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I read a question on mathematics.I have not been able to figure out the answer.

the question is

given a set $Q=\{1,2,3,4,5,6,7\}$ such that I can have a subset $L$ from this set $Q$. I have been given a number string $Y$ in such a way that I know its starting digit and the end digit.

Now the rest of the digits from second digit to the last but one digit can be have any numbers of digits from the subset $L$.

Now the question how can i decide whether $Y$ can be made divisible by $3$ or $7$.

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    I'm not sure if this is what you're looking for, but there's a pretty simple test for divisibility by 3. Namely, $3|Y \Leftrightarrow $ the sum of the digits in $Y$ is divisible by 3.So as long as you choose elements from $L$ that make $Y$ satisfy this condition, you'll be fine. There's another test for 7 though it's more complicated. Is this in the right direction or have I misunderstood?2012-05-06
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    This might help: http://en.wikipedia.org/wiki/Divisibility_rule2012-05-06
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    It might be useful to know that 1001 is divisible by 72012-05-06

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