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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 475 · 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 48 children, 25 play chess, 18 play carrom and 10 play both. How many play only chess?
  2. 2.In a group of 29 children, 14 play cricket, 12 play football and 9 play both. How many play exactly one of the two?
  3. 3.In a group of 55 children, 24 sing Hindi songs, 29 sing English songs and 9 sing both. How many sing only Hindi songs?
  4. 4.In a group of 16 children, 6 play cricket, 10 play football and 3 play both. How many play at least one of the two?
  5. 5.In a group of 34 children, 17 like mangoes, 10 like bananas and 6 like both. How many like only mangoes?
  6. 6.In a group of 35 children, 18 enjoy drawing, 17 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  7. 7.In a group of 35 children, 15 like mangoes, 21 like bananas and 10 like both. How many like at least one of the two?
  8. 8.In a group of 23 grown-ups, 14 drink tea, 16 drink coffee and 9 drink both. How many drink only tea?
  9. 9.In a group of 47 grown-ups, 27 drink tea, 31 drink coffee and 12 drink both. How many drink exactly one of the two?
  10. 10.In a group of 33 children, 14 play cricket, 22 play football and 6 play both. How many play at least one of the two?
  11. 11.In a group of 28 children, 16 enjoy drawing, 16 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  12. 12.In a group of 28 children, 9 like mangoes, 18 like bananas and 6 like both. How many like only bananas?
  13. 13.In a group of 33 children, 11 play cricket, 15 play football and 4 play both. How many play only cricket?
  14. 14.In a group of 48 children, 16 sing Hindi songs, 23 sing English songs and 4 sing both. How many sing exactly one of the two?
  15. 15.In a group of 31 children, 6 enjoy drawing, 12 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  16. 16.In a group of 43 children, 11 play chess, 24 play carrom and 4 play both. How many play only carrom?
  17. 17.In a group of 40 children, 20 play cricket, 20 play football and 9 play both. How many play exactly one of the two?
  18. 18.In a group of 52 children, 28 play cricket, 26 play football and 12 play both. How many play neither of the two?
  19. 19.In a group of 43 grown-ups, 20 drink tea, 23 drink coffee and 11 drink both. How many drink only coffee?
  20. 20.In a group of 29 children, 21 play cricket, 15 play football and 9 play both. How many play only football?
  21. 21.In a group of 27 children, 21 sing Hindi songs, 10 sing English songs and 6 sing both. How many sing at least one of the two?
  22. 22.In a group of 22 children, 12 sing Hindi songs, 9 sing English songs and 2 sing both. How many sing neither of the two?
  23. 23.In a group of 30 children, 9 enjoy drawing, 11 enjoy dancing and 5 enjoy both. How many enjoy at least one of the two?
  24. 24.In a group of 28 children, 16 play chess, 19 play carrom and 11 play both. How many play only carrom?
  25. 25.In a group of 43 grown-ups, 18 drink tea, 15 drink coffee and 4 drink both. How many drink only coffee?
  26. 26.In a group of 38 children, 22 enjoy drawing, 20 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  27. 27.In a group of 38 children, 24 enjoy drawing, 9 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  28. 28.In a group of 24 children, 14 like mangoes, 13 like bananas and 10 like both. How many like only bananas?
  29. 29.In a group of 24 children, 6 sing Hindi songs, 9 sing English songs and 2 sing both. How many sing only Hindi songs?
  30. 30.In a group of 19 children, 8 play chess, 9 play carrom and 4 play both. How many play only chess?
  31. 31.In a group of 34 children, 7 play chess, 21 play carrom and 3 play both. How many play exactly one of the two?
  32. 32.In a group of 28 children, 12 play chess, 14 play carrom and 5 play both. How many play neither of the two?
  33. 33.In a group of 47 children, 22 enjoy drawing, 20 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  34. 34.In a group of 33 children, 11 play chess, 25 play carrom and 6 play both. How many play exactly one of the two?
  35. 35.In a group of 27 children, 12 play cricket, 16 play football and 3 play both. How many play only football?
  36. 36.In a group of 28 children, 16 enjoy drawing, 13 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  37. 37.In a group of 32 children, 14 sing Hindi songs, 19 sing English songs and 8 sing both. How many sing at least one of the two?
  38. 38.In a group of 33 children, 13 play chess, 27 play carrom and 10 play both. How many play neither of the two?
  39. 39.In a group of 37 children, 7 enjoy drawing, 21 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  40. 40.In a group of 44 children, 21 play cricket, 26 play football and 9 play both. How many play only cricket?

Answer key

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

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