This is DS question #240 of the OG10
Here is the official explanation for statement 2:
statement 2 implies that y is a multiple of of 12 or that 12 is a divisor of y. Since x = 8y + 12, it follows that 12 is a divisor of x, and thus 12 is a common divisor of x and y. Since 12 = x - 8y (rephrase the stem), any common divisor of x and y must be a divisor of 12. Therefore no integer greater than 12 is a common divisor of x and y, and 12 is the GCD of x and y.
this question gets me everytime.