If x and y are nonzero integers, is y + 10x divisible by 3?

Useful rule: If j and k are positive integers, and each is divisible by d, then the sum (j + k) is also divisible by d

Target question: Is y + 10x divisible by 3

Statement 1: y + x is divisible by 3
Since x is an integer, we know that 9x is divisible by 3
We're also told that y + x is divisible by 3
So, by the above rule, we can conclude that the sum (y+x) + 9x is divisible by 3
Simplify to get: y + 10x is divisible by 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: y – x is divisible by 3
If I want to apply the above rule, I need to recognize that (y - x) + 11x = y + 10x
However, we can't definitively say whether or not 11x is divisible by 3, which means we can't determine whether y + 10x is divisible by 3.
Here's what I mean:
Case a: y = 6 and x = 3. Notice that y - x = 6 - 3 = 3, and 3 is divisible by 3. In this case, y + 10x = 6 + 10(3) = 36, which IS divisible by 3
Case b: y = 5 and x = 2. Notice that y - x = 5 - 2 = 3, and 3 is divisible by 3. In this case, y + 10x = 5 + 10(2) = 25, which is NOT divisible by 3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent