This is a DS remainder question from Manhattan Cat 3. I have a quick question about statement 1:


If a and b are the digits of the two-digit number X, what is the remainder when X is divided by 9?

(1) a + b = 11

(2) X + 7 is divisible by 9

This is the explanation given:

(1) SUFFICIENT: The sum of the digits a and b here is not divisible by 9, so X is not divisible by 9. It turns out, however, that the sum of the digits here can also be used to find the remainder. Since the sum of the digits here has a remainder of 2 when divided by 9, the number itself has a remainder of 2 when divided by 9.

We can use a few values for a and b to show that this is the case:

When a = 5 and b = 6, 56 divided by 9 has a remainder of 56 - 54 = 2
When a = 7 and b = 4, 74 divided by 9 has a remainder of 74 - 72 = 2

My Question

Can the sum of the digits always be used to find the remainder, or only when dividing by 9?

Thanks