Subject 1 Find the numbers of the form $\overline{a b c}$ which, when divided by $\overline{b c}$, give a quotient of 4 and a remainder of $\overline{b c}-8$
## Solution and Scoring

Write $\overline{a b c}=4 \cdot \overline{b c}+\overline{b c}-8$

$\overline{b c}=25 \cdot a+2$

$25 a+2<100=a<4$

$a=1 \Rightarrow \overline{b c}=27$ $1 \mathrm{p}$

$a=2 \Rightarrow \overline{b c}=52$

$a=3 \Rightarrow \overline{b c}=77$

$\overline{a b c} \in\{127,252,377\}$

$1 \mathrm{p}$