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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 148 · 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 45 children, 21 like mangoes, 18 like bananas and 4 like both. How many like exactly one of the two?
  2. 2.In a group of 33 grown-ups, 13 drink tea, 19 drink coffee and 3 drink both. How many drink only coffee?
  3. 3.In a group of 53 grown-ups, 24 drink tea, 20 drink coffee and 6 drink both. How many drink exactly one of the two?
  4. 4.In a group of 21 children, 11 play chess, 14 play carrom and 8 play both. How many play only chess?
  5. 5.In a group of 28 children, 12 enjoy drawing, 23 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  6. 6.In a group of 41 children, 15 play chess, 19 play carrom and 7 play both. How many play neither of the two?
  7. 7.In a group of 46 children, 32 enjoy drawing, 16 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  8. 8.In a group of 43 grown-ups, 24 drink tea, 21 drink coffee and 8 drink both. How many drink exactly one of the two?
  9. 9.In a group of 57 children, 22 like mangoes, 23 like bananas and 3 like both. How many like neither of the two?
  10. 10.In a group of 31 children, 15 enjoy drawing, 21 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  11. 11.In a group of 38 children, 16 play cricket, 22 play football and 4 play both. How many play only football?
  12. 12.In a group of 39 children, 20 play chess, 19 play carrom and 3 play both. How many play only carrom?
  13. 13.In a group of 34 children, 17 sing Hindi songs, 22 sing English songs and 12 sing both. How many sing only English songs?
  14. 14.In a group of 45 children, 19 enjoy drawing, 26 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  15. 15.In a group of 23 children, 12 play cricket, 13 play football and 3 play both. How many play exactly one of the two?
  16. 16.In a group of 41 children, 14 sing Hindi songs, 25 sing English songs and 11 sing both. How many sing exactly one of the two?
  17. 17.In a group of 34 children, 19 like mangoes, 23 like bananas and 10 like both. How many like neither of the two?
  18. 18.In a group of 29 children, 16 play cricket, 14 play football and 11 play both. How many play neither of the two?
  19. 19.In a group of 56 children, 32 sing Hindi songs, 29 sing English songs and 12 sing both. How many sing at least one of the two?
  20. 20.In a group of 31 children, 22 like mangoes, 17 like bananas and 9 like both. How many like neither of the two?
  21. 21.In a group of 44 children, 18 like mangoes, 23 like bananas and 4 like both. How many like exactly one of the two?
  22. 22.In a group of 47 children, 22 play chess, 20 play carrom and 2 play both. How many play only chess?
  23. 23.In a group of 42 children, 18 like mangoes, 26 like bananas and 8 like both. How many like only bananas?
  24. 24.In a group of 25 children, 20 like mangoes, 9 like bananas and 6 like both. How many like at least one of the two?
  25. 25.In a group of 30 children, 22 like mangoes, 12 like bananas and 5 like both. How many like only bananas?
  26. 26.In a group of 23 children, 8 play cricket, 11 play football and 4 play both. How many play only football?
  27. 27.In a group of 43 children, 20 sing Hindi songs, 16 sing English songs and 6 sing both. How many sing neither of the two?
  28. 28.In a group of 31 children, 13 sing Hindi songs, 12 sing English songs and 3 sing both. How many sing at least one of the two?
  29. 29.In a group of 27 children, 15 enjoy drawing, 11 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  30. 30.In a group of 41 children, 9 play chess, 24 play carrom and 5 play both. How many play neither of the two?
  31. 31.In a group of 28 children, 10 sing Hindi songs, 17 sing English songs and 5 sing both. How many sing at least one of the two?
  32. 32.In a group of 31 children, 12 play cricket, 9 play football and 2 play both. How many play only football?
  33. 33.In a group of 37 children, 23 like mangoes, 20 like bananas and 11 like both. How many like only bananas?
  34. 34.In a group of 56 children, 27 sing Hindi songs, 26 sing English songs and 10 sing both. How many sing only English songs?
  35. 35.In a group of 29 children, 13 like mangoes, 19 like bananas and 10 like both. How many like at least one of the two?
  36. 36.In a group of 37 children, 22 play chess, 14 play carrom and 10 play both. How many play at least one of the two?
  37. 37.In a group of 39 children, 22 play chess, 21 play carrom and 6 play both. How many play neither of the two?
  38. 38.In a group of 17 children, 11 enjoy drawing, 12 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  39. 39.In a group of 26 grown-ups, 18 drink tea, 16 drink coffee and 10 drink both. How many drink only tea?
  40. 40.In a group of 44 children, 13 enjoy drawing, 20 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?

Answer key

  1. 31
  2. 16
  3. 32
  4. 3
  5. 15
  6. 14
  7. 10
  8. 29
  9. 15
  10. 14
  11. 18
  12. 16
  13. 10
  14. 7
  15. 19
  16. 17
  17. 2
  18. 10
  19. 49
  20. 1
  21. 33
  22. 20
  23. 18
  24. 23
  25. 7
  26. 7
  27. 13
  28. 22
  29. 18
  30. 13
  31. 22
  32. 7
  33. 9
  34. 16
  35. 22
  36. 26
  37. 2
  38. 9
  39. 8
  40. 25

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