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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 473 · 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 30 children, 26 play chess, 13 play carrom and 10 play both. How many play only chess?
  2. 2.In a group of 34 children, 18 sing Hindi songs, 19 sing English songs and 12 sing both. How many sing exactly one of the two?
  3. 3.In a group of 38 children, 27 play chess, 14 play carrom and 7 play both. How many play neither of the two?
  4. 4.In a group of 25 children, 10 enjoy drawing, 18 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  5. 5.In a group of 27 children, 12 enjoy drawing, 18 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  6. 6.In a group of 34 grown-ups, 14 drink tea, 19 drink coffee and 4 drink both. How many drink only tea?
  7. 7.In a group of 32 children, 9 sing Hindi songs, 13 sing English songs and 5 sing both. How many sing exactly one of the two?
  8. 8.In a group of 41 children, 16 play cricket, 25 play football and 5 play both. How many play neither of the two?
  9. 9.In a group of 50 children, 16 play chess, 27 play carrom and 7 play both. How many play exactly one of the two?
  10. 10.In a group of 22 children, 18 play cricket, 8 play football and 5 play both. How many play exactly one of the two?
  11. 11.In a group of 50 children, 28 play chess, 22 play carrom and 12 play both. How many play neither of the two?
  12. 12.In a group of 35 children, 17 play cricket, 18 play football and 4 play both. How many play exactly one of the two?
  13. 13.In a group of 30 grown-ups, 23 drink tea, 11 drink coffee and 8 drink both. How many drink only coffee?
  14. 14.In a group of 33 grown-ups, 9 drink tea, 20 drink coffee and 4 drink both. How many drink exactly one of the two?
  15. 15.In a group of 45 children, 22 play cricket, 26 play football and 12 play both. How many play neither of the two?
  16. 16.In a group of 45 children, 28 play cricket, 19 play football and 9 play both. How many play at least one of the two?
  17. 17.In a group of 43 children, 26 enjoy drawing, 15 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  18. 18.In a group of 44 children, 22 play cricket, 14 play football and 4 play both. How many play exactly one of the two?
  19. 19.In a group of 56 grown-ups, 31 drink tea, 25 drink coffee and 12 drink both. How many drink exactly one of the two?
  20. 20.In a group of 34 children, 21 like mangoes, 15 like bananas and 12 like both. How many like neither of the two?
  21. 21.In a group of 21 children, 13 play chess, 8 play carrom and 4 play both. How many play only carrom?
  22. 22.In a group of 31 children, 12 enjoy drawing, 16 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  23. 23.In a group of 36 children, 21 like mangoes, 18 like bananas and 10 like both. How many like exactly one of the two?
  24. 24.In a group of 35 grown-ups, 21 drink tea, 11 drink coffee and 5 drink both. How many drink at least one of the two?
  25. 25.In a group of 26 children, 19 play cricket, 8 play football and 2 play both. How many play neither of the two?
  26. 26.In a group of 39 children, 14 enjoy drawing, 21 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  27. 27.In a group of 53 children, 28 sing Hindi songs, 25 sing English songs and 12 sing both. How many sing only English songs?
  28. 28.In a group of 30 children, 17 play cricket, 11 play football and 2 play both. How many play at least one of the two?
  29. 29.In a group of 28 children, 17 sing Hindi songs, 15 sing English songs and 12 sing both. How many sing at least one of the two?
  30. 30.In a group of 33 children, 22 sing Hindi songs, 12 sing English songs and 8 sing both. How many sing only English songs?
  31. 31.In a group of 37 children, 22 play cricket, 9 play football and 5 play both. How many play exactly one of the two?
  32. 32.In a group of 22 children, 7 enjoy drawing, 13 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  33. 33.In a group of 37 children, 20 like mangoes, 16 like bananas and 7 like both. How many like only mangoes?
  34. 34.In a group of 44 children, 25 play cricket, 27 play football and 9 play both. How many play only cricket?
  35. 35.In a group of 43 children, 29 play cricket, 23 play football and 10 play both. How many play only cricket?
  36. 36.In a group of 41 children, 12 play chess, 23 play carrom and 4 play both. How many play exactly one of the two?
  37. 37.In a group of 45 children, 21 sing Hindi songs, 15 sing English songs and 5 sing both. How many sing only Hindi songs?
  38. 38.In a group of 38 children, 19 play cricket, 10 play football and 2 play both. How many play only cricket?
  39. 39.In a group of 31 children, 23 sing Hindi songs, 16 sing English songs and 10 sing both. How many sing at least one of the two?
  40. 40.In a group of 36 children, 11 enjoy drawing, 19 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?

Answer key

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

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