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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 636 · 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 46 children, 25 like mangoes, 18 like bananas and 5 like both. How many like at least one of the two?
  2. 2.In a group of 12 children, 7 like mangoes, 6 like bananas and 3 like both. How many like exactly one of the two?
  3. 3.In a group of 54 children, 25 like mangoes, 23 like bananas and 8 like both. How many like at least one of the two?
  4. 4.In a group of 33 children, 15 play chess, 14 play carrom and 2 play both. How many play at least one of the two?
  5. 5.In a group of 41 children, 22 play cricket, 22 play football and 6 play both. How many play at least one of the two?
  6. 6.In a group of 43 children, 26 sing Hindi songs, 16 sing English songs and 8 sing both. How many sing at least one of the two?
  7. 7.In a group of 25 children, 11 play chess, 9 play carrom and 2 play both. How many play only chess?
  8. 8.In a group of 48 children, 24 like mangoes, 23 like bananas and 4 like both. How many like exactly one of the two?
  9. 9.In a group of 44 children, 25 enjoy drawing, 16 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  10. 10.In a group of 22 children, 12 play cricket, 10 play football and 7 play both. How many play neither of the two?
  11. 11.In a group of 40 children, 15 sing Hindi songs, 22 sing English songs and 12 sing both. How many sing only English songs?
  12. 12.In a group of 53 children, 27 enjoy drawing, 27 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  13. 13.In a group of 49 children, 21 play cricket, 15 play football and 2 play both. How many play only football?
  14. 14.In a group of 40 children, 19 like mangoes, 18 like bananas and 11 like both. How many like only bananas?
  15. 15.In a group of 43 children, 15 play chess, 23 play carrom and 3 play both. How many play only carrom?
  16. 16.In a group of 27 children, 12 play cricket, 12 play football and 4 play both. How many play only football?
  17. 17.In a group of 31 grown-ups, 21 drink tea, 6 drink coffee and 2 drink both. How many drink only coffee?
  18. 18.In a group of 30 children, 20 enjoy drawing, 8 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  19. 19.In a group of 45 children, 21 sing Hindi songs, 21 sing English songs and 6 sing both. How many sing at least one of the two?
  20. 20.In a group of 37 children, 19 like mangoes, 18 like bananas and 10 like both. How many like only bananas?
  21. 21.In a group of 20 children, 11 sing Hindi songs, 13 sing English songs and 8 sing both. How many sing neither of the two?
  22. 22.In a group of 43 children, 16 play cricket, 27 play football and 7 play both. How many play neither of the two?
  23. 23.In a group of 27 children, 12 like mangoes, 19 like bananas and 8 like both. How many like only bananas?
  24. 24.In a group of 49 children, 22 enjoy drawing, 17 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  25. 25.In a group of 33 children, 21 like mangoes, 15 like bananas and 6 like both. How many like at least one of the two?
  26. 26.In a group of 25 children, 19 like mangoes, 10 like bananas and 6 like both. How many like neither of the two?
  27. 27.In a group of 19 children, 9 enjoy drawing, 8 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  28. 28.In a group of 41 children, 20 enjoy drawing, 15 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  29. 29.In a group of 29 children, 7 play chess, 13 play carrom and 2 play both. How many play only chess?
  30. 30.In a group of 49 children, 18 sing Hindi songs, 30 sing English songs and 11 sing both. How many sing only English songs?
  31. 31.In a group of 54 children, 19 sing Hindi songs, 27 sing English songs and 7 sing both. How many sing only Hindi songs?
  32. 32.In a group of 48 children, 16 play cricket, 32 play football and 12 play both. How many play exactly one of the two?
  33. 33.In a group of 32 children, 14 like mangoes, 14 like bananas and 2 like both. How many like neither of the two?
  34. 34.In a group of 42 children, 26 play cricket, 21 play football and 12 play both. How many play only cricket?
  35. 35.In a group of 20 children, 13 sing Hindi songs, 11 sing English songs and 7 sing both. How many sing only English songs?
  36. 36.In a group of 33 children, 15 enjoy drawing, 9 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  37. 37.In a group of 32 children, 20 play chess, 8 play carrom and 4 play both. How many play only carrom?
  38. 38.In a group of 42 children, 13 sing Hindi songs, 24 sing English songs and 9 sing both. How many sing only English songs?
  39. 39.In a group of 42 children, 26 play chess, 22 play carrom and 12 play both. How many play only chess?
  40. 40.In a group of 32 children, 16 enjoy drawing, 11 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?

Answer key

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

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