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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 239 · 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 grown-ups, 23 drink tea, 19 drink coffee and 10 drink both. How many drink at least one of the two?
  2. 2.In a group of 25 children, 13 play cricket, 14 play football and 4 play both. How many play only football?
  3. 3.In a group of 35 children, 16 sing Hindi songs, 22 sing English songs and 4 sing both. How many sing neither of the two?
  4. 4.In a group of 51 children, 31 sing Hindi songs, 29 sing English songs and 11 sing both. How many sing neither of the two?
  5. 5.In a group of 46 children, 20 like mangoes, 21 like bananas and 8 like both. How many like exactly one of the two?
  6. 6.In a group of 52 children, 29 enjoy drawing, 28 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  7. 7.In a group of 44 children, 17 like mangoes, 21 like bananas and 2 like both. How many like at least one of the two?
  8. 8.In a group of 42 children, 28 like mangoes, 15 like bananas and 9 like both. How many like at least one of the two?
  9. 9.In a group of 25 children, 7 like mangoes, 9 like bananas and 3 like both. How many like only bananas?
  10. 10.In a group of 30 children, 20 play chess, 13 play carrom and 6 play both. How many play at least one of the two?
  11. 11.In a group of 44 grown-ups, 17 drink tea, 22 drink coffee and 4 drink both. How many drink only coffee?
  12. 12.In a group of 37 children, 19 play cricket, 23 play football and 9 play both. How many play only football?
  13. 13.In a group of 35 grown-ups, 17 drink tea, 15 drink coffee and 3 drink both. How many drink at least one of the two?
  14. 14.In a group of 37 children, 14 sing Hindi songs, 15 sing English songs and 3 sing both. How many sing exactly one of the two?
  15. 15.In a group of 37 children, 16 like mangoes, 16 like bananas and 2 like both. How many like neither of the two?
  16. 16.In a group of 32 children, 25 like mangoes, 13 like bananas and 9 like both. How many like neither of the two?
  17. 17.In a group of 30 children, 14 play chess, 13 play carrom and 10 play both. How many play only carrom?
  18. 18.In a group of 27 children, 15 sing Hindi songs, 16 sing English songs and 8 sing both. How many sing only Hindi songs?
  19. 19.In a group of 35 children, 16 like mangoes, 22 like bananas and 6 like both. How many like exactly one of the two?
  20. 20.In a group of 45 children, 25 enjoy drawing, 15 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  21. 21.In a group of 24 children, 19 sing Hindi songs, 13 sing English songs and 9 sing both. How many sing neither of the two?
  22. 22.In a group of 27 children, 18 play cricket, 9 play football and 6 play both. How many play only football?
  23. 23.In a group of 23 children, 17 play cricket, 6 play football and 2 play both. How many play only football?
  24. 24.In a group of 44 children, 23 enjoy drawing, 24 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  25. 25.In a group of 45 grown-ups, 20 drink tea, 29 drink coffee and 11 drink both. How many drink at least one of the two?
  26. 26.In a group of 35 children, 21 enjoy drawing, 19 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  27. 27.In a group of 33 children, 17 enjoy drawing, 17 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  28. 28.In a group of 42 children, 16 play cricket, 22 play football and 2 play both. How many play at least one of the two?
  29. 29.In a group of 48 children, 30 play cricket, 20 play football and 10 play both. How many play only cricket?
  30. 30.In a group of 32 children, 21 enjoy drawing, 13 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  31. 31.In a group of 40 grown-ups, 21 drink tea, 8 drink coffee and 2 drink both. How many drink exactly one of the two?
  32. 32.In a group of 28 grown-ups, 10 drink tea, 11 drink coffee and 4 drink both. How many drink neither of the two?
  33. 33.In a group of 34 children, 15 play cricket, 23 play football and 12 play both. How many play neither of the two?
  34. 34.In a group of 22 grown-ups, 9 drink tea, 17 drink coffee and 5 drink both. How many drink exactly one of the two?
  35. 35.In a group of 38 children, 10 enjoy drawing, 22 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  36. 36.In a group of 58 children, 27 sing Hindi songs, 25 sing English songs and 7 sing both. How many sing at least one of the two?
  37. 37.In a group of 28 children, 14 like mangoes, 14 like bananas and 3 like both. How many like only mangoes?
  38. 38.In a group of 40 children, 28 like mangoes, 11 like bananas and 8 like both. How many like only mangoes?
  39. 39.In a group of 42 children, 26 play chess, 12 play carrom and 8 play both. How many play neither of the two?
  40. 40.In a group of 48 children, 23 play cricket, 31 play football and 11 play both. How many play at least one of the two?

Answer key

  1. 32
  2. 10
  3. 1
  4. 2
  5. 25
  6. 19
  7. 36
  8. 34
  9. 6
  10. 27
  11. 18
  12. 14
  13. 29
  14. 23
  15. 7
  16. 3
  17. 3
  18. 7
  19. 26
  20. 30
  21. 1
  22. 3
  23. 4
  24. 17
  25. 38
  26. 31
  27. 8
  28. 36
  29. 20
  30. 14
  31. 25
  32. 11
  33. 8
  34. 16
  35. 24
  36. 45
  37. 11
  38. 20
  39. 12
  40. 43

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