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javzprobz wrote:Hi Brent,

I would appreciate it if you answer these two questions.

First one: In the video 12 of Integer Properties, you mention one useful rule for divisors. "If jk is a divisor of N, then j is a divisor of N and k is a divisor of N."

Just a few days ago, I came across this DS question, which belongs to Manhattan:

"Is n divisible by 108? 1)n is divisible by 12 2)n is divisible by 9 "

I started solving this q by saying that statement 1 is insufficient and statement 2 is also insufficient, then I said wait a minute if I consider both statements together, I can say that if n is divisible by j and if n is divisible by k, then n is divisible by j*k too.

So, I said since 12*9 is equal to 108, then the answer to the above question should be C!

However, when I read the answer explanation for this q, I saw that the correct answer is E. The explanation said that from the q we can get this, "is n=(2^2)*(3^3)*?", and from the first statement we can get this, "n=(2^2)*3*", and from the second statement we can get this, "n=3^2". The explanation said that when combining statement 1 and 2, we can't say with certainty whether the 3 factor in the first statement is one of the two 'threes' in the second statement or it is a new 3. If it is a new 3, then n will be divisible by 108. But if it is not a new 3 (meaning it is one of those threes in the second statement), then we're not sure whether n is divisible by 108. Hence E. While I really understand the given explanation by Manhattan, I would like to know whether I used that 'Divisor Rule' in the video 12 in a wrong way to get to C or if there's a sort-of limitation or consideration when using that divisor rule.

And my second question is that, again, somewhere in Manhattan I saw this DS question:

"Is p an odd integer? 1)p^2 is odd 2)root(p) is odd"

I solved this question by saying that OK p^2=p*p=odd and we know that only the product of 2 odd numbers can be odd, so p should be odd. And root(p)*root(p)=p, since root(p) is odd and odd*odd=odd, then p should be odd. Hence D. But the given correct answer was B! Sorry, I couldn't find any explanations for that B answer. Maybe the given answer by that expert was just a mistake. Do you think my way of solving this super easy question is OK and my answer is correct?

Thank you so much in advance.