For 2.24, try writing $10a + b$ like $7k + (3a + b)$ for some integer $k$. This way both $10a + b$ and $3a + b$ have the same remainder when dividing by $7$.

On 2.28, for part (a) try to use repeatedly that $\gcd(a,b) = \gcd(b-a,a)$. For (b), let $d = \gcd(a,b)$ and $e = \gcd(r,a)$; then show that $d \mid e$ and $e \mid d$, so $e = d$.

For 2.29, try rewriting $\overline{abcd} + \overline{bcde}$ using place values. Use this to write $\overline{abcd} + \overline{bcde}$ in the form $11k + m$, and then find conditions for the digits $a$, $b$, $c$, $d$, and $e$.