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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 92 · 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 39 children, 28 sing Hindi songs, 20 sing English songs and 11 sing both. How many sing exactly one of the two?
  2. 2.In a group of 44 children, 23 enjoy drawing, 15 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  3. 3.In a group of 23 children, 12 like mangoes, 9 like bananas and 4 like both. How many like exactly one of the two?
  4. 4.In a group of 33 children, 10 enjoy drawing, 11 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  5. 5.In a group of 19 children, 7 play chess, 5 play carrom and 2 play both. How many play neither of the two?
  6. 6.In a group of 43 children, 30 enjoy drawing, 23 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  7. 7.In a group of 25 children, 10 play chess, 10 play carrom and 5 play both. How many play only chess?
  8. 8.In a group of 43 children, 13 play chess, 26 play carrom and 6 play both. How many play exactly one of the two?
  9. 9.In a group of 48 children, 30 play chess, 15 play carrom and 12 play both. How many play neither of the two?
  10. 10.In a group of 38 children, 24 enjoy drawing, 14 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  11. 11.In a group of 42 grown-ups, 27 drink tea, 24 drink coffee and 12 drink both. How many drink exactly one of the two?
  12. 12.In a group of 27 grown-ups, 17 drink tea, 15 drink coffee and 11 drink both. How many drink exactly one of the two?
  13. 13.In a group of 34 children, 21 play cricket, 13 play football and 8 play both. How many play exactly one of the two?
  14. 14.In a group of 49 children, 24 sing Hindi songs, 20 sing English songs and 7 sing both. How many sing neither of the two?
  15. 15.In a group of 28 children, 22 like mangoes, 10 like bananas and 7 like both. How many like only mangoes?
  16. 16.In a group of 34 children, 21 like mangoes, 17 like bananas and 8 like both. How many like only bananas?
  17. 17.In a group of 24 children, 10 sing Hindi songs, 15 sing English songs and 5 sing both. How many sing only English songs?
  18. 18.In a group of 47 grown-ups, 24 drink tea, 20 drink coffee and 8 drink both. How many drink only tea?
  19. 19.In a group of 32 children, 11 sing Hindi songs, 9 sing English songs and 2 sing both. How many sing only English songs?
  20. 20.In a group of 30 children, 20 like mangoes, 9 like bananas and 6 like both. How many like neither of the two?
  21. 21.In a group of 34 children, 17 play cricket, 14 play football and 2 play both. How many play at least one of the two?
  22. 22.In a group of 37 grown-ups, 9 drink tea, 17 drink coffee and 4 drink both. How many drink at least one of the two?
  23. 23.In a group of 39 children, 17 play cricket, 24 play football and 11 play both. How many play only cricket?
  24. 24.In a group of 29 children, 13 play cricket, 13 play football and 8 play both. How many play only football?
  25. 25.In a group of 45 children, 26 enjoy drawing, 25 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  26. 26.In a group of 44 children, 20 like mangoes, 24 like bananas and 9 like both. How many like at least one of the two?
  27. 27.In a group of 46 grown-ups, 24 drink tea, 21 drink coffee and 8 drink both. How many drink only tea?
  28. 28.In a group of 47 children, 25 enjoy drawing, 24 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  29. 29.In a group of 49 children, 22 play cricket, 23 play football and 11 play both. How many play only football?
  30. 30.In a group of 17 children, 10 like mangoes, 10 like bananas and 7 like both. How many like exactly one of the two?
  31. 31.In a group of 28 children, 13 enjoy drawing, 23 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  32. 32.In a group of 39 children, 18 enjoy drawing, 19 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  33. 33.In a group of 21 children, 12 like mangoes, 16 like bananas and 8 like both. How many like exactly one of the two?
  34. 34.In a group of 35 children, 6 play chess, 21 play carrom and 3 play both. How many play only carrom?
  35. 35.In a group of 43 children, 25 like mangoes, 20 like bananas and 8 like both. How many like at least one of the two?
  36. 36.In a group of 23 grown-ups, 14 drink tea, 7 drink coffee and 2 drink both. How many drink neither of the two?
  37. 37.In a group of 33 children, 12 enjoy drawing, 15 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  38. 38.In a group of 43 children, 27 play cricket, 23 play football and 8 play both. How many play neither of the two?
  39. 39.In a group of 53 children, 26 play chess, 30 play carrom and 10 play both. How many play only carrom?
  40. 40.In a group of 21 children, 11 play chess, 13 play carrom and 5 play both. How many play at least one of the two?

Answer key

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

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