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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 225 · 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 54 children, 19 play cricket, 26 play football and 6 play both. How many play neither of the two?
  2. 2.In a group of 31 children, 16 play chess, 20 play carrom and 10 play both. How many play neither of the two?
  3. 3.In a group of 35 children, 14 play chess, 18 play carrom and 6 play both. How many play only chess?
  4. 4.In a group of 29 children, 12 enjoy drawing, 19 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  5. 5.In a group of 43 children, 25 sing Hindi songs, 21 sing English songs and 6 sing both. How many sing only English songs?
  6. 6.In a group of 39 children, 21 like mangoes, 7 like bananas and 2 like both. How many like only bananas?
  7. 7.In a group of 51 children, 29 play cricket, 24 play football and 12 play both. How many play exactly one of the two?
  8. 8.In a group of 50 grown-ups, 29 drink tea, 25 drink coffee and 12 drink both. How many drink neither of the two?
  9. 9.In a group of 47 children, 24 enjoy drawing, 23 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  10. 10.In a group of 35 children, 17 play chess, 8 play carrom and 2 play both. How many play exactly one of the two?
  11. 11.In a group of 35 children, 17 enjoy drawing, 19 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  12. 12.In a group of 44 children, 23 play chess, 20 play carrom and 9 play both. How many play only chess?
  13. 13.In a group of 30 children, 12 play chess, 22 play carrom and 8 play both. How many play neither of the two?
  14. 14.In a group of 45 children, 21 like mangoes, 15 like bananas and 3 like both. How many like exactly one of the two?
  15. 15.In a group of 34 children, 15 like mangoes, 13 like bananas and 5 like both. How many like only mangoes?
  16. 16.In a group of 49 children, 20 sing Hindi songs, 30 sing English songs and 12 sing both. How many sing at least one of the two?
  17. 17.In a group of 42 children, 21 play cricket, 20 play football and 8 play both. How many play only football?
  18. 18.In a group of 45 children, 26 like mangoes, 25 like bananas and 12 like both. How many like exactly one of the two?
  19. 19.In a group of 50 children, 27 enjoy drawing, 26 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  20. 20.In a group of 38 children, 19 enjoy drawing, 25 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  21. 21.In a group of 37 grown-ups, 18 drink tea, 20 drink coffee and 11 drink both. How many drink at least one of the two?
  22. 22.In a group of 32 grown-ups, 10 drink tea, 12 drink coffee and 5 drink both. How many drink only coffee?
  23. 23.In a group of 35 children, 21 sing Hindi songs, 18 sing English songs and 6 sing both. How many sing at least one of the two?
  24. 24.In a group of 41 children, 24 sing Hindi songs, 9 sing English songs and 4 sing both. How many sing neither of the two?
  25. 25.In a group of 24 children, 16 sing Hindi songs, 18 sing English songs and 12 sing both. How many sing exactly one of the two?
  26. 26.In a group of 43 children, 25 play chess, 15 play carrom and 8 play both. How many play at least one of the two?
  27. 27.In a group of 21 children, 14 sing Hindi songs, 7 sing English songs and 3 sing both. How many sing at least one of the two?
  28. 28.In a group of 27 children, 14 enjoy drawing, 8 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  29. 29.In a group of 42 children, 27 play chess, 17 play carrom and 11 play both. How many play neither of the two?
  30. 30.In a group of 44 children, 19 enjoy drawing, 25 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?
  31. 31.In a group of 52 children, 27 like mangoes, 22 like bananas and 7 like both. How many like only mangoes?
  32. 32.In a group of 30 children, 25 like mangoes, 11 like bananas and 8 like both. How many like neither of the two?
  33. 33.In a group of 28 children, 13 play cricket, 9 play football and 5 play both. How many play neither of the two?
  34. 34.In a group of 37 children, 26 like mangoes, 11 like bananas and 6 like both. How many like neither of the two?
  35. 35.In a group of 39 children, 23 like mangoes, 17 like bananas and 12 like both. How many like exactly one of the two?
  36. 36.In a group of 27 children, 14 like mangoes, 16 like bananas and 8 like both. How many like only mangoes?
  37. 37.In a group of 49 children, 22 play cricket, 26 play football and 7 play both. How many play only cricket?
  38. 38.In a group of 33 children, 10 sing Hindi songs, 24 sing English songs and 5 sing both. How many sing at least one of the two?
  39. 39.In a group of 44 children, 18 like mangoes, 22 like bananas and 6 like both. How many like only bananas?
  40. 40.In a group of 13 children, 6 play cricket, 7 play football and 3 play both. How many play only cricket?

Answer key

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

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