Clearing up some math concept

[OneTwoThreeFour]

I have a minor quibble I want to iron out. The problem is from OG pg. 312 #72

Is x > y ?

(1) x = y + 2
(2) x/2= y - 1

Correct answer is a

My question is approaching the second statement from a mathematically conceptual approach.
x/2= y-1 is also:

x= 2y-2

This means that x is a number that is 2 less than twice the value of y. Therefore, we don't have enough information to answer the question because it doesn't provide any direct relationship strictly between x and y.
On the other hand for the first statement, x will always be two greater than y. Thus, x has to be always greater than y no matter what the number x is. If we are never given any direct relationship between x and y, then it is impossible to conclude one is greater than the other. Is my reasoning valid?

[Night reader]

your deduction is correct
st(1) LHS[y+2] and [y]RHS, y+2>y ---> 2>0 Sufficient
st(2) x=2y-2, LHS[2y-2] AND RHS[y] and y>2? Or y<2? Not Sufficient

I have a minor quibble I want to iron out. The problem is from OG pg. 312 #72

Is x > y ?

(1) x = y + 2
(2) x/2= y - 1

Correct answer is a

My question is approaching the second statement from a mathematically conceptual approach.
x/2= y-1 is also:

x= 2y-2

This means that x is a number that is 2 less than twice the value of y. Therefore, we don't have enough information to answer the question because it doesn't provide any direct relationship strictly between x and y.
On the other hand for the first statement, x will always be two greater than y. Thus, x has to be always greater than y no matter what the number x is. If we are never given any direct relationship between x and y, then it is impossible to conclude one is greater than the other. Is my reasoning valid?

[OneTwoThreeFour]

Thanks again Night Reader! Best of luck on the next gmat!