Help with drill

[BlasP747]

Hello everyone

I'm checking divisibility drills and came across the following question:

If a and b are integers and a > b > 1, which of the following could not be a multiple of a or b?
A) a-1
B) b+1
C) b-1
D) a+b
E) ab

Now, from my point of view it is asking whether a or b could be a multiple, which means that is conditional (sometimes yes, sometimes no) valid for each of a or b (not necessarily both)

Manhattan says that the correct answer is C, however I have to differ. Here is my train fo thought:

1. We choose a=3 and b=2, respecting the initial premise of a>b>1 (3>2>1) and these are the translations:

A) a-1= 3-1=2 (2 is a multiple of b=2)
B) b+1=2+1=3 (3 is a multiple of a=3)
C) b-1=2-1=1 (by definition 1 is a multiple of every number)
D) a+b=3+2=5 (5 is not a multiple of 3 or 2, but if we choose a'=4 b'=2 -> a+b=4+2=6, 6 is a multiple of b'=2)
E) ab=2*3=6 (6 is a multiple of b=2)

From my point of view this question has no valid answer. It is true that with other numbers on a and b, c) becomes invalid, but the question is asking which one could not be, and so D) could also not bee valid for some numbers

Please share you point of view on the matter, I would really appreciate it (perhaps I'm missing something)

Thanks

[Sage Pearce-Higgins]

Please could you quote the source of this problem? If it's not a GMAT Prep problem, please repost in the relevant folder and I'll answer it asap.