Official ANS According to GRE Tutor Economist: Don't understand the explanation

In order for the remainder to be 1 when m + n is divided by 9, the remainders when m and n are divided by 9 should add up to 1.

Since you know that m is divisible by 9, it follows that its remainder must be 0 when divided by 9.

So, you needed to find an answer choice stating that when n is divided by 9, the remainder is 1.
The first thing to recall here is the Rule of Divisibility by 9 states that a number is divisible by 9 if its sum is divisible by 9. In fact, the remainder you get when dividing the sum of the digits of a number by 9 will be the same remainder obtained by dividing the original number by 9.

Out of the answer choices given, only 37 works since the remainder when dividing 37 by 9 is 1.

bad question.

On one hand, m+n divided by 9 and remainder is 1 is for instance 10.

But the question ask for the sum of n and m is divisible by 9. it should be the sum of m+n NOT n.

In fact, m+n= 36 is divisible by 9 and + 1 you do have 1 as remainder.

Hope this helps.

Regards

I didn't understand this question, please explain it once more

This was a question I got a long time back from the source as mentioned. I have modified the question to better reflect the official ans.

When m + n is divided by 9, the remainder is 1

Theory: Dividend = Divisor*Quotient + Remainder

m + n -> Dividend
9 -> Divisor
a -> Quotient (Assume)
1 -> Remainder

=> m + n = 9*a + 1 = 9a + 1

If m is divisible by 9, which of the following could be n

Let m = 9k
=> m + n = 9k + n = 9a + 1
=> n - 1 = 9a - 9k = 9*(a-k) => a multiple of 9

37 - 1 = 36 => A Multiple of 9

So, Answer will be D
Hope it helps!

Watch the following video to learn the Basics of Remainders