Answer
a) Yes
b) $\Delta t=7.1y$
c) The person is 23 years old and his sister is 24 years old.
Work Step by Step
(a) Yes, it is possible due to the phenomenon of time dilation that you are younger than your sister who stays at home.
(b) We know that
$\Delta t=\frac{\Delta t_{\circ}}{1-\frac{v^2}{c^2}}$
We plug in the known values to obtain:
$\Delta t=\frac{1y}{\sqrt{1-\frac{(0.99c)^2}{c^2}}}$
$\Delta t=7.1y$
(c) It is given that the age of the person when he leaves his home is $22y$ and his sister's age is $17y$.
When he returns home, his age is $22y+1y=23y$
and his sister's age is $17y+7y=24y$.
Thus, the person is 23 years old and his sister is 24 years old.
