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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 621 · 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 54 children, 19 enjoy drawing, 23 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  2. 2.In a group of 41 children, 25 like mangoes, 25 like bananas and 11 like both. How many like only bananas?
  3. 3.In a group of 48 children, 29 play chess, 28 play carrom and 11 play both. How many play at least one of the two?
  4. 4.In a group of 52 grown-ups, 29 drink tea, 28 drink coffee and 11 drink both. How many drink exactly one of the two?
  5. 5.In a group of 51 children, 25 sing Hindi songs, 26 sing English songs and 6 sing both. How many sing only English songs?
  6. 6.In a group of 38 children, 16 play cricket, 16 play football and 7 play both. How many play neither of the two?
  7. 7.In a group of 39 children, 22 play chess, 19 play carrom and 8 play both. How many play exactly one of the two?
  8. 8.In a group of 38 children, 13 like mangoes, 13 like bananas and 3 like both. How many like only mangoes?
  9. 9.In a group of 50 children, 23 sing Hindi songs, 26 sing English songs and 12 sing both. How many sing neither of the two?
  10. 10.In a group of 40 children, 22 sing Hindi songs, 17 sing English songs and 9 sing both. How many sing exactly one of the two?
  11. 11.In a group of 48 children, 23 sing Hindi songs, 21 sing English songs and 9 sing both. How many sing only Hindi songs?
  12. 12.In a group of 30 children, 19 like mangoes, 16 like bananas and 10 like both. How many like only mangoes?
  13. 13.In a group of 50 children, 22 like mangoes, 24 like bananas and 9 like both. How many like only mangoes?
  14. 14.In a group of 37 children, 26 play cricket, 11 play football and 8 play both. How many play only football?
  15. 15.In a group of 44 children, 11 play cricket, 21 play football and 3 play both. How many play only cricket?
  16. 16.In a group of 32 children, 16 like mangoes, 20 like bananas and 10 like both. How many like at least one of the two?
  17. 17.In a group of 36 children, 12 like mangoes, 22 like bananas and 7 like both. How many like only mangoes?
  18. 18.In a group of 33 children, 18 sing Hindi songs, 11 sing English songs and 8 sing both. How many sing at least one of the two?
  19. 19.In a group of 36 grown-ups, 27 drink tea, 18 drink coffee and 11 drink both. How many drink exactly one of the two?
  20. 20.In a group of 30 children, 10 sing Hindi songs, 8 sing English songs and 2 sing both. How many sing only English songs?
  21. 21.In a group of 20 children, 14 like mangoes, 13 like bananas and 10 like both. How many like only bananas?
  22. 22.In a group of 40 children, 31 play chess, 16 play carrom and 11 play both. How many play neither of the two?
  23. 23.In a group of 44 grown-ups, 25 drink tea, 10 drink coffee and 6 drink both. How many drink exactly one of the two?
  24. 24.In a group of 22 children, 15 play cricket, 14 play football and 9 play both. How many play only cricket?
  25. 25.In a group of 47 children, 13 like mangoes, 23 like bananas and 4 like both. How many like only mangoes?
  26. 26.In a group of 27 children, 11 play cricket, 12 play football and 4 play both. How many play only football?
  27. 27.In a group of 21 children, 6 play cricket, 9 play football and 3 play both. How many play only cricket?
  28. 28.In a group of 40 children, 22 like mangoes, 12 like bananas and 2 like both. How many like neither of the two?
  29. 29.In a group of 43 children, 11 play cricket, 20 play football and 3 play both. How many play only cricket?
  30. 30.In a group of 37 children, 20 sing Hindi songs, 23 sing English songs and 9 sing both. How many sing only English songs?
  31. 31.In a group of 15 children, 5 play cricket, 8 play football and 2 play both. How many play only football?
  32. 32.In a group of 28 grown-ups, 21 drink tea, 9 drink coffee and 3 drink both. How many drink only tea?
  33. 33.In a group of 35 children, 23 play chess, 10 play carrom and 3 play both. How many play neither of the two?
  34. 34.In a group of 39 children, 24 like mangoes, 13 like bananas and 4 like both. How many like only mangoes?
  35. 35.In a group of 24 grown-ups, 8 drink tea, 12 drink coffee and 3 drink both. How many drink neither of the two?
  36. 36.In a group of 29 grown-ups, 17 drink tea, 6 drink coffee and 2 drink both. How many drink only coffee?
  37. 37.In a group of 38 children, 28 play cricket, 15 play football and 9 play both. How many play only football?
  38. 38.In a group of 41 children, 23 play chess, 10 play carrom and 7 play both. How many play only carrom?
  39. 39.In a group of 43 children, 16 play cricket, 22 play football and 6 play both. How many play only football?
  40. 40.In a group of 43 children, 26 sing Hindi songs, 23 sing English songs and 11 sing both. How many sing at least one of the two?

Answer key

  1. 16
  2. 14
  3. 46
  4. 35
  5. 20
  6. 13
  7. 25
  8. 10
  9. 13
  10. 21
  11. 14
  12. 9
  13. 13
  14. 3
  15. 8
  16. 26
  17. 5
  18. 21
  19. 23
  20. 6
  21. 3
  22. 4
  23. 23
  24. 6
  25. 9
  26. 8
  27. 3
  28. 8
  29. 8
  30. 14
  31. 6
  32. 18
  33. 5
  34. 20
  35. 7
  36. 4
  37. 6
  38. 3
  39. 16
  40. 38

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