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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 498 · 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 33 children, 26 play chess, 11 play carrom and 8 play both. How many play at least one of the two?
  2. 2.In a group of 50 children, 28 enjoy drawing, 24 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  3. 3.In a group of 27 children, 11 enjoy drawing, 11 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  4. 4.In a group of 49 children, 16 play chess, 27 play carrom and 8 play both. How many play neither of the two?
  5. 5.In a group of 31 children, 11 sing Hindi songs, 10 sing English songs and 3 sing both. How many sing only English songs?
  6. 6.In a group of 24 grown-ups, 9 drink tea, 13 drink coffee and 2 drink both. How many drink neither of the two?
  7. 7.In a group of 35 children, 16 sing Hindi songs, 16 sing English songs and 12 sing both. How many sing only English songs?
  8. 8.In a group of 40 children, 19 like mangoes, 20 like bananas and 5 like both. How many like exactly one of the two?
  9. 9.In a group of 26 children, 15 play cricket, 13 play football and 5 play both. How many play only cricket?
  10. 10.In a group of 28 children, 19 sing Hindi songs, 11 sing English songs and 6 sing both. How many sing only English songs?
  11. 11.In a group of 24 children, 16 play cricket, 18 play football and 12 play both. How many play at least one of the two?
  12. 12.In a group of 37 children, 14 like mangoes, 23 like bananas and 9 like both. How many like exactly one of the two?
  13. 13.In a group of 34 children, 9 sing Hindi songs, 16 sing English songs and 3 sing both. How many sing only Hindi songs?
  14. 14.In a group of 47 children, 16 play cricket, 25 play football and 9 play both. How many play only cricket?
  15. 15.In a group of 26 children, 14 play cricket, 9 play football and 2 play both. How many play at least one of the two?
  16. 16.In a group of 36 children, 14 play chess, 29 play carrom and 10 play both. How many play only carrom?
  17. 17.In a group of 27 children, 11 sing Hindi songs, 9 sing English songs and 5 sing both. How many sing at least one of the two?
  18. 18.In a group of 33 children, 19 sing Hindi songs, 19 sing English songs and 12 sing both. How many sing at least one of the two?
  19. 19.In a group of 40 children, 11 enjoy drawing, 23 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  20. 20.In a group of 24 children, 15 enjoy drawing, 11 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  21. 21.In a group of 54 children, 25 like mangoes, 24 like bananas and 6 like both. How many like only bananas?
  22. 22.In a group of 23 children, 10 play cricket, 17 play football and 5 play both. How many play only football?
  23. 23.In a group of 41 grown-ups, 20 drink tea, 19 drink coffee and 5 drink both. How many drink neither of the two?
  24. 24.In a group of 48 children, 21 sing Hindi songs, 15 sing English songs and 3 sing both. How many sing neither of the two?
  25. 25.In a group of 47 children, 20 like mangoes, 21 like bananas and 2 like both. How many like only bananas?
  26. 26.In a group of 41 children, 23 like mangoes, 25 like bananas and 10 like both. How many like only mangoes?
  27. 27.In a group of 43 children, 22 enjoy drawing, 22 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  28. 28.In a group of 24 grown-ups, 20 drink tea, 9 drink coffee and 6 drink both. How many drink neither of the two?
  29. 29.In a group of 56 children, 27 enjoy drawing, 23 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  30. 30.In a group of 37 grown-ups, 10 drink tea, 23 drink coffee and 5 drink both. How many drink exactly one of the two?
  31. 31.In a group of 36 children, 12 sing Hindi songs, 26 sing English songs and 8 sing both. How many sing at least one of the two?
  32. 32.In a group of 48 children, 21 play chess, 19 play carrom and 4 play both. How many play exactly one of the two?
  33. 33.In a group of 51 children, 32 play chess, 27 play carrom and 12 play both. How many play only chess?
  34. 34.In a group of 31 children, 16 play cricket, 19 play football and 5 play both. How many play exactly one of the two?
  35. 35.In a group of 51 children, 26 enjoy drawing, 28 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  36. 36.In a group of 38 children, 14 enjoy drawing, 20 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  37. 37.In a group of 43 children, 22 enjoy drawing, 20 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  38. 38.In a group of 31 children, 16 play cricket, 20 play football and 6 play both. How many play only cricket?
  39. 39.In a group of 41 children, 19 like mangoes, 18 like bananas and 4 like both. How many like at least one of the two?
  40. 40.In a group of 24 grown-ups, 18 drink tea, 17 drink coffee and 12 drink both. How many drink only coffee?

Answer key

  1. 29
  2. 13
  3. 3
  4. 14
  5. 7
  6. 4
  7. 4
  8. 29
  9. 10
  10. 5
  11. 22
  12. 19
  13. 6
  14. 7
  15. 21
  16. 19
  17. 15
  18. 26
  19. 28
  20. 8
  21. 18
  22. 12
  23. 7
  24. 15
  25. 19
  26. 13
  27. 42
  28. 1
  29. 13
  30. 23
  31. 30
  32. 32
  33. 20
  34. 25
  35. 36
  36. 25
  37. 24
  38. 10
  39. 33
  40. 5

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