Remainder problem. Need help

[xxdevilicangelxx]

Hi. Im new to this forum.
i needed help with this problem. I cant understand how to do this. PLz help me n explain it.
the question is as following
The remainder when n is divided by 9 is 6. What is the remainder when 7n is divided by 9.
a 1
b 2
c 3
d 6
e 13
plz reply asap. i really need to do this.

[rajkapoor]

couple of ways

n divided by 9 leaves remainder 6.
7n will leave the same remainder as 7*(remainder of n when divided by 9)
= 7*6/ 9
= 42/9
= 6

alternate way to understand the above.

7 and 9 and prime to each other , in other words , they dont have any common factor. so 7 divided by 9 will leave remainder of 7
we already know 9 leaves a remainder of 6 ,and.

so 7 n will leave a remainder of 7*6 = 42
but remainder should be 0 < r < 9
dividing 42 with 9 , leaves the remainder 6

-
if you can understand the above , great ,
else pick a number that leaves remainder 6 when divided by 9

9+6 = 15

multiply it by 7 = 105
divide it by 9 = 105-99 = 6

i pray that answer to your question is 6 ..lol..

[xxdevilicangelxx]

thnk u very much.
n yeah i did understand it.

[RonPurewal]

if you can understand the above , great ,
else pick a number that leaves remainder 6 when divided by 9

9+6 = 15

multiply it by 7 = 105
divide it by 9 = 105-99 = 6

even though it's not a "textbook method", this is BY FAR the best way to solve this problem.

the answers don't involve the variable.
therefore,
if you can find ANY workable value for the variable, you've got the answer!

if that's the case, as in this problem, it's really just a waste of your time to go through the textbook-style solution.

[sharok50]

Methodical approach.
n=9q+6

so
7n=7(9q+6)
=>7n= 7X9q+42
=>7n= 7X9q+36+6
=>7n=7X9q+4x9+6
=>7n=9(7q+4)+6

so remainder should be 6.