If n is an integer, what is the remainder when n is divided

Although there is a better method, my Finding The Pattern method-- when in doubt, FTP!!!!!!!!
Because there is always a pattern.

Question: (N/7 remainder?)

(1)N+1 is divisible by 7

N=6,13,20,27,34,...
Question=6,6,6,6,6,......

Sufficient

(2)N+8 is divisible by 7

N=6,13,20,27,34,...
Question=6,6,6,6,6...

Sufficient

General rule of thumb generate the possible values and check the remainder really fast... if it changes insufficient, otherwise sufficient.

Wikipedia has an interesting article on remainder. https://en.wikipedia.org/wiki/Remainder
It says Remainder can have negative values as well, unless specified by the condition x < r ≤ x+|d| (or x ≤ r < x+|d|), where x is a constant, d is the divisor, and r is the remainder.

Several points here:

-First, as that wikipedia article makes clear, mathematicians do not allow remainders to be negative (see where they say "as is usual for mathematicians", when giving the positive solution). ;

-So, when you divide an integer by 7, there are only seven possible remainders: 0, 1, 2, 3, 4, 5 and 6. Remainders can't be negative, they can't be decimals, and they can't be greater than or equal to what you're dividing by;

-I have never seen a real GMAT question that asks about remainders when dividing by a negative number. Nor have I seen questions which ask for the remainder when dividing a negative by a positive number;

-Still, we can see how to find the remainder when dividing, say, -15 by 7. First, we find the remainder when dividing, for example, 20 by 7 as follows:

--we find the nearest multiple of 7 which is *smaller* than 20. That's 14;
--we subtract: 20 - 14 = 6. That is, 20 is 6 larger than the nearest smaller multiple of 7, so the remainder is 6 when we divide 20 by 7;

-Doing the same for -15:

--the nearest multiple of 7 which is *smaller* than -15 is -21;
--now, -15 - (-21) = 6. That is, -15 is 6 greater than the nearest multiple of 7 which is smaller than -15, and the remainder is 6 when -15 is divided by 7.

So, going back to the original question in this post, the remainder is the same regardless of whether n is positive or negative, and the answer is D.