Data Sufficiency

If x and y are integers greater than 1, is x a multiple of y ?

1. 3y^2 + 7y = x
2. x^2 - x is a multiple of y

Can any one explain how to solve this?
OA is A

tanyajoseph wrote:If x and y are integers greater than 1, is x a multiple of y ?

1. 3y^2 + 7y = x
2. x^2 - x is a multiple of y

Can any one explain how to solve this?
OA is A

Answer [A]. Here is why:

Statement (1) simplified:
y(3y + 7) = x
x/y = 3y + 7 (integer because y is an integer greater than 1)
hence x is a multiple of y, sufficient

Statement (2) simplified:
x(x-1) = y.m (where m is an integer)
which means, either x is a multiple of y or (x-1) is a multiple of y.
Since we can't say for certain which one, this is Not Sufficient

is x = y * k ?
Given:
x,y={2.....n}

1. 3y^2 + 7y = x
y(3y+7) = x;
y * k = x : , since y ={2.......n}; k={13.....}
Sufficient:
Answer choice : AD

2. x^2 - x is a multiple of y
x(x-1)=y;
x = y * (1/(x-1))
x is multiple of y and/or 1/(x-1) : Not Sufficient.

Ans:A.