We have positive integers $a,$ $b,$ and $c$ such that $a > b > c.$ When $a,$ $b,$ and $c$ are divided by $19$, the remainders are $4,$ $2,$ and $18,$ respectively.

When the number $2a + b - c$ is divided by $19$, what is the remainder?
To find the remainder when $2a + b - c$ is divided by $19$, I need to use the properties of modular arithmetic. That means I can work with the remainders of $a,$ $b,$ and $c$ instead of the actual numbers, since they are equivalent modulo $19$. So, I can write $2a + b - c \equiv 2(4) + 2 - 18 \pmod{19}$. Combining the terms, I get $2a + b - c \equiv -8 \pmod{19}$. So, the remainder is $-8 + 19 = 11$. 