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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 287 · 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, 14 sing Hindi songs, 24 sing English songs and 8 sing both. How many sing at least one of the two?
  2. 2.In a group of 48 children, 22 like mangoes, 24 like bananas and 11 like both. How many like only mangoes?
  3. 3.In a group of 43 children, 12 enjoy drawing, 22 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  4. 4.In a group of 45 children, 17 play cricket, 27 play football and 11 play both. How many play exactly one of the two?
  5. 5.In a group of 46 grown-ups, 19 drink tea, 28 drink coffee and 10 drink both. How many drink at least one of the two?
  6. 6.In a group of 20 children, 10 sing Hindi songs, 11 sing English songs and 6 sing both. How many sing only Hindi songs?
  7. 7.In a group of 36 children, 30 sing Hindi songs, 15 sing English songs and 10 sing both. How many sing at least one of the two?
  8. 8.In a group of 47 children, 22 play cricket, 26 play football and 11 play both. How many play only cricket?
  9. 9.In a group of 49 children, 29 sing Hindi songs, 18 sing English songs and 10 sing both. How many sing only Hindi songs?
  10. 10.In a group of 41 grown-ups, 16 drink tea, 16 drink coffee and 5 drink both. How many drink only tea?
  11. 11.In a group of 31 children, 17 enjoy drawing, 10 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  12. 12.In a group of 32 children, 14 like mangoes, 7 like bananas and 4 like both. How many like exactly one of the two?
  13. 13.In a group of 40 children, 18 enjoy drawing, 26 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  14. 14.In a group of 44 children, 22 enjoy drawing, 15 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  15. 15.In a group of 21 children, 15 enjoy drawing, 10 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  16. 16.In a group of 16 children, 7 sing Hindi songs, 5 sing English songs and 2 sing both. How many sing at least one of the two?
  17. 17.In a group of 34 children, 19 enjoy drawing, 10 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  18. 18.In a group of 44 children, 21 play chess, 28 play carrom and 12 play both. How many play only carrom?
  19. 19.In a group of 22 children, 11 play cricket, 5 play football and 2 play both. How many play only cricket?
  20. 20.In a group of 29 grown-ups, 22 drink tea, 12 drink coffee and 6 drink both. How many drink neither of the two?
  21. 21.In a group of 38 children, 26 enjoy drawing, 17 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  22. 22.In a group of 28 children, 18 play cricket, 11 play football and 4 play both. How many play only football?
  23. 23.In a group of 44 children, 21 enjoy drawing, 14 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  24. 24.In a group of 45 children, 25 like mangoes, 29 like bananas and 12 like both. How many like only bananas?
  25. 25.In a group of 23 children, 18 like mangoes, 9 like bananas and 5 like both. How many like only bananas?
  26. 26.In a group of 20 grown-ups, 5 drink tea, 7 drink coffee and 2 drink both. How many drink exactly one of the two?
  27. 27.In a group of 40 children, 26 enjoy drawing, 15 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  28. 28.In a group of 49 grown-ups, 25 drink tea, 21 drink coffee and 5 drink both. How many drink only coffee?
  29. 29.In a group of 37 children, 20 play chess, 12 play carrom and 3 play both. How many play only carrom?
  30. 30.In a group of 20 children, 9 enjoy drawing, 9 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  31. 31.In a group of 39 children, 15 play chess, 19 play carrom and 4 play both. How many play only chess?
  32. 32.In a group of 29 children, 12 sing Hindi songs, 14 sing English songs and 2 sing both. How many sing at least one of the two?
  33. 33.In a group of 28 grown-ups, 17 drink tea, 16 drink coffee and 11 drink both. How many drink at least one of the two?
  34. 34.In a group of 32 children, 14 play cricket, 15 play football and 3 play both. How many play at least one of the two?
  35. 35.In a group of 26 children, 7 play cricket, 7 play football and 3 play both. How many play exactly one of the two?
  36. 36.In a group of 28 grown-ups, 18 drink tea, 17 drink coffee and 8 drink both. How many drink at least one of the two?
  37. 37.In a group of 56 children, 25 like mangoes, 29 like bananas and 9 like both. How many like only bananas?
  38. 38.In a group of 25 children, 17 like mangoes, 10 like bananas and 4 like both. How many like exactly one of the two?
  39. 39.In a group of 50 grown-ups, 17 drink tea, 26 drink coffee and 8 drink both. How many drink exactly one of the two?
  40. 40.In a group of 44 children, 11 enjoy drawing, 23 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?

Answer key

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

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