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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 6 · 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 42 children, 15 like mangoes, 32 like bananas and 12 like both. How many like neither of the two?
  2. 2.In a group of 36 children, 18 play cricket, 17 play football and 4 play both. How many play at least one of the two?
  3. 3.In a group of 44 children, 25 play cricket, 28 play football and 10 play both. How many play only cricket?
  4. 4.In a group of 38 children, 25 like mangoes, 17 like bananas and 8 like both. How many like only bananas?
  5. 5.In a group of 44 children, 27 play cricket, 15 play football and 9 play both. How many play neither of the two?
  6. 6.In a group of 20 children, 11 sing Hindi songs, 13 sing English songs and 8 sing both. How many sing exactly one of the two?
  7. 7.In a group of 40 children, 11 like mangoes, 25 like bananas and 5 like both. How many like only mangoes?
  8. 8.In a group of 24 children, 6 sing Hindi songs, 13 sing English songs and 2 sing both. How many sing only English songs?
  9. 9.In a group of 29 children, 19 sing Hindi songs, 17 sing English songs and 9 sing both. How many sing at least one of the two?
  10. 10.In a group of 30 children, 5 play cricket, 21 play football and 2 play both. How many play neither of the two?
  11. 11.In a group of 25 children, 16 play cricket, 13 play football and 9 play both. How many play at least one of the two?
  12. 12.In a group of 38 grown-ups, 22 drink tea, 26 drink coffee and 11 drink both. How many drink neither of the two?
  13. 13.In a group of 38 children, 21 sing Hindi songs, 19 sing English songs and 7 sing both. How many sing neither of the two?
  14. 14.In a group of 35 grown-ups, 27 drink tea, 13 drink coffee and 10 drink both. How many drink neither of the two?
  15. 15.In a group of 29 children, 21 play chess, 12 play carrom and 6 play both. How many play at least one of the two?
  16. 16.In a group of 27 children, 10 like mangoes, 10 like bananas and 3 like both. How many like only mangoes?
  17. 17.In a group of 23 children, 8 play chess, 13 play carrom and 5 play both. How many play at least one of the two?
  18. 18.In a group of 48 children, 18 like mangoes, 31 like bananas and 11 like both. How many like at least one of the two?
  19. 19.In a group of 37 children, 18 sing Hindi songs, 23 sing English songs and 12 sing both. How many sing at least one of the two?
  20. 20.In a group of 48 children, 26 play chess, 20 play carrom and 10 play both. How many play at least one of the two?
  21. 21.In a group of 32 children, 15 sing Hindi songs, 16 sing English songs and 7 sing both. How many sing at least one of the two?
  22. 22.In a group of 27 children, 18 play chess, 12 play carrom and 6 play both. How many play only chess?
  23. 23.In a group of 37 children, 19 sing Hindi songs, 17 sing English songs and 3 sing both. How many sing at least one of the two?
  24. 24.In a group of 24 grown-ups, 13 drink tea, 8 drink coffee and 3 drink both. How many drink only tea?
  25. 25.In a group of 29 children, 18 play chess, 12 play carrom and 5 play both. How many play only carrom?
  26. 26.In a group of 39 grown-ups, 20 drink tea, 19 drink coffee and 6 drink both. How many drink at least one of the two?
  27. 27.In a group of 42 children, 21 enjoy drawing, 21 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  28. 28.In a group of 41 children, 20 play chess, 20 play carrom and 3 play both. How many play neither of the two?
  29. 29.In a group of 43 children, 10 sing Hindi songs, 23 sing English songs and 3 sing both. How many sing only Hindi songs?
  30. 30.In a group of 37 children, 20 play chess, 22 play carrom and 11 play both. How many play at least one of the two?
  31. 31.In a group of 50 children, 29 play chess, 20 play carrom and 9 play both. How many play exactly one of the two?
  32. 32.In a group of 23 children, 13 play cricket, 11 play football and 8 play both. How many play exactly one of the two?
  33. 33.In a group of 25 children, 13 play cricket, 9 play football and 3 play both. How many play exactly one of the two?
  34. 34.In a group of 30 children, 13 sing Hindi songs, 13 sing English songs and 10 sing both. How many sing neither of the two?
  35. 35.In a group of 39 children, 25 play chess, 9 play carrom and 6 play both. How many play neither of the two?
  36. 36.In a group of 9 children, 5 play cricket, 5 play football and 2 play both. How many play only football?
  37. 37.In a group of 16 children, 5 play cricket, 12 play football and 2 play both. How many play only football?
  38. 38.In a group of 45 children, 24 play cricket, 21 play football and 10 play both. How many play only football?
  39. 39.In a group of 30 grown-ups, 14 drink tea, 18 drink coffee and 7 drink both. How many drink at least one of the two?
  40. 40.In a group of 36 children, 13 like mangoes, 29 like bananas and 10 like both. How many like neither of the two?

Answer key

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

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