number properties discrepancy

Hi everybody!
I am stuck with a solution method for two similar questions from the area of number properties.

Here is the first:
The sum of three consecutive even integers is always divisible by which of the following?

I. 2
II. 3
III. 4
IV. 8

A) I and II only
B) I and IV only
C) II and IV only
D) I, II and III only
E) I, II and IV only

OA: D

The solution method is the following:
Sum of three integers = n+n+2+n+4= 3n+6
3n+6 is divisible by 2, 3, 4, but not by 8 for all n=(2,4,6,8...)

(the Source: Winners' Guide to GMAT Math - Part II)

Here is the second question:

Three consecutive even numbers are such that thrice the first number exceeds double the third by two, the third number is

a) 12
b) 6
c) 8
d) 10
e) 14

OA: e

The solution method is the following:
Let the three even numbers be (x-2), x, (x+2)
Then 3(x-2)-2(x+2)=2
3x-6-2x-4=2, x=2
The third number= 12+2=14 Hence: e

(the Source: Math Question Bank for GMAT Winners)

But there is there is one point I cannot understand:

The starting point of both questions is the same because they both deal with three consecutive even integers. This is why both solution methods can presumably be applied alternatively to each other.

In other words, both questions must be soluable regardless whether we take three consecitive even integers as n, n+2, n+3 or as (x-2), x, (x+2).
However, it does not work if we take (x-2), x, (x+2) as a starting point for the first question or if we take n, n+2, n+3 as a starting point for the second question.

Pls., can someone disprove my remark and give better explanation?