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hba

  • 2 years ago

When n is divided by 12,the remainder is 6.What is the remainder when n is divided by 6 ?

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  1. waterineyes
    • 2 years ago
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    According to first statement : n = 12q + 6 According to second statement: n = 6p + r We are to find r..

  2. hba
    • 2 years ago
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    I am not very sure on how you generated the statements ?Please explain.

  3. waterineyes
    • 2 years ago
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    See, there is formula : \[Dividend = Divisor \times Quotient + Remainder\]

  4. waterineyes
    • 2 years ago
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    If I say 4 divides 12 leaving quotient as 3 and 0 : Then we can represent it as : \[12 = 4 \times 3 + 0\]

  5. waterineyes
    • 2 years ago
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    and *remainder as 0..

  6. hba
    • 2 years ago
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    Ok then how is the Q(x) p and q

  7. waterineyes
    • 2 years ago
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    I have assumed them as p and q in that two cases because we don't know them..

  8. Rosh007
    • 2 years ago
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    @waterineyes what you given is true but there is two eqns and 3 unknowns... am I wrong?

  9. waterineyes
    • 2 years ago
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    Yes we have 3 unknowns and this time I am remembering @mukushla because he is expert in finding 3 unknowns out of 1 equation given only.. Ha ha ha ha...

  10. tamtoan
    • 2 years ago
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    n = 12q + 6 = 6(2q +1) so n is a multiple of 6 ...:) when you that a multiple of 6 divide 6...is there a remainder ? :)

  11. jobs
    • 2 years ago
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    when 6,,,...remainder should be 0 !!!!!

  12. jobs
    • 2 years ago
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    tamtoan got the correct way..

  13. hba
    • 2 years ago
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    i have options so we can put them and check ?

  14. waterineyes
    • 2 years ago
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    Sure..

  15. jobs
    • 2 years ago
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    yep....

  16. waterineyes
    • 2 years ago
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    18, 30, 42, 54 all leaves remainder as 6 when divided by 12.. So, you can easily see that they all are fully divided by 6, leaving remainder as 0..

  17. waterineyes
    • 2 years ago
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    *leave

  18. Rosh007
    • 2 years ago
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    Thanks to all........ I never think of bunchy equations but only facts... My bad.... i thought how it is possibl to solve it... my bad,... but thanks I got it

  19. hba
    • 2 years ago
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    0,1,2,3

  20. hba
    • 2 years ago
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    ^ options ?

  21. hba
    • 2 years ago
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    Now you guys have pretty confused me lol

  22. hba
    • 2 years ago
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    @waterineyes Now tell me the math behind this :(

  23. Rosh007
    • 2 years ago
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    I think @hba will be able to comprehend Ida behind it when you again check the first response of waterineyes

  24. waterineyes
    • 2 years ago
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    Are you still not able to find the correct choice??

  25. Rosh007
    • 2 years ago
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    followed by tamtoan's first response

  26. hba
    • 2 years ago
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    Well the answer is 0 but i could not understand the math behind it :(

  27. waterineyes
    • 2 years ago
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    Till here you got : \[n = 12q + 6\]

  28. hba
    • 2 years ago
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    yes

  29. waterineyes
    • 2 years ago
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    Now can you factor out 6 from that ??

  30. hba
    • 2 years ago
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    no.

  31. hba
    • 2 years ago
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    how to do that ?

  32. waterineyes
    • 2 years ago
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    By using distributive property??

  33. waterineyes
    • 2 years ago
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    \[ab + ac = a(b+c)\]

  34. hba
    • 2 years ago
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    n=6(2q+1)

  35. waterineyes
    • 2 years ago
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    Yep. Now if I say that \(n = 3\times 4\) then it means that 3 and 4 are the factors of n.. Okay??

  36. hba
    • 2 years ago
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    ok

  37. hba
    • 2 years ago
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    so here the factors are 6 and 2q+1

  38. waterineyes
    • 2 years ago
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    Good going..

  39. waterineyes
    • 2 years ago
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    And you must remember that factors divide the number fully leaving NO REMAINDER BEHIND.. If \(n = 3 \times 4\) then 3 and 4 both will divide n fully leaving remainder as 0.. Getting or more explanation you want??

  40. hba
    • 2 years ago
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    more..

  41. waterineyes
    • 2 years ago
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    See, here \(3 \times 4 = 12\) So here n = 12.. Now divide 12 by 3 first : Quotient - 4 Remainder - 0 Now divide 12 by 4: Quotient - 3 Remainder - 0 What did you get as remainder??

  42. waterineyes
    • 2 years ago
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    It means that factors of any number will divide it fully leaving No Remainder.. It is obvious hba..

  43. waterineyes
    • 2 years ago
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    More ??

  44. waterineyes
    • 2 years ago
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    Still not getting tell me @hba

  45. hba
    • 2 years ago
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    gotcha:D

  46. hba
    • 2 years ago
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    So, 6/n=0 and 6/2q+1 = 0

  47. hba
    • 2 years ago
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    what next ?

  48. waterineyes
    • 2 years ago
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    You have to find remainder no??

  49. waterineyes
    • 2 years ago
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    That you have found I think... Why do you want to go next in this??

  50. waterineyes
    • 2 years ago
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    Sorry, remainder of n/6 will be 0.. And not 6/n..

  51. waterineyes
    • 2 years ago
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    Net got crushed??

  52. hba
    • 2 years ago
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    Sorry some issue with my internet connection,So the answer is 0 @waterineyes

  53. waterineyes
    • 2 years ago
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    Yes it is...

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