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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 251 · 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 37 children, 13 enjoy drawing, 14 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  2. 2.In a group of 20 children, 12 play cricket, 16 play football and 9 play both. How many play exactly one of the two?
  3. 3.In a group of 36 children, 23 play chess, 19 play carrom and 11 play both. How many play at least one of the two?
  4. 4.In a group of 34 children, 18 like mangoes, 11 like bananas and 3 like both. How many like only mangoes?
  5. 5.In a group of 31 children, 13 sing Hindi songs, 21 sing English songs and 9 sing both. How many sing exactly one of the two?
  6. 6.In a group of 54 children, 24 sing Hindi songs, 24 sing English songs and 8 sing both. How many sing exactly one of the two?
  7. 7.In a group of 44 children, 24 play chess, 23 play carrom and 11 play both. How many play neither of the two?
  8. 8.In a group of 49 grown-ups, 24 drink tea, 26 drink coffee and 8 drink both. How many drink at least one of the two?
  9. 9.In a group of 47 children, 31 enjoy drawing, 22 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  10. 10.In a group of 33 children, 15 play cricket, 17 play football and 7 play both. How many play exactly one of the two?
  11. 11.In a group of 22 grown-ups, 10 drink tea, 12 drink coffee and 4 drink both. How many drink neither of the two?
  12. 12.In a group of 22 children, 10 enjoy drawing, 13 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  13. 13.In a group of 38 children, 22 play chess, 14 play carrom and 4 play both. How many play neither of the two?
  14. 14.In a group of 26 children, 5 play cricket, 12 play football and 2 play both. How many play only football?
  15. 15.In a group of 32 children, 22 play cricket, 9 play football and 2 play both. How many play exactly one of the two?
  16. 16.In a group of 37 children, 18 enjoy drawing, 18 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  17. 17.In a group of 37 children, 17 enjoy drawing, 24 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  18. 18.In a group of 43 children, 24 like mangoes, 24 like bananas and 8 like both. How many like only bananas?
  19. 19.In a group of 27 children, 12 play cricket, 20 play football and 8 play both. How many play only cricket?
  20. 20.In a group of 38 children, 12 sing Hindi songs, 23 sing English songs and 5 sing both. How many sing only Hindi songs?
  21. 21.In a group of 37 children, 21 play cricket, 13 play football and 5 play both. How many play neither of the two?
  22. 22.In a group of 29 children, 12 play chess, 19 play carrom and 8 play both. How many play exactly one of the two?
  23. 23.In a group of 37 children, 20 enjoy drawing, 24 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  24. 24.In a group of 41 children, 24 play cricket, 20 play football and 5 play both. How many play at least one of the two?
  25. 25.In a group of 30 children, 14 enjoy drawing, 17 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  26. 26.In a group of 27 children, 15 play chess, 9 play carrom and 5 play both. How many play neither of the two?
  27. 27.In a group of 51 children, 23 play cricket, 20 play football and 4 play both. How many play exactly one of the two?
  28. 28.In a group of 32 children, 6 enjoy drawing, 22 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  29. 29.In a group of 44 children, 25 sing Hindi songs, 30 sing English songs and 12 sing both. How many sing at least one of the two?
  30. 30.In a group of 23 children, 7 play cricket, 6 play football and 3 play both. How many play neither of the two?
  31. 31.In a group of 50 children, 21 play chess, 29 play carrom and 12 play both. How many play neither of the two?
  32. 32.In a group of 45 children, 30 enjoy drawing, 19 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  33. 33.In a group of 48 children, 22 play chess, 27 play carrom and 10 play both. How many play at least one of the two?
  34. 34.In a group of 33 children, 13 play cricket, 24 play football and 9 play both. How many play only football?
  35. 35.In a group of 43 children, 19 sing Hindi songs, 15 sing English songs and 5 sing both. How many sing neither of the two?
  36. 36.In a group of 40 children, 17 like mangoes, 25 like bananas and 7 like both. How many like only mangoes?
  37. 37.In a group of 37 children, 20 sing Hindi songs, 19 sing English songs and 4 sing both. How many sing only Hindi songs?
  38. 38.In a group of 40 children, 19 play chess, 16 play carrom and 3 play both. How many play only chess?
  39. 39.In a group of 38 children, 20 play cricket, 13 play football and 8 play both. How many play neither of the two?
  40. 40.In a group of 51 children, 27 play cricket, 25 play football and 7 play both. How many play neither of the two?

Answer key

  1. 21
  2. 10
  3. 31
  4. 15
  5. 16
  6. 32
  7. 8
  8. 42
  9. 31
  10. 18
  11. 4
  12. 6
  13. 6
  14. 10
  15. 27
  16. 16
  17. 6
  18. 16
  19. 4
  20. 7
  21. 8
  22. 15
  23. 3
  24. 39
  25. 17
  26. 8
  27. 35
  28. 26
  29. 43
  30. 13
  31. 12
  32. 18
  33. 39
  34. 15
  35. 14
  36. 10
  37. 16
  38. 16
  39. 13
  40. 6

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