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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 325 · 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, 19 like mangoes, 13 like bananas and 5 like both. How many like only bananas?
  2. 2.In a group of 36 children, 20 like mangoes, 15 like bananas and 3 like both. How many like only mangoes?
  3. 3.In a group of 19 children, 11 sing Hindi songs, 9 sing English songs and 2 sing both. How many sing at least one of the two?
  4. 4.In a group of 50 children, 23 sing Hindi songs, 26 sing English songs and 9 sing both. How many sing exactly one of the two?
  5. 5.In a group of 35 children, 11 enjoy drawing, 18 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  6. 6.In a group of 43 children, 22 sing Hindi songs, 25 sing English songs and 8 sing both. How many sing only English songs?
  7. 7.In a group of 38 children, 29 enjoy drawing, 14 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  8. 8.In a group of 54 children, 24 enjoy drawing, 30 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  9. 9.In a group of 41 children, 18 enjoy drawing, 21 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  10. 10.In a group of 33 children, 11 play cricket, 12 play football and 2 play both. How many play exactly one of the two?
  11. 11.In a group of 35 children, 11 sing Hindi songs, 21 sing English songs and 4 sing both. How many sing at least one of the two?
  12. 12.In a group of 41 children, 18 sing Hindi songs, 27 sing English songs and 8 sing both. How many sing only Hindi songs?
  13. 13.In a group of 20 children, 8 like mangoes, 10 like bananas and 2 like both. How many like only mangoes?
  14. 14.In a group of 33 children, 12 play cricket, 22 play football and 6 play both. How many play neither of the two?
  15. 15.In a group of 35 children, 24 enjoy drawing, 16 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  16. 16.In a group of 37 children, 31 enjoy drawing, 16 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  17. 17.In a group of 25 children, 13 play cricket, 15 play football and 5 play both. How many play at least one of the two?
  18. 18.In a group of 30 grown-ups, 17 drink tea, 18 drink coffee and 10 drink both. How many drink at least one of the two?
  19. 19.In a group of 28 children, 20 play cricket, 14 play football and 10 play both. How many play only cricket?
  20. 20.In a group of 38 children, 29 play chess, 20 play carrom and 12 play both. How many play neither of the two?
  21. 21.In a group of 32 children, 9 play chess, 12 play carrom and 3 play both. How many play only carrom?
  22. 22.In a group of 36 grown-ups, 16 drink tea, 23 drink coffee and 5 drink both. How many drink only coffee?
  23. 23.In a group of 56 children, 26 sing Hindi songs, 29 sing English songs and 9 sing both. How many sing only Hindi songs?
  24. 24.In a group of 50 children, 21 sing Hindi songs, 20 sing English songs and 2 sing both. How many sing only English songs?
  25. 25.In a group of 27 children, 8 play cricket, 9 play football and 4 play both. How many play only cricket?
  26. 26.In a group of 21 children, 9 enjoy drawing, 8 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  27. 27.In a group of 39 children, 25 play cricket, 11 play football and 5 play both. How many play only cricket?
  28. 28.In a group of 22 children, 10 sing Hindi songs, 9 sing English songs and 4 sing both. How many sing at least one of the two?
  29. 29.In a group of 29 children, 13 enjoy drawing, 14 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  30. 30.In a group of 32 children, 14 play chess, 15 play carrom and 4 play both. How many play neither of the two?
  31. 31.In a group of 38 children, 23 play chess, 24 play carrom and 11 play both. How many play neither of the two?
  32. 32.In a group of 31 children, 15 like mangoes, 16 like bananas and 6 like both. How many like at least one of the two?
  33. 33.In a group of 38 children, 15 play cricket, 24 play football and 5 play both. How many play only football?
  34. 34.In a group of 42 children, 20 play cricket, 21 play football and 7 play both. How many play only football?
  35. 35.In a group of 47 children, 24 enjoy drawing, 21 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  36. 36.In a group of 35 children, 9 play cricket, 22 play football and 2 play both. How many play only cricket?
  37. 37.In a group of 43 children, 27 play chess, 20 play carrom and 9 play both. How many play exactly one of the two?
  38. 38.In a group of 36 children, 17 play cricket, 13 play football and 9 play both. How many play neither of the two?
  39. 39.In a group of 51 grown-ups, 25 drink tea, 17 drink coffee and 6 drink both. How many drink exactly one of the two?
  40. 40.In a group of 53 grown-ups, 20 drink tea, 24 drink coffee and 6 drink both. How many drink at least one of the two?

Answer key

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

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