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  • hba

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

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According to first statement : n = 12q + 6 According to second statement: n = 6p + r We are to find r..
  • hba
I am not very sure on how you generated the statements ?Please explain.
See, there is formula : \[Dividend = Divisor \times Quotient + Remainder\]

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Other answers:

If I say 4 divides 12 leaving quotient as 3 and 0 : Then we can represent it as : \[12 = 4 \times 3 + 0\]
and *remainder as 0..
  • hba
Ok then how is the Q(x) p and q
I have assumed them as p and q in that two cases because we don't know them..
@waterineyes what you given is true but there is two eqns and 3 unknowns... am I wrong?
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...
n = 12q + 6 = 6(2q +1) so n is a multiple of 6 ...:) when you that a multiple of 6 divide there a remainder ? :)
when 6,,,...remainder should be 0 !!!!!
tamtoan got the correct way..
  • hba
i have options so we can put them and check ?
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..
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
  • hba
  • hba
^ options ?
  • hba
Now you guys have pretty confused me lol
  • hba
@waterineyes Now tell me the math behind this :(
I think @hba will be able to comprehend Ida behind it when you again check the first response of waterineyes
Are you still not able to find the correct choice??
followed by tamtoan's first response
  • hba
Well the answer is 0 but i could not understand the math behind it :(
Till here you got : \[n = 12q + 6\]
  • hba
Now can you factor out 6 from that ??
  • hba
  • hba
how to do that ?
By using distributive property??
\[ab + ac = a(b+c)\]
  • hba
Yep. Now if I say that \(n = 3\times 4\) then it means that 3 and 4 are the factors of n.. Okay??
  • hba
  • hba
so here the factors are 6 and 2q+1
Good going..
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??
  • hba
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??
It means that factors of any number will divide it fully leaving No Remainder.. It is obvious hba..
More ??
Still not getting tell me @hba
  • hba
  • hba
So, 6/n=0 and 6/2q+1 = 0
  • hba
what next ?
You have to find remainder no??
That you have found I think... Why do you want to go next in this??
Sorry, remainder of n/6 will be 0.. And not 6/n..
Net got crushed??
  • hba
Sorry some issue with my internet connection,So the answer is 0 @waterineyes
Yes it is...

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