harpott wrote:Why is everyone complicating this question with rules of divisibility? Why are you even bringing in the point that the you can find out if a number is divisible by 9 if the digit sum adds up to a certain number? The question just asks what is the remainder.
The simple answer is that no matter what the value of k is, it will always be a multiple of 80. Since the remainder is the same whether you do 80/9 or 800/9 or 8000/9, the only difference to the remainder will depend on what the value of J is. Thats all you need to know to answer this question correctly.
Who cares if 800+j is divisible by 9?
There is no need to bring in 'trivia' about what numbers are divisible by 9.
You're right when you say that "
the remainder is the same whether you do 80/9 or 800/9 or 8000/9."
Yes, it's true that 80 divided by 9 leaves us with remainder 8, 800 divided by 9 leaves us with remainder 8, 8000 divided by 9 leaves us with remainder 8, and so on. But how do you know that this is true for ALL possible values? Since the solution depends on this fact, we need some way to verify/prove that your statement is true, otherwise we're just waving our arms.
One way to show that 80, 800, 8000, 80000, etc will leave the same remainder when divided by 9 is to use the fact that numbers divisible by 9 are such that the sum of their digits is divisible by 9. This is why this divisibility rule is mentioned.
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
