Remainder problems require us to translate words into math. The question asks us to find the remainder when X is divided by Y. So:

X/Y = Z | R: ?

where Z is some whole number variable. We'll start by going through the statements individually.

Statement 1

This statement tells us that

X/2Y = K | R: 4

where K is some whole number variable. We could go ahead and use this to build an equation (dividend = divisor * constant + remainder) ... but we don't really need to if we use small, simple integers.

For example, let's let Y = 2 and K = 1:

X/2(2) = 1 | R: 4
X/4 = 1 | R: 4
X = 4 | R: 4 → X = 8

Then we can plug this into our initial equation:

X/Y = Z | R = ?
8/2 = 4 | R = 0

So X/Y can have a remainder of 0. Let's try a different set of integers, introducing a small change to see if we can create a remainder: maybe Y = 3 and K = 1:

X/2(3) = 1 | R: 4
X/6 = 1 | R: 4
X = 6 | R = 4 → X = 10

Plugging back into our initial equation:

X/Y = Z | R = ?
10/3 = 3 | R = 1
We quickly find that we can have either remainder 0 or remainder 1. Statement 1 is NOT sufficient.

Statement 2

Using N as our whole number variable, this statement tells us that

(X+Y)/Y = N | R: 4

Before we start plugging things in, we should notice that we can rearrange this equation a bit by splitting up the denominator on the left half of the equation:

X/Y + Y/Y = N | R: 4
X/Y + 1 = N | R: 4
X/Y = N + 1 | R: 4

Since N is a variable, we can set N + 1 as a new variable - let's use M.

X/Y = M | R: 4

This means that whenever we divide X by Y, the remainder will always be 4 ... which is exactly what we want to know! No need to plug in numbers here. Statement 2 is sufficient.

The correct answer is B.