Question

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

Answer 1

According to first statement :

n = 12q + 6

According to second statement:

n = 6p + r

We are to find r..

Answer 2

I am not very sure on how you generated the statements ?Please explain.

Answer 3

See, there is formula :

\[Dividend = Divisor \times Quotient + Remainder\]

Answer 4

If I say 4 divides 12 leaving quotient as 3 and 0 :

Then we can represent it as :

\[12 = 4 \times 3 + 0\]

Answer 5

and *remainder as 0..

Answer 6

Ok then how is the Q(x) p and q

Answer 7

I have assumed them as p and q in that two cases because we don't know them..

Answer 8

@waterineyes what you given is true but there is two eqns and 3 unknowns...
am I wrong?

Answer 9

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...

Answer 10

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 ? :)

Answer 11

when 6,,,...remainder should be 0 !!!!!

Answer 12

tamtoan got the correct way..

Answer 13

i have options so we can put them and check ?

Answer 14

Sure..

Answer 15

yep....

Answer 16

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..

Answer 17

*leave

Answer 18

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

Answer 19

0,1,2,3

Answer 20

^ options ?

Answer 21

Now you guys have pretty confused me lol

Answer 22

@waterineyes Now tell me the math behind this :(

Answer 23

I think @hba will be able to comprehend Ida behind it when you again check the first response of waterineyes

Answer 24

Are you still not able to find the correct choice??

Answer 25

followed by tamtoan's first response

Answer 26

Well the answer is 0 but i could not understand the math behind it :(

Answer 27

Till here you got :

\[n = 12q + 6\]

Answer 28

yes

Answer 29

Now can you factor out 6 from that ??

Answer 30

no.

Answer 31

how to do that ?

Answer 32

By using distributive property??

Answer 33

\[ab + ac = a(b+c)\]

Answer 34

n=6(2q+1)

Answer 35

Yep.

Now if I say that \(n = 3\times 4\) then it means that 3 and 4 are the factors of n..

Okay??

Answer 36

ok

Answer 37

so here the factors are 6 and 2q+1

Answer 38

Good going..

Answer 39

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??

Answer 40

more..

Answer 41

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??

Answer 42

It means that factors of any number will divide it fully leaving No Remainder..

It is obvious hba..

Answer 43

More ??

Answer 44

Still not getting tell me @hba

Answer 45

gotcha:D

Answer 46

So, 6/n=0 and 6/2q+1 = 0

Answer 47

what next ?

Answer 48

You have to find remainder no??

Answer 49

That you have found I think...

Why do you want to go next in this??

Answer 50

Sorry, remainder of n/6 will be 0..

And not 6/n..

Answer 51

Net got crushed??

Answer 52

Sorry some issue with my internet connection,So the answer is 0 @waterineyes

Answer 53

Yes it is...