There are n consecutive positive integers, what is the value of n?

Dear petrified17,

I'm happy to respond.

My friend, I believe something about the way the question is posted here is flawed. I don't know whether there was a copying mistake or whether the flaw is in the source. The problem is that the two DS statements must be consistent with each other. It may be that there is only one numerical possibility or several, but it can't be the case that no numerical value of n can possibly work with both statements. In other words, regardless of whether we can compute the value of n from the statements, it absolutely must be true that the question writer has at least one value of n in mind that consistently works throughout the whole question. This is the deep flaw in this question: as this stands, this is not a valid question.

You see, consider any case of n consecutive numbers in which four numbers are divisible by n. We would have to have four consecutive multiples of 4, which would have a difference of 12 from each other. Say, we go from 32 to 44, which has exactly four numbers divisible by 4 {32, 36, 40, 44}. In that range, we have at least four divisible by 3: {33, 36, 39, 42} and possibly more if we include 45 and/or 30. There is absolutely no way we could have only three numbers divisible by 3 if we have four numbers divisible by four. The two statements, as they stand now, are inconsistent, and this makes the question invalid.

Is it possible that the question was mistyped?

Mike