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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 172 · 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, 19 like mangoes, 15 like bananas and 3 like both. How many like only bananas?
  2. 2.In a group of 25 children, 8 like mangoes, 8 like bananas and 3 like both. How many like only bananas?
  3. 3.In a group of 27 children, 15 sing Hindi songs, 13 sing English songs and 7 sing both. How many sing at least one of the two?
  4. 4.In a group of 35 grown-ups, 27 drink tea, 15 drink coffee and 11 drink both. How many drink at least one of the two?
  5. 5.In a group of 60 children, 29 sing Hindi songs, 29 sing English songs and 10 sing both. How many sing at least one of the two?
  6. 6.In a group of 36 children, 22 play cricket, 23 play football and 12 play both. How many play neither of the two?
  7. 7.In a group of 33 children, 21 play cricket, 11 play football and 3 play both. How many play exactly one of the two?
  8. 8.In a group of 26 children, 14 play cricket, 14 play football and 10 play both. How many play at least one of the two?
  9. 9.In a group of 35 children, 24 like mangoes, 11 like bananas and 4 like both. How many like at least one of the two?
  10. 10.In a group of 34 children, 15 enjoy drawing, 20 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  11. 11.In a group of 33 children, 12 play cricket, 16 play football and 2 play both. How many play only football?
  12. 12.In a group of 43 children, 13 play chess, 22 play carrom and 5 play both. How many play only chess?
  13. 13.In a group of 25 children, 18 play chess, 9 play carrom and 5 play both. How many play only chess?
  14. 14.In a group of 13 children, 7 sing Hindi songs, 8 sing English songs and 3 sing both. How many sing at least one of the two?
  15. 15.In a group of 24 children, 12 enjoy drawing, 14 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  16. 16.In a group of 35 children, 15 play cricket, 16 play football and 3 play both. How many play only football?
  17. 17.In a group of 38 children, 13 play chess, 28 play carrom and 10 play both. How many play exactly one of the two?
  18. 18.In a group of 41 children, 15 play chess, 21 play carrom and 8 play both. How many play neither of the two?
  19. 19.In a group of 21 children, 7 enjoy drawing, 15 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  20. 20.In a group of 33 children, 14 like mangoes, 15 like bananas and 7 like both. How many like exactly one of the two?
  21. 21.In a group of 50 grown-ups, 25 drink tea, 22 drink coffee and 10 drink both. How many drink only coffee?
  22. 22.In a group of 35 children, 28 sing Hindi songs, 14 sing English songs and 11 sing both. How many sing at least one of the two?
  23. 23.In a group of 39 children, 12 enjoy drawing, 14 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  24. 24.In a group of 45 children, 23 play chess, 16 play carrom and 6 play both. How many play neither of the two?
  25. 25.In a group of 20 children, 7 play cricket, 12 play football and 4 play both. How many play at least one of the two?
  26. 26.In a group of 50 children, 19 enjoy drawing, 24 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  27. 27.In a group of 44 children, 27 sing Hindi songs, 17 sing English songs and 8 sing both. How many sing neither of the two?
  28. 28.In a group of 39 children, 19 enjoy drawing, 17 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  29. 29.In a group of 36 children, 19 enjoy drawing, 27 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  30. 30.In a group of 31 children, 7 play chess, 16 play carrom and 4 play both. How many play at least one of the two?
  31. 31.In a group of 33 children, 11 like mangoes, 24 like bananas and 8 like both. How many like neither of the two?
  32. 32.In a group of 27 children, 12 enjoy drawing, 22 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  33. 33.In a group of 35 children, 17 sing Hindi songs, 24 sing English songs and 12 sing both. How many sing only English songs?
  34. 34.In a group of 28 children, 10 play cricket, 20 play football and 5 play both. How many play only cricket?
  35. 35.In a group of 37 children, 15 play cricket, 12 play football and 4 play both. How many play exactly one of the two?
  36. 36.In a group of 37 children, 23 sing Hindi songs, 13 sing English songs and 9 sing both. How many sing only Hindi songs?
  37. 37.In a group of 25 children, 14 play chess, 16 play carrom and 6 play both. How many play neither of the two?
  38. 38.In a group of 27 children, 17 like mangoes, 15 like bananas and 8 like both. How many like neither of the two?
  39. 39.In a group of 23 children, 7 enjoy drawing, 19 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  40. 40.In a group of 22 children, 14 play chess, 17 play carrom and 10 play both. How many play only chess?

Answer key

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

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