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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 160 · 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 33 children, 15 like mangoes, 17 like bananas and 11 like both. How many like only bananas?
  2. 2.In a group of 48 children, 23 sing Hindi songs, 23 sing English songs and 12 sing both. How many sing only English songs?
  3. 3.In a group of 37 children, 19 play cricket, 24 play football and 8 play both. How many play neither of the two?
  4. 4.In a group of 40 children, 23 play chess, 17 play carrom and 11 play both. How many play neither of the two?
  5. 5.In a group of 33 children, 16 like mangoes, 16 like bananas and 4 like both. How many like at least one of the two?
  6. 6.In a group of 54 children, 22 sing Hindi songs, 30 sing English songs and 12 sing both. How many sing neither of the two?
  7. 7.In a group of 35 children, 17 play cricket, 21 play football and 4 play both. How many play exactly one of the two?
  8. 8.In a group of 38 children, 16 play cricket, 15 play football and 4 play both. How many play at least one of the two?
  9. 9.In a group of 22 children, 8 play cricket, 5 play football and 2 play both. How many play only cricket?
  10. 10.In a group of 25 children, 8 play cricket, 7 play football and 4 play both. How many play at least one of the two?
  11. 11.In a group of 43 children, 24 sing Hindi songs, 18 sing English songs and 6 sing both. How many sing neither of the two?
  12. 12.In a group of 42 children, 11 enjoy drawing, 27 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  13. 13.In a group of 28 children, 12 play cricket, 16 play football and 8 play both. How many play at least one of the two?
  14. 14.In a group of 26 children, 18 enjoy drawing, 18 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  15. 15.In a group of 27 children, 6 like mangoes, 14 like bananas and 3 like both. How many like only mangoes?
  16. 16.In a group of 45 children, 22 enjoy drawing, 21 enjoy dancing and 10 enjoy both. How many enjoy only dancing?
  17. 17.In a group of 39 children, 19 like mangoes, 14 like bananas and 9 like both. How many like exactly one of the two?
  18. 18.In a group of 35 children, 25 play cricket, 18 play football and 11 play both. How many play at least one of the two?
  19. 19.In a group of 45 children, 18 enjoy drawing, 22 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  20. 20.In a group of 47 children, 19 play chess, 19 play carrom and 3 play both. How many play only chess?
  21. 21.In a group of 32 children, 10 enjoy drawing, 24 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  22. 22.In a group of 35 children, 13 like mangoes, 21 like bananas and 4 like both. How many like only mangoes?
  23. 23.In a group of 32 children, 14 enjoy drawing, 8 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  24. 24.In a group of 45 children, 25 play cricket, 17 play football and 5 play both. How many play at least one of the two?
  25. 25.In a group of 35 children, 18 enjoy drawing, 20 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  26. 26.In a group of 36 grown-ups, 10 drink tea, 16 drink coffee and 4 drink both. How many drink at least one of the two?
  27. 27.In a group of 30 children, 16 play cricket, 10 play football and 4 play both. How many play at least one of the two?
  28. 28.In a group of 42 children, 23 sing Hindi songs, 16 sing English songs and 5 sing both. How many sing at least one of the two?
  29. 29.In a group of 35 children, 14 sing Hindi songs, 18 sing English songs and 7 sing both. How many sing at least one of the two?
  30. 30.In a group of 48 children, 22 enjoy drawing, 29 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  31. 31.In a group of 37 children, 14 play cricket, 18 play football and 9 play both. How many play at least one of the two?
  32. 32.In a group of 37 children, 16 play chess, 23 play carrom and 11 play both. How many play at least one of the two?
  33. 33.In a group of 40 grown-ups, 17 drink tea, 28 drink coffee and 11 drink both. How many drink only coffee?
  34. 34.In a group of 22 children, 14 play cricket, 7 play football and 4 play both. How many play only football?
  35. 35.In a group of 31 children, 16 play cricket, 21 play football and 7 play both. How many play only cricket?
  36. 36.In a group of 40 children, 17 enjoy drawing, 18 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  37. 37.In a group of 27 children, 12 play chess, 8 play carrom and 4 play both. How many play only chess?
  38. 38.In a group of 26 children, 18 enjoy drawing, 6 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  39. 39.In a group of 34 children, 12 play cricket, 27 play football and 8 play both. How many play neither of the two?
  40. 40.In a group of 35 children, 24 enjoy drawing, 13 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?

Answer key

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

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