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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waterineyes
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According to first statement :
n = 12q + 6
According to second statement:
n = 6p + r
We are to find r..
hba
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I am not very sure on how you generated the statements ?Please explain.
waterineyes
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See, there is formula :
\[Dividend = Divisor \times Quotient + Remainder\]
waterineyes
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If I say 4 divides 12 leaving quotient as 3 and 0 :
Then we can represent it as :
\[12 = 4 \times 3 + 0\]
waterineyes
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and *remainder as 0..
hba
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Ok then how is the Q(x) p and q
waterineyes
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I have assumed them as p and q in that two cases because we don't know them..
Rosh007
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@waterineyes what you given is true but there is two eqns and 3 unknowns...
am I wrong?
waterineyes
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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...
tamtoan
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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 ? :)
jobs
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when 6,,,...remainder should be 0 !!!!!
jobs
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tamtoan got the correct way..
hba
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i have options so we can put them and check ?
waterineyes
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Sure..
jobs
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yep....
waterineyes
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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..
waterineyes
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*leave
Rosh007
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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
hba
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0,1,2,3
hba
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^ options ?
hba
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Now you guys have pretty confused me lol
hba
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@waterineyes Now tell me the math behind this :(
Rosh007
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I think @hba will be able to comprehend Ida behind it when you again check the first response of waterineyes
waterineyes
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Are you still not able to find the correct choice??
Rosh007
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followed by tamtoan's first response
hba
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Well the answer is 0 but i could not understand the math behind it :(
waterineyes
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Till here you got :
\[n = 12q + 6\]
hba
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yes
waterineyes
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Now can you factor out 6 from that ??
hba
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no.
hba
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how to do that ?
waterineyes
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By using distributive property??
waterineyes
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\[ab + ac = a(b+c)\]
hba
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n=6(2q+1)
waterineyes
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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??
hba
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ok
hba
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so here the factors are 6 and 2q+1
waterineyes
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Good going..
waterineyes
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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??
hba
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more..
waterineyes
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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??
waterineyes
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It means that factors of any number will divide it fully leaving No Remainder..
It is obvious hba..
waterineyes
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More ??
waterineyes
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Still not getting tell me @hba
hba
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gotcha:D
hba
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So, 6/n=0 and 6/2q+1 = 0
hba
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what next ?
waterineyes
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You have to find remainder no??
waterineyes
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That you have found I think...
Why do you want to go next in this??
waterineyes
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Sorry, remainder of n/6 will be 0..
And not 6/n..
waterineyes
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Net got crushed??
hba
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Sorry some issue with my internet connection,So the answer is 0 @waterineyes
waterineyes
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Yes it is...