If \(p\) and \(q\) are consecutive positive integers, is \(p\) a multiple of 3 ?
(1) \(q\) is not a multiple of 3.
(2) \(q - 1\) is not a multiple of 3.
The question is easy; however, I have a doubt in relation to the number 0. Should we consider 0 a multiple of 3? I think we should because a multiple of an integer is that integer multiplied by other integer. So , if 0 is that other integer, \(3 x 0 = 0\); thereofore, 0 is a multiple of 3. In other words, 0 would be a multiple of every number.
But I don't know whether it is the reasoning of the GMAT. Or, do they consider only positive multiples? In other words, they don't consider 0 "the other integer" to create a multiple. If they think in that way, how is the answer for this question affected?
For example, in statement (2), could \(q\) be 1? In that sense, \(q-1\) would be 0, and if they only consider positive multiples, \(q-1\) would not be a multiple of 3.
I know that the answer to my question is not necessary to solve this problem, but I prefer to solve that doubt for future problems.
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