There's a formal, "right" explanation which is probably described in the book. I'll let someone else describe that because I'm too lazy to write it all out right now. But here are some tips.
The overall goal is to balance the sum of atomic numbers before and after the radiation (i.e. balance the atomic numbers on the left and right side of the rxn). Likewise for mass numbers.
Alpha decay is the only way you can change the mass number. So if you see radioactive decay where the mass number changes, you can be sure that alpha decay happened.
All beta decay/emission changes only the atomic number and never the mass number. So if it asks about beta emission, ignore the mass number and look for changes in atomic number (identity of element).
Example: Na-22 undergoes some type of beta emission (beta +, beta -, or electron capture). If the question asks, "what is the daughter nucleus" you can cross out anything that doesn't have a mass of 22.
If the number of protons go up (atomic number increases), it's B- decay (regular "beta emission").
Example: Cs-137 undergoes beta emission. What is the daughter cell? It's a type of beta emission, so the mass number is 137. We cross out all answers on the MCAT that doesn't have a mass of 137. Since it's B- decay, we look for the answer that increases the proton number by 1.
Electron capture and B+ decay do the same thing.
Gamma radiation does not change number of protons or neutrons. Thus, atomic number and mass number stay the same.
Disclaimer: I don't know if the elements I described in the examples are actually radioactive or undergo the decay that I talked about. I just wiki'd examples, but didn't double check.
Also, you should know which ones convert protons to neutrons because the MCAT may ask about proton:neutron ratio.
