Is there a trick to solve this besides Algebra?

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If x and y are integers, is 6 a factor of y?

(1) y - 4 = 7x

(2) 6 is a factor of 7x - 2

[GMATGuruNY]

If x and y are integers, is 6 a factor of y?

(1) y - 4 = 7x

(2) 6 is a factor of 7x - 2

Question stem rephrased: Is y a multiple of 6?

Statement 1: y-4 = 7x
y = 7x+4.

If x=1, then y = 7*1 + 4 = 11.
In this case, y is NOT a multiple of 6.

If x=2, then y = 7*2 + 4 = 18.
In this case, y is a multiple of 6.
INSUFFICIENT.

Statement 2: 6 is a factor of 7x-2
In other words, 7x-2 is a multiple of 6.
No information about y.
INSUFFICIENT.

Statements combined:
What is the purpose of statement 2?
It probably has an effect upon statement 1.

Rephrase statement 1 so that it looks like statement 2:
y = (7x-2) + 6.

Since statement 2 indicates that 7x-2 is a multiple of 6, we get:
y = (7x-2) + 6 = (multiple of 6) + 6 = multiple of 6.
SUFFICIENT.

The correct answer is C.