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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 376 · 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 24 children, 11 play cricket, 8 play football and 3 play both. How many play neither of the two?
  2. 2.In a group of 54 children, 23 sing Hindi songs, 28 sing English songs and 8 sing both. How many sing neither of the two?
  3. 3.In a group of 45 children, 28 like mangoes, 15 like bananas and 8 like both. How many like exactly one of the two?
  4. 4.In a group of 45 children, 20 sing Hindi songs, 19 sing English songs and 6 sing both. How many sing only English songs?
  5. 5.In a group of 44 children, 21 enjoy drawing, 26 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  6. 6.In a group of 34 grown-ups, 15 drink tea, 27 drink coffee and 9 drink both. How many drink only coffee?
  7. 7.In a group of 45 children, 19 sing Hindi songs, 30 sing English songs and 12 sing both. How many sing neither of the two?
  8. 8.In a group of 20 children, 9 play cricket, 9 play football and 2 play both. How many play exactly one of the two?
  9. 9.In a group of 40 children, 27 play cricket, 22 play football and 10 play both. How many play at least one of the two?
  10. 10.In a group of 47 children, 25 play cricket, 26 play football and 7 play both. How many play only cricket?
  11. 11.In a group of 52 children, 26 play chess, 21 play carrom and 10 play both. How many play only chess?
  12. 12.In a group of 28 children, 12 play cricket, 16 play football and 5 play both. How many play only football?
  13. 13.In a group of 28 children, 14 play chess, 13 play carrom and 9 play both. How many play only carrom?
  14. 14.In a group of 34 children, 17 sing Hindi songs, 9 sing English songs and 3 sing both. How many sing at least one of the two?
  15. 15.In a group of 23 children, 17 play chess, 9 play carrom and 5 play both. How many play exactly one of the two?
  16. 16.In a group of 23 children, 5 play cricket, 18 play football and 2 play both. How many play neither of the two?
  17. 17.In a group of 36 children, 10 play cricket, 16 play football and 5 play both. How many play only football?
  18. 18.In a group of 33 children, 7 like mangoes, 17 like bananas and 4 like both. How many like at least one of the two?
  19. 19.In a group of 40 children, 15 enjoy drawing, 13 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  20. 20.In a group of 38 grown-ups, 9 drink tea, 20 drink coffee and 5 drink both. How many drink exactly one of the two?
  21. 21.In a group of 30 children, 15 play chess, 24 play carrom and 10 play both. How many play only chess?
  22. 22.In a group of 48 grown-ups, 19 drink tea, 19 drink coffee and 5 drink both. How many drink neither of the two?
  23. 23.In a group of 36 children, 22 like mangoes, 16 like bananas and 6 like both. How many like only bananas?
  24. 24.In a group of 22 children, 14 play cricket, 16 play football and 10 play both. How many play exactly one of the two?
  25. 25.In a group of 35 children, 21 play cricket, 10 play football and 2 play both. How many play at least one of the two?
  26. 26.In a group of 41 children, 17 enjoy drawing, 21 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  27. 27.In a group of 45 children, 12 sing Hindi songs, 21 sing English songs and 2 sing both. How many sing exactly one of the two?
  28. 28.In a group of 41 grown-ups, 18 drink tea, 29 drink coffee and 12 drink both. How many drink only coffee?
  29. 29.In a group of 33 children, 22 like mangoes, 16 like bananas and 12 like both. How many like only bananas?
  30. 30.In a group of 56 children, 28 enjoy drawing, 30 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  31. 31.In a group of 51 children, 30 play chess, 30 play carrom and 12 play both. How many play neither of the two?
  32. 32.In a group of 34 grown-ups, 22 drink tea, 11 drink coffee and 2 drink both. How many drink exactly one of the two?
  33. 33.In a group of 31 children, 13 enjoy drawing, 21 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  34. 34.In a group of 31 grown-ups, 11 drink tea, 19 drink coffee and 2 drink both. How many drink at least one of the two?
  35. 35.In a group of 32 children, 9 play cricket, 20 play football and 2 play both. How many play at least one of the two?
  36. 36.In a group of 39 children, 6 like mangoes, 22 like bananas and 3 like both. How many like exactly one of the two?
  37. 37.In a group of 35 children, 18 like mangoes, 15 like bananas and 12 like both. How many like at least one of the two?
  38. 38.In a group of 34 children, 14 enjoy drawing, 10 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  39. 39.In a group of 30 grown-ups, 15 drink tea, 22 drink coffee and 8 drink both. How many drink only coffee?
  40. 40.In a group of 40 children, 12 play cricket, 26 play football and 7 play both. How many play only cricket?

Answer key

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

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