How many numbers between $1$ and $200$ are divisible by exactly two of $3$, $9$, and $27$?

$\mathrm{L}=\mathrm{x}+\mathrm{y}$, where $\mathrm{x}$ and $\mathrm{y}$ are prime numbers. Which of the following statements are true?

I. The unit's digit of $\mathrm{L}$ cannot be $5$.
II. The unit's digit of $\mathrm{L}$ cannot be $0$.
III. L cannot be odd.