Finding the remainder of a division

Question

$75$ is the remainder of $X$ divided by $132$. What is the remainder of $X$ divided by $12$? I know the answer is $3$ but how do we get that answer?

Answer 1

If $X=132y+75$, $y$ is integer. Then $X=12*(11y)+6*12+3=12(11y+6)+3$. Therefore the remainder of the division by $12$ is $3$.

Answer 2

Hint: if you have a remainder of $75$ when you devide $X$ by $132$, then this must mean that $X=132q+75$ for some integer $q$.....

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Full answer: So we know that $X=132q+75$. Next we wonder what will happen if we devide $X$ by $12$...
Well, we'll get something like this:$$\frac X{12}=\frac{132q+75}{12}=\frac{132q}{12}+\frac{75}{12}$$$132q=12\times11\times q $, so this leaves us with no remainder. $75=12\times6+3$, which leaves us with a remainder of $3$.

So in conclusion $X$ has a remainder of $3$ when devided by $12$.