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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 348 · 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 44 children, 19 like mangoes, 19 like bananas and 9 like both. How many like at least one of the two?
  2. 2.In a group of 30 children, 17 like mangoes, 15 like bananas and 7 like both. How many like at least one of the two?
  3. 3.In a group of 39 children, 30 like mangoes, 18 like bananas and 10 like both. How many like at least one of the two?
  4. 4.In a group of 39 children, 19 enjoy drawing, 18 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  5. 5.In a group of 24 children, 16 enjoy drawing, 8 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  6. 6.In a group of 24 children, 14 enjoy drawing, 15 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  7. 7.In a group of 34 grown-ups, 21 drink tea, 18 drink coffee and 10 drink both. How many drink exactly one of the two?
  8. 8.In a group of 45 children, 16 like mangoes, 23 like bananas and 4 like both. How many like only mangoes?
  9. 9.In a group of 36 children, 19 sing Hindi songs, 18 sing English songs and 12 sing both. How many sing only English songs?
  10. 10.In a group of 42 children, 26 enjoy drawing, 15 enjoy dancing and 10 enjoy both. How many enjoy only dancing?
  11. 11.In a group of 22 children, 10 like mangoes, 8 like bananas and 2 like both. How many like only bananas?
  12. 12.In a group of 41 children, 9 sing Hindi songs, 22 sing English songs and 2 sing both. How many sing at least one of the two?
  13. 13.In a group of 47 children, 26 play cricket, 18 play football and 11 play both. How many play only cricket?
  14. 14.In a group of 34 children, 26 play cricket, 15 play football and 10 play both. How many play at least one of the two?
  15. 15.In a group of 63 children, 30 sing Hindi songs, 29 sing English songs and 11 sing both. How many sing at least one of the two?
  16. 16.In a group of 33 children, 21 play cricket, 20 play football and 12 play both. How many play only cricket?
  17. 17.In a group of 32 children, 5 sing Hindi songs, 20 sing English songs and 2 sing both. How many sing only English songs?
  18. 18.In a group of 52 children, 22 sing Hindi songs, 23 sing English songs and 3 sing both. How many sing exactly one of the two?
  19. 19.In a group of 38 children, 23 enjoy drawing, 15 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  20. 20.In a group of 33 children, 27 enjoy drawing, 12 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  21. 21.In a group of 19 children, 10 play cricket, 10 play football and 3 play both. How many play neither of the two?
  22. 22.In a group of 51 children, 31 like mangoes, 29 like bananas and 11 like both. How many like at least one of the two?
  23. 23.In a group of 26 children, 14 enjoy drawing, 8 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  24. 24.In a group of 31 children, 8 like mangoes, 22 like bananas and 2 like both. How many like at least one of the two?
  25. 25.In a group of 38 children, 15 play cricket, 26 play football and 12 play both. How many play only cricket?
  26. 26.In a group of 43 children, 23 like mangoes, 31 like bananas and 12 like both. How many like neither of the two?
  27. 27.In a group of 23 children, 11 like mangoes, 12 like bananas and 2 like both. How many like neither of the two?
  28. 28.In a group of 33 children, 14 sing Hindi songs, 19 sing English songs and 8 sing both. How many sing exactly one of the two?
  29. 29.In a group of 49 children, 25 play cricket, 24 play football and 11 play both. How many play exactly one of the two?
  30. 30.In a group of 21 children, 7 play chess, 6 play carrom and 3 play both. How many play only chess?
  31. 31.In a group of 39 grown-ups, 14 drink tea, 22 drink coffee and 4 drink both. How many drink exactly one of the two?
  32. 32.In a group of 32 children, 20 sing Hindi songs, 7 sing English songs and 4 sing both. How many sing neither of the two?
  33. 33.In a group of 26 children, 21 sing Hindi songs, 12 sing English songs and 9 sing both. How many sing only English songs?
  34. 34.In a group of 34 grown-ups, 22 drink tea, 15 drink coffee and 7 drink both. How many drink neither of the two?
  35. 35.In a group of 49 children, 24 play chess, 21 play carrom and 9 play both. How many play at least one of the two?
  36. 36.In a group of 44 grown-ups, 19 drink tea, 24 drink coffee and 4 drink both. How many drink exactly one of the two?
  37. 37.In a group of 49 children, 26 like mangoes, 27 like bananas and 11 like both. How many like only bananas?
  38. 38.In a group of 32 children, 21 play cricket, 13 play football and 5 play both. How many play only football?
  39. 39.In a group of 39 children, 17 like mangoes, 25 like bananas and 10 like both. How many like only mangoes?
  40. 40.In a group of 36 children, 16 enjoy drawing, 25 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?

Answer key

  1. 29
  2. 25
  3. 38
  4. 16
  5. 4
  6. 6
  7. 19
  8. 12
  9. 6
  10. 5
  11. 6
  12. 29
  13. 15
  14. 31
  15. 48
  16. 9
  17. 18
  18. 39
  19. 30
  20. 18
  21. 2
  22. 49
  23. 3
  24. 28
  25. 3
  26. 1
  27. 2
  28. 17
  29. 27
  30. 4
  31. 28
  32. 9
  33. 3
  34. 4
  35. 36
  36. 35
  37. 16
  38. 8
  39. 7
  40. 1

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