Data Sufficiency

If ab = 1, what is the value of (axb)(ayb)?
(1) ax = by = 2
(2) 2xy = 4

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.

I understand that what the question is really asking is what is the value of xy?

(2) Clealy states what xy is equal to, so it if sufficient. What about (1). If ab=1 then ab could both be equal to 1, or a 1/2 and b 2 or a 1/3 and b 3 and so on and so forth. The value of xy changes with every combination of x and y that multiplied equals 1. For example, if a=1/3 and b=3 then for ax=2 x=6 and for by=2 y=2/3. 6x2/3 equals 4. This is the same when a=1/4 and b=4 and so on. (1) xy=4 and in (2) xy=2. They are different. How come the answer is D?

Thanks for your help.

If ab = 1, what is the value of (axb)(ayb)?
(1) ax = by = 2

let's rewrite the original expression as:

(ax)(ba)(yb)

based on statment (1), we know that ax=2 and yb = 2. Based on the original info, we know that ba=1.

So, (ax)(ba)(yb) = 2*1*2 = 4

This is from Official Guide: DS Qn 89

If @ represents one of operations +.- and x, is k@(l+m) = (k@l) + (k@m) for all numbers k, l, m?

1. k@1 is not equal to 1@k for some numbers k.
2. @ represents subtraction.

The answer says D.

--- However i see that the above expression would hold good for multiplication and not subtraction or addition.

Can someone please explain if I am missing somthing here?