sing both. How many sing exactly one of the two?
  7. 7.In a group of 45 children, 28 enjoy drawing, 15 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  8. 8.In a group of 40 children, 21 enjoy drawing, 23 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  9. 9.In a group of 34 children, 15 like mangoes, 16 like bananas and 10 like both. How many like only mangoes?
  10. 10.In a group of 40 children, 15 play cricket, 28 play football and 10 play both. How many play at least one of the two?
  11. 11.In a group of 40 children, 13 play cricket, 23 play football and 4 play both. How many play only football?
  12. 12.In a group of 41 children, 15 play cricket, 18 play football and 2 play both. How many play at least one of the two?
  13. 13.In a group of 21 children, 13 like mangoes, 10 like bananas and 7 like both. How many like neither of the two?
  14. 14.In a group of 42 grown-ups, 21 drink tea, 14 drink coffee and 2 drink both. How many drink only tea?
  15. 15.In a group of 26 children, 6 play cricket, 20 play football and 3 play both. How many play neither of the two?
  16. 16.In a group of 40 children, 23 enjoy drawing, 23 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  17. 17.In a group of 37 children, 13 sing Hindi songs, 16 sing English songs and 7 sing both. How many sing only English songs?
  18. 18.In a group of 15 children, 8 like mangoes, 8 like bananas and 2 like both. How many like neither of the two?
  19. 19.In a group of 43 children, 24 like mangoes, 24 like bananas and 7 like both. How many like only bananas?
  20. 20.In a group of 53 grown-ups, 20 drink tea, 20 drink coffee and 2 drink both. How many drink only tea?
  21. 21.In a group of 37 children, 23 sing Hindi songs, 14 sing English songs and 5 sing both. How many sing only Hindi songs?
  22. 22.In a group of 34 children, 16 play cricket, 16 play football and 12 play both. How many play at least one of the two?
  23. 23.In a group of 27 children, 16 enjoy drawing, 17 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  24. 24.In a group of 36 children, 15 sing Hindi songs, 29 sing English songs and 11 sing both. How many sing exactly one of the two?
  25. 25.In a group of 34 children, 6 like mangoes, 20 like bananas and 3 like both. How many like exactly one of the two?
  26. 26.In a group of 31 children, 15 enjoy drawing, 17 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  27. 27.In a group of 36 children, 19 play cricket, 18 play football and 6 play both. How many play at least one of the two?
  28. 28.In a group of 42 children, 13 play cricket, 19 play football and 3 play both. How many play neither of the two?
  29. 29.In a group of 49 children, 21 like mangoes, 22 like bananas and 2 like both. How many like exactly one of the two?
  30. 30.In a group of 49 children, 22 play cricket, 19 play football and 3 play both. How many play exactly one of the two?
  31. 31.In a group of 37 children, 18 like mangoes, 28 like bananas and 12 like both. How many like only mangoes?
  32. 32.In a group of 52 children, 23 play chess, 18 play carrom and 4 play both. How many play at least one of the two?
  33. 33.In a group of 22 children, 13 enjoy drawing, 17 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  34. 34.In a group of 37 children, 19 like mangoes, 16 like bananas and 12 like both. How many like only mangoes?
  35. 35.In a group of 26 children, 17 play chess, 11 play carrom and 6 play both. How many play at least one of the two?
  36. 36.In a group of 24 children, 18 enjoy drawing, 5 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  37. 37.In a group of 45 children, 15 play cricket, 18 play football and 2 play both. How many play exactly one of the two?
  38. 38.In a group of 43 children, 26 play chess, 12 play carrom and 8 play both. How many play at least one of the two?
  39. 39.In a group of 46 grown-ups, 31 drink tea, 25 drink coffee and 11 drink both. How many drink only coffee?
  40. 40.In a group of 21 children, 15 enjoy drawing, 5 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?

Answer key

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

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