Distortion of a signal consisting of two periodic components
The question is trying to make you understand Aliasing

The low-pass filter is introduced (as a hint) to imply that the output is band-limited to half the Sampling frequency (Why ? See below for aliases).
This would allow you to understand how out of band signals can sneak into your sampled signals if left unchecked. Look at p5 here

You should read in detail about sampling.
Skipping the real math, as rule of thumb you can do as below to answer your questions quick


  a) for $f_0=1\,\text{kHz}$ the signal cannot be reconstructed


Once you sample your signal with a rate you create aliases at frequencies 
$\pm f_{signal}\pm n*f_{sampling}$
where n can take any positive value

If you calculate all combinations for all your frequencies you end up with
[100 400 600 900 1100 1600 1900 2100 2900 ...]

Since you'd sampled with 1000Hz, and are using an (ideal) LPF at 500Hz, you'd take all components from the set above between [0-500Hz] in which case you end up with [100 400].

Do you see the 400Hz odd man out here?This is termed as the alias of the 600Hz signal.

So, for an input of [100 600] and you end up with [100 400].


  b) for $f_0=1.3\,\text{kHz}$ reconstruction works


Repeat steps above.

You'll find that the only components between [0-650Hz] are [100 600].

There you go !