divisibility

[szDave]

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.

a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d) EACH statement ALONE is sufficient.
e) Statements (1) and (2) TOGETHER are NOT sufficient.

If x is equal to 3y^2 + 7y then it is divisible by y?

[Brent@GMATPrepNow]

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.

Target question: Is x a multiple of y?

What does it mean for x to be a multiple of y?
This means that we can express x as ky, where k is some integer.
For example, 15 is a multiple of 3, since we can express 15 as (3)(5), where 5 is an integer.

Statement 1: 3y^2 + 7y = x
Factor to get: x = y(3y + 7)
Note that (3y+7) evaluates to be an integer.
So, we can be certain that x = y(some integer)
In other words, x is a multiple of y
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x^2 - x is a multiple of y
There are several pairs of values that meet this condition. Here are two:
Case a: x=6 and y=3, in which case x is a multiple of y
Case b: x=6 and y=15, in which case x is not a multiple of y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent

[Anurag@Gurome]

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.

a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d) EACH statement ALONE is sufficient.
e) Statements (1) and (2) TOGETHER are NOT sufficient.

If x is equal to 3y^2 + 7y then it is divisible by y?

I have posted a solution here: https://www.beatthegmat.com/is-x-a-multi ... 85339.html