Let $n$ be a positive integer and $s(n)$ be defined as the sum of digits of $n$. Also, let $$q(n) :=\frac{s(2n)}{s(n)}.$$If $a$ is the smallest possible value of $q(n)$ and $b$ is the biggest possible value of $q(n)$, then enter $100(a + b).$
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Tags: number theory, sum of digits, Digits
Let $n$ be a positive integer and $s(n)$ be defined as the sum of digits of $n$. Also, let $$q(n) :=\frac{s(2n)}{s(n)}.$$If $a$ is the smallest possible value of $q(n)$ and $b$ is the biggest possible value of $q(n)$, then enter $100(a + b).$