[tex]\displaystyle
4) \\
2x+7y=77~~~~~\text{ x si y sunt cifre} \\
2x = 77 - 7y \\ \\
x= \frac{77-7y}{2} \\ \\
x= \frac{7(11-y)}{2} ~~~~\text{Acum dam valori lui y.} \\ \\
\text{Pentru a se imparti la 2, y trebuie sa fie cifra impara.} \\
\text{Solutia 1: } \\
y=9 ~~\Longrightarrow~~ x=\frac{7(11-9)}{2} = 7 ~~\Longrightarrow~~ \overline{xy} = \boxed{79} \\ \\
\text{Solutia 2:} \\
y=7 ~~\Longrightarrow~~ x=\frac{7(11-7)}{2} = 28~~\text{Nu e cifra} [/tex]
[tex]\displaystyle \\
5) \\
\text{Descompunem numarul 118 in cele doua numere prime: } \\
118 = 2 \times 59 \\
\text{Suma lor } = 2 + 59 = \boxed{61 } \\ \\ \\
6) \\
10^{2014}+2015 = 1\underbrace{0000000....000000}_{2014 ~zerouri} +2015 = \\ \\
= 1\underbrace{0000000....00}_{2010 ~zerouri} 2015 \\ \\
\text{Suma cifrelor acestui numar este } = 1 + 2 + 1 + 5 = 9 \\
\Longrightarrow~~\text{Numarul este divizibil cu 3} \\ \\
\Longrightarrow~~\text{Restul } = \boxed{0}[/tex]
