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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 581 · 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 26 children, 15 enjoy drawing, 16 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  2. 2.In a group of 58 children, 25 sing Hindi songs, 24 sing English songs and 5 sing both. How many sing only English songs?
  3. 3.In a group of 39 children, 26 play cricket, 16 play football and 8 play both. How many play only cricket?
  4. 4.In a group of 45 children, 23 enjoy drawing, 27 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  5. 5.In a group of 44 children, 18 play chess, 26 play carrom and 11 play both. How many play exactly one of the two?
  6. 6.In a group of 32 children, 15 play cricket, 15 play football and 12 play both. How many play only football?
  7. 7.In a group of 36 children, 17 play chess, 24 play carrom and 6 play both. How many play only chess?
  8. 8.In a group of 47 children, 21 like mangoes, 20 like bananas and 8 like both. How many like exactly one of the two?
  9. 9.In a group of 36 children, 23 play cricket, 23 play football and 11 play both. How many play neither of the two?
  10. 10.In a group of 45 children, 18 enjoy drawing, 25 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  11. 11.In a group of 27 children, 12 sing Hindi songs, 16 sing English songs and 9 sing both. How many sing only Hindi songs?
  12. 12.In a group of 43 children, 14 sing Hindi songs, 22 sing English songs and 7 sing both. How many sing only English songs?
  13. 13.In a group of 26 children, 14 sing Hindi songs, 15 sing English songs and 5 sing both. How many sing only English songs?
  14. 14.In a group of 31 grown-ups, 11 drink tea, 13 drink coffee and 4 drink both. How many drink only coffee?
  15. 15.In a group of 31 children, 16 play chess, 16 play carrom and 2 play both. How many play only chess?
  16. 16.In a group of 36 children, 10 play cricket, 25 play football and 5 play both. How many play at least one of the two?
  17. 17.In a group of 31 children, 19 like mangoes, 12 like bananas and 9 like both. How many like at least one of the two?
  18. 18.In a group of 40 children, 11 enjoy drawing, 23 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  19. 19.In a group of 41 children, 16 play cricket, 24 play football and 6 play both. How many play only football?
  20. 20.In a group of 27 children, 8 like mangoes, 14 like bananas and 2 like both. How many like only bananas?
  21. 21.In a group of 29 children, 13 play cricket, 16 play football and 7 play both. How many play only cricket?
  22. 22.In a group of 46 children, 27 play cricket, 16 play football and 10 play both. How many play only football?
  23. 23.In a group of 27 grown-ups, 15 drink tea, 13 drink coffee and 7 drink both. How many drink only coffee?
  24. 24.In a group of 55 children, 31 play cricket, 31 play football and 11 play both. How many play at least one of the two?
  25. 25.In a group of 33 children, 23 like mangoes, 16 like bananas and 9 like both. How many like only bananas?
  26. 26.In a group of 19 children, 8 sing Hindi songs, 12 sing English songs and 2 sing both. How many sing only English songs?
  27. 27.In a group of 28 children, 12 play cricket, 17 play football and 4 play both. How many play only football?
  28. 28.In a group of 20 children, 14 play chess, 6 play carrom and 3 play both. How many play only chess?
  29. 29.In a group of 33 grown-ups, 12 drink tea, 18 drink coffee and 5 drink both. How many drink exactly one of the two?
  30. 30.In a group of 33 children, 10 play cricket, 21 play football and 6 play both. How many play neither of the two?
  31. 31.In a group of 35 children, 22 like mangoes, 15 like bananas and 8 like both. How many like at least one of the two?
  32. 32.In a group of 25 children, 5 enjoy drawing, 16 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  33. 33.In a group of 50 children, 18 sing Hindi songs, 26 sing English songs and 6 sing both. How many sing exactly one of the two?
  34. 34.In a group of 39 children, 19 play cricket, 13 play football and 6 play both. How many play exactly one of the two?
  35. 35.In a group of 27 children, 16 like mangoes, 20 like bananas and 10 like both. How many like at least one of the two?
  36. 36.In a group of 27 children, 6 enjoy drawing, 16 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  37. 37.In a group of 44 children, 23 sing Hindi songs, 18 sing English songs and 6 sing both. How many sing only Hindi songs?
  38. 38.In a group of 43 children, 19 like mangoes, 13 like bananas and 2 like both. How many like exactly one of the two?
  39. 39.In a group of 47 children, 22 like mangoes, 19 like bananas and 8 like both. How many like neither of the two?
  40. 40.In a group of 43 children, 27 sing Hindi songs, 22 sing English songs and 10 sing both. How many sing only Hindi songs?

Answer key

  1. 4
  2. 19
  3. 18
  4. 26
  5. 22
  6. 3
  7. 11
  8. 25
  9. 1
  10. 21
  11. 3
  12. 15
  13. 10
  14. 9
  15. 14
  16. 30
  17. 22
  18. 14
  19. 18
  20. 12
  21. 6
  22. 6
  23. 6
  24. 51
  25. 7
  26. 10
  27. 13
  28. 11
  29. 20
  30. 8
  31. 29
  32. 17
  33. 32
  34. 20
  35. 26
  36. 18
  37. 17
  38. 28
  39. 14
  40. 17

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