In this particular style of question they are not going to ask you to calculate fuel required and then work out minimum ballast fuel. Those two activities are testing separate areas of knowledge. The fuel required is going to be irrelevant anyway since min ballast fuel exam questions are invariably going to be where the aircraft is outside the aft limit at ZFW.
So, in this situation you can either:
- fix the problem with hard ballast only
- fix the problem with ballast fuel only
- fix the problem with a combination of both.
If you use hard ballast alone, you will most certainly find you either bust the max ZFW limit or the compartment limit (i.e. the nose locker). You could solve the problem with ballast fuel alone, but the problem wants minimum ballast fuel so that is not an option.
The last solution is going to be the most likely situation in the exam.
First, you will move the CofG forward as much as possible with hard ballast up to either the compartment or ZFW limit then look at how much ballast fuel you need to bring the aircraft the rest of the way to the aft limit. Once the problem is solved at ZFW, adding the fuel required for the trip is only going to move the CofG forward anyway so who cares
Cheers,
Rich