Volume change inside a balloon upon decreasing the the outer pressure
The relationship between pressure and volume is given by Boyle's Law.
$$\mathrm{P}_1\mathrm{V}_1 =  \mathrm{P}_2\mathrm{V}_2$$

      P       V
     0.199    11.41
     0.20     11.35
     0.201    11.29 

     1.0      2.27


So yes, you're right. Using Boyle's Law, the volume should be more than 11.35L so the pressure stays below 0.20 bar. 



However this doesn't make real world sense. When you blow up a balloon, as the pressure increases the volume increases.

Edit - Thanks @Mithoron here is a version of the problem that works...


  
    A balloon is filled with hydrogen at room temperature (25 C) and pressure (1.00 bar) to a volume of 2.27 L in a chamber. The pressure in the chamber is then reduced isothermally. The balloon will burst when the pressure in the chamber is reduced to 0.200 bar. What will the volume of the balloon be just as it explodes?