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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 307 · 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, 10 like mangoes, 15 like bananas and 7 like both. How many like at least one of the two?
  2. 2.In a group of 25 children, 6 sing Hindi songs, 14 sing English songs and 3 sing both. How many sing at least one of the two?
  3. 3.In a group of 26 children, 19 like mangoes, 11 like bananas and 5 like both. How many like at least one of the two?
  4. 4.In a group of 29 children, 14 play cricket, 14 play football and 9 play both. How many play only football?
  5. 5.In a group of 53 children, 18 sing Hindi songs, 23 sing English songs and 3 sing both. How many sing at least one of the two?
  6. 6.In a group of 31 children, 19 play chess, 9 play carrom and 4 play both. How many play only carrom?
  7. 7.In a group of 53 children, 31 play chess, 26 play carrom and 12 play both. How many play only carrom?
  8. 8.In a group of 43 children, 25 like mangoes, 9 like bananas and 6 like both. How many like at least one of the two?
  9. 9.In a group of 55 children, 23 like mangoes, 29 like bananas and 10 like both. How many like neither of the two?
  10. 10.In a group of 36 children, 18 play cricket, 16 play football and 3 play both. How many play neither of the two?
  11. 11.In a group of 57 children, 24 play chess, 24 play carrom and 5 play both. How many play at least one of the two?
  12. 12.In a group of 37 children, 19 play chess, 7 play carrom and 2 play both. How many play only chess?
  13. 13.In a group of 40 children, 21 play cricket, 26 play football and 11 play both. How many play exactly one of the two?
  14. 14.In a group of 42 children, 20 play cricket, 22 play football and 3 play both. How many play neither of the two?
  15. 15.In a group of 20 children, 10 like mangoes, 12 like bananas and 3 like both. How many like only mangoes?
  16. 16.In a group of 17 children, 8 play cricket, 11 play football and 3 play both. How many play only football?
  17. 17.In a group of 28 children, 5 enjoy drawing, 20 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  18. 18.In a group of 26 grown-ups, 11 drink tea, 19 drink coffee and 5 drink both. How many drink neither of the two?
  19. 19.In a group of 42 children, 21 play cricket, 18 play football and 3 play both. How many play exactly one of the two?
  20. 20.In a group of 44 children, 21 sing Hindi songs, 18 sing English songs and 4 sing both. How many sing neither of the two?
  21. 21.In a group of 27 children, 10 enjoy drawing, 19 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  22. 22.In a group of 39 children, 19 play chess, 21 play carrom and 9 play both. How many play at least one of the two?
  23. 23.In a group of 36 grown-ups, 17 drink tea, 17 drink coffee and 3 drink both. How many drink exactly one of the two?
  24. 24.In a group of 46 children, 21 play cricket, 31 play football and 12 play both. How many play only cricket?
  25. 25.In a group of 39 children, 20 enjoy drawing, 14 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  26. 26.In a group of 51 grown-ups, 31 drink tea, 17 drink coffee and 11 drink both. How many drink at least one of the two?
  27. 27.In a group of 44 children, 26 enjoy drawing, 11 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  28. 28.In a group of 43 children, 20 enjoy drawing, 19 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  29. 29.In a group of 49 grown-ups, 25 drink tea, 26 drink coffee and 8 drink both. How many drink exactly one of the two?
  30. 30.In a group of 30 children, 17 play cricket, 15 play football and 11 play both. How many play at least one of the two?
  31. 31.In a group of 25 children, 20 enjoy drawing, 5 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  32. 32.In a group of 34 children, 18 like mangoes, 19 like bananas and 6 like both. How many like only mangoes?
  33. 33.In a group of 47 children, 13 like mangoes, 23 like bananas and 4 like both. How many like neither of the two?
  34. 34.In a group of 30 children, 13 play cricket, 15 play football and 8 play both. How many play exactly one of the two?
  35. 35.In a group of 50 children, 25 sing Hindi songs, 22 sing English songs and 11 sing both. How many sing only English songs?
  36. 36.In a group of 39 children, 20 play chess, 17 play carrom and 3 play both. How many play only chess?
  37. 37.In a group of 33 children, 20 enjoy drawing, 16 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  38. 38.In a group of 19 grown-ups, 5 drink tea, 9 drink coffee and 2 drink both. How many drink only tea?
  39. 39.In a group of 31 children, 13 play cricket, 18 play football and 4 play both. How many play only cricket?
  40. 40.In a group of 29 children, 14 play chess, 12 play carrom and 5 play both. How many play exactly one of the two?

Answer key

  1. 18
  2. 17
  3. 25
  4. 5
  5. 38
  6. 5
  7. 14
  8. 28
  9. 13
  10. 5
  11. 43
  12. 17
  13. 25
  14. 3
  15. 7
  16. 8
  17. 23
  18. 1
  19. 33
  20. 9
  21. 1
  22. 31
  23. 28
  24. 9
  25. 6
  26. 37
  27. 18
  28. 8
  29. 35
  30. 21
  31. 23
  32. 12
  33. 15
  34. 12
  35. 11
  36. 17
  37. 13
  38. 3
  39. 9
  40. 16

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