You have more than the mass number,
You know that the atom is sodium.
That tells you that the atom has 11 protons and 11 electrons.
Your atom contains 11 electrons, 11 protons, and 12 neutrons.
Your diagram might look something like this:
You can't solve the problem if you really have the mass number only.
The same mass number often corresponds to several isotopes of different elements, having different numbers of protons, neutrons and electrons.
For example, if your mass number is 50, you may have
Titanium 50: 22 protons, 28 neutrons, 22 electrons
Vanadium 50: 23 protons, 27 neutrons, 23 electrons
Chromium 50: 24 protons, 26 neutrons, 24 electrons
These are three stable atoms representing respectively the 5.4 %, 0.25% and the 4.3 % of natural distribution of the three elements.
In the example you gave with sodium you didn't know "just the mass number A", but also the atomic number Z, i.e. the element (sodium) with its characteristic number of protons.
You can find other cases of diads or triads of stable atoms belonging to different elements with the same A, from this graph by searching two or three black dots aligned in a descending diagonal.