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Number theory Difficulty 1.5 Junior Find the answer Canada

When a positive integer $n$ is
divided by $10$ , the remainder is
$8$ . When $n$ is divided by $5$ , the remainder is

Pick one

Solution

Given that $n$ has a remainder
of $8$ when divided by $10$ , then $n$ is $8$ more than a multiple of $10$ .

This means that $n$ has a units digit
of $8$ , which is $3$ more than a units digit of $5$ , and thus $n$ has a remainder of $3$ when divided by $5$ .

We may confirm that examples of numbers that are equal to $8$ more than a multiple of $10$ , such as $8$ , $18$ , $28$ , $38$ , do indeed leave a remainder of $3$ when divided by $5$ .

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.