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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 445 · 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 43 children, 20 sing Hindi songs, 16 sing English songs and 8 sing both. How many sing exactly one of the two?
  2. 2.In a group of 18 children, 11 play cricket, 6 play football and 3 play both. How many play only cricket?
  3. 3.In a group of 41 children, 23 enjoy drawing, 25 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  4. 4.In a group of 32 children, 15 sing Hindi songs, 7 sing English songs and 3 sing both. How many sing at least one of the two?
  5. 5.In a group of 34 grown-ups, 15 drink tea, 20 drink coffee and 8 drink both. How many drink only coffee?
  6. 6.In a group of 54 children, 26 enjoy drawing, 23 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  7. 7.In a group of 30 children, 16 sing Hindi songs, 22 sing English songs and 12 sing both. How many sing at least one of the two?
  8. 8.In a group of 29 children, 11 like mangoes, 13 like bananas and 3 like both. How many like only bananas?
  9. 9.In a group of 34 grown-ups, 16 drink tea, 21 drink coffee and 5 drink both. How many drink at least one of the two?
  10. 10.In a group of 50 children, 27 play cricket, 24 play football and 12 play both. How many play neither of the two?
  11. 11.In a group of 47 children, 21 enjoy drawing, 20 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  12. 12.In a group of 51 grown-ups, 25 drink tea, 23 drink coffee and 5 drink both. How many drink neither of the two?
  13. 13.In a group of 45 children, 16 enjoy drawing, 22 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  14. 14.In a group of 36 children, 21 like mangoes, 13 like bananas and 6 like both. How many like exactly one of the two?
  15. 15.In a group of 35 grown-ups, 14 drink tea, 21 drink coffee and 2 drink both. How many drink only tea?
  16. 16.In a group of 31 children, 17 like mangoes, 10 like bananas and 3 like both. How many like only mangoes?
  17. 17.In a group of 46 children, 21 like mangoes, 31 like bananas and 11 like both. How many like only bananas?
  18. 18.In a group of 22 grown-ups, 13 drink tea, 15 drink coffee and 10 drink both. How many drink neither of the two?
  19. 19.In a group of 50 children, 26 sing Hindi songs, 30 sing English songs and 12 sing both. How many sing only Hindi songs?
  20. 20.In a group of 33 children, 11 like mangoes, 20 like bananas and 2 like both. How many like at least one of the two?
  21. 21.In a group of 29 children, 8 enjoy drawing, 10 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  22. 22.In a group of 36 children, 11 enjoy drawing, 19 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  23. 23.In a group of 44 children, 18 like mangoes, 32 like bananas and 12 like both. How many like only mangoes?
  24. 24.In a group of 39 children, 20 sing Hindi songs, 11 sing English songs and 6 sing both. How many sing neither of the two?
  25. 25.In a group of 20 children, 8 play cricket, 16 play football and 5 play both. How many play exactly one of the two?
  26. 26.In a group of 41 children, 18 like mangoes, 15 like bananas and 2 like both. How many like at least one of the two?
  27. 27.In a group of 32 children, 16 like mangoes, 12 like bananas and 5 like both. How many like only bananas?
  28. 28.In a group of 44 children, 22 sing Hindi songs, 20 sing English songs and 12 sing both. How many sing only English songs?
  29. 29.In a group of 34 children, 30 sing Hindi songs, 15 sing English songs and 12 sing both. How many sing only English songs?
  30. 30.In a group of 27 grown-ups, 8 drink tea, 19 drink coffee and 5 drink both. How many drink only tea?
  31. 31.In a group of 43 children, 19 like mangoes, 26 like bananas and 9 like both. How many like at least one of the two?
  32. 32.In a group of 39 children, 11 sing Hindi songs, 18 sing English songs and 2 sing both. How many sing at least one of the two?
  33. 33.In a group of 16 children, 9 sing Hindi songs, 6 sing English songs and 3 sing both. How many sing neither of the two?
  34. 34.In a group of 37 children, 18 like mangoes, 11 like bananas and 6 like both. How many like exactly one of the two?
  35. 35.In a group of 41 children, 28 play chess, 21 play carrom and 12 play both. How many play only carrom?
  36. 36.In a group of 34 children, 20 play cricket, 12 play football and 9 play both. How many play neither of the two?
  37. 37.In a group of 23 children, 5 sing Hindi songs, 10 sing English songs and 2 sing both. How many sing only Hindi songs?
  38. 38.In a group of 33 children, 13 enjoy drawing, 18 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  39. 39.In a group of 40 children, 15 play chess, 18 play carrom and 2 play both. How many play at least one of the two?
  40. 40.In a group of 22 children, 7 like mangoes, 13 like bananas and 2 like both. How many like at least one of the two?

Answer key

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

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