4.Determine the numbers $\overline{a b c}$ such that:

$$
2 \cdot(\overline{a b}+\overline{b a})+2^{c}=67
$$

## Note:

- All subjects are mandatory;
- Working time: 2 hours.


## Solutions for 5th grade:




直接输出了翻译结果，保留了源文本的换行和格式。
4.If $\mathrm{c}=0$ then $2 \cdot(\overline{a b}+\overline{b a})=66 \Rightarrow \overline{a b}+\overline{b a}=33 \Rightarrow$

$\Rightarrow 11(a+b)=33 \Rightarrow a+b=3$.

Since $a$ and $b$ are non-zero, we get: $a=1$ and $b=2$ or $a=2$ and $b=1$.

Therefore, the numbers are: 120 and 210.

If $c \neq 0$, then $2^{c}$ is an even number and since $2 \cdot(\overline{a b}+\overline{b a})$ is also an even number, their sum cannot be 67.