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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 426 · 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, 16 like mangoes, 29 like bananas and 11 like both. How many like at least one of the two?
  2. 2.In a group of 32 children, 11 sing Hindi songs, 22 sing English songs and 8 sing both. How many sing at least one of the two?
  3. 3.In a group of 40 children, 27 play cricket, 18 play football and 9 play both. How many play exactly one of the two?
  4. 4.In a group of 41 children, 28 play chess, 18 play carrom and 10 play both. How many play at least one of the two?
  5. 5.In a group of 20 grown-ups, 15 drink tea, 11 drink coffee and 8 drink both. How many drink only coffee?
  6. 6.In a group of 43 children, 26 like mangoes, 25 like bananas and 9 like both. How many like exactly one of the two?
  7. 7.In a group of 61 children, 28 like mangoes, 29 like bananas and 10 like both. How many like exactly one of the two?
  8. 8.In a group of 33 children, 19 enjoy drawing, 19 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  9. 9.In a group of 30 children, 19 like mangoes, 16 like bananas and 8 like both. How many like only bananas?
  10. 10.In a group of 40 children, 32 sing Hindi songs, 16 sing English songs and 12 sing both. How many sing neither of the two?
  11. 11.In a group of 44 grown-ups, 17 drink tea, 22 drink coffee and 9 drink both. How many drink at least one of the two?
  12. 12.In a group of 48 children, 18 play cricket, 18 play football and 2 play both. How many play exactly one of the two?
  13. 13.In a group of 49 children, 16 enjoy drawing, 25 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  14. 14.In a group of 40 children, 14 play cricket, 28 play football and 10 play both. How many play only football?
  15. 15.In a group of 45 children, 28 like mangoes, 17 like bananas and 9 like both. How many like neither of the two?
  16. 16.In a group of 33 children, 22 like mangoes, 12 like bananas and 7 like both. How many like at least one of the two?
  17. 17.In a group of 42 children, 19 play chess, 23 play carrom and 5 play both. How many play exactly one of the two?
  18. 18.In a group of 25 grown-ups, 12 drink tea, 20 drink coffee and 8 drink both. How many drink exactly one of the two?
  19. 19.In a group of 47 grown-ups, 18 drink tea, 19 drink coffee and 5 drink both. How many drink at least one of the two?
  20. 20.In a group of 45 children, 22 play cricket, 21 play football and 2 play both. How many play neither of the two?
  21. 21.In a group of 40 children, 18 play chess, 24 play carrom and 11 play both. How many play neither of the two?
  22. 22.In a group of 34 children, 16 like mangoes, 16 like bananas and 5 like both. How many like neither of the two?
  23. 23.In a group of 29 children, 13 enjoy drawing, 9 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  24. 24.In a group of 25 children, 18 play cricket, 12 play football and 7 play both. How many play only cricket?
  25. 25.In a group of 47 children, 31 sing Hindi songs, 23 sing English songs and 11 sing both. How many sing at least one of the two?
  26. 26.In a group of 41 children, 20 play chess, 20 play carrom and 4 play both. How many play neither of the two?
  27. 27.In a group of 38 grown-ups, 21 drink tea, 14 drink coffee and 2 drink both. How many drink neither of the two?
  28. 28.In a group of 33 children, 16 play cricket, 26 play football and 10 play both. How many play exactly one of the two?
  29. 29.In a group of 43 children, 18 enjoy drawing, 17 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  30. 30.In a group of 26 children, 8 like mangoes, 7 like bananas and 4 like both. How many like neither of the two?
  31. 31.In a group of 37 children, 22 enjoy drawing, 16 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  32. 32.In a group of 24 children, 11 play cricket, 9 play football and 3 play both. How many play at least one of the two?
  33. 33.In a group of 32 grown-ups, 25 drink tea, 13 drink coffee and 8 drink both. How many drink exactly one of the two?
  34. 34.In a group of 31 children, 14 like mangoes, 26 like bananas and 11 like both. How many like only bananas?
  35. 35.In a group of 51 children, 22 sing Hindi songs, 21 sing English songs and 4 sing both. How many sing neither of the two?
  36. 36.In a group of 47 children, 26 play chess, 26 play carrom and 10 play both. How many play neither of the two?
  37. 37.In a group of 46 children, 22 like mangoes, 20 like bananas and 4 like both. How many like neither of the two?
  38. 38.In a group of 50 children, 26 play chess, 20 play carrom and 8 play both. How many play exactly one of the two?
  39. 39.In a group of 17 children, 6 play chess, 13 play carrom and 3 play both. How many play only chess?
  40. 40.In a group of 22 children, 11 like mangoes, 11 like bananas and 2 like both. How many like exactly one of the two?

Answer key

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

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