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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 516 · 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 49 children, 27 play chess, 26 play carrom and 12 play both. How many play only chess?
  2. 2.In a group of 30 children, 10 sing Hindi songs, 21 sing English songs and 7 sing both. How many sing only English songs?
  3. 3.In a group of 34 children, 19 play chess, 14 play carrom and 4 play both. How many play neither of the two?
  4. 4.In a group of 32 children, 22 play cricket, 19 play football and 10 play both. How many play exactly one of the two?
  5. 5.In a group of 64 children, 31 play chess, 31 play carrom and 12 play both. How many play neither of the two?
  6. 6.In a group of 44 children, 19 play chess, 22 play carrom and 3 play both. How many play neither of the two?
  7. 7.In a group of 20 grown-ups, 11 drink tea, 12 drink coffee and 6 drink both. How many drink at least one of the two?
  8. 8.In a group of 26 grown-ups, 16 drink tea, 12 drink coffee and 3 drink both. How many drink at least one of the two?
  9. 9.In a group of 33 children, 14 enjoy drawing, 23 enjoy dancing and 10 enjoy both. How many enjoy only dancing?
  10. 10.In a group of 37 children, 20 sing Hindi songs, 18 sing English songs and 8 sing both. How many sing neither of the two?
  11. 11.In a group of 37 children, 22 sing Hindi songs, 11 sing English songs and 6 sing both. How many sing neither of the two?
  12. 12.In a group of 36 children, 26 play cricket, 12 play football and 9 play both. How many play at least one of the two?
  13. 13.In a group of 23 children, 6 like mangoes, 6 like bananas and 2 like both. How many like at least one of the two?
  14. 14.In a group of 37 grown-ups, 19 drink tea, 16 drink coffee and 10 drink both. How many drink neither of the two?
  15. 15.In a group of 28 children, 13 enjoy drawing, 22 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  16. 16.In a group of 46 children, 23 sing Hindi songs, 14 sing English songs and 4 sing both. How many sing only Hindi songs?
  17. 17.In a group of 35 grown-ups, 15 drink tea, 10 drink coffee and 4 drink both. How many drink only tea?
  18. 18.In a group of 37 children, 14 play cricket, 15 play football and 3 play both. How many play at least one of the two?
  19. 19.In a group of 35 children, 20 play cricket, 13 play football and 8 play both. How many play only football?
  20. 20.In a group of 53 grown-ups, 26 drink tea, 26 drink coffee and 6 drink both. How many drink only tea?
  21. 21.In a group of 29 children, 9 enjoy drawing, 16 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  22. 22.In a group of 41 children, 23 play cricket, 16 play football and 6 play both. How many play neither of the two?
  23. 23.In a group of 48 children, 22 sing Hindi songs, 15 sing English songs and 3 sing both. How many sing neither of the two?
  24. 24.In a group of 38 children, 20 like mangoes, 12 like bananas and 8 like both. How many like only mangoes?
  25. 25.In a group of 43 children, 27 like mangoes, 18 like bananas and 12 like both. How many like at least one of the two?
  26. 26.In a group of 54 children, 29 play cricket, 26 play football and 9 play both. How many play only football?
  27. 27.In a group of 41 children, 10 enjoy drawing, 22 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  28. 28.In a group of 38 children, 19 sing Hindi songs, 24 sing English songs and 6 sing both. How many sing neither of the two?
  29. 29.In a group of 44 children, 28 sing Hindi songs, 20 sing English songs and 11 sing both. How many sing only English songs?
  30. 30.In a group of 22 children, 16 sing Hindi songs, 15 sing English songs and 12 sing both. How many sing exactly one of the two?
  31. 31.In a group of 22 children, 14 play chess, 9 play carrom and 2 play both. How many play only carrom?
  32. 32.In a group of 41 children, 19 play cricket, 30 play football and 11 play both. How many play only football?
  33. 33.In a group of 55 children, 23 like mangoes, 29 like bananas and 9 like both. How many like neither of the two?
  34. 34.In a group of 51 children, 23 sing Hindi songs, 21 sing English songs and 3 sing both. How many sing exactly one of the two?
  35. 35.In a group of 48 children, 15 play chess, 22 play carrom and 2 play both. How many play exactly one of the two?
  36. 36.In a group of 26 children, 20 sing Hindi songs, 8 sing English songs and 3 sing both. How many sing neither of the two?
  37. 37.In a group of 48 children, 17 play chess, 29 play carrom and 12 play both. How many play exactly one of the two?
  38. 38.In a group of 27 grown-ups, 18 drink tea, 11 drink coffee and 8 drink both. How many drink only tea?
  39. 39.In a group of 43 children, 20 sing Hindi songs, 14 sing English songs and 3 sing both. How many sing at least one of the two?
  40. 40.In a group of 45 children, 24 play chess, 28 play carrom and 10 play both. How many play neither of the two?

Answer key

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

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