I think that you may want to know approximate pKa values. Not memorize the list, but know about the groups you have used in class.
You might be able to organize by class of compound:
alcohol= around 15
sp carbon= around 25
sp2 carbon= about 50
sp3 carbon= greater than 50
carboxylic acid: usually 4 or less.
etc
Combining knowledge of relative base and acid strength is important to getting these questions right. You will always have the conjugate base of the strongest acid on the product side if the reaction is favorable. In other words, the molecule with the lowest pKa will exist in deprotonated form.
Stronger acid (lower pKa): most stable conjugate base. Strong acids have their dissociation ability because the conjugate base can stabilize a negative charge and therefore have decreased reactivity compared to the conjugate base of a weaker acid.
Weaker acid (higher pKa): not so good at stabilizing negative charges. Therefore, the conjugate base is more reactive and can do deprotonations more effectively than the conjugate base of a stronger acid.
When you have problems like this, look at the protonated species on each side of the reaction equation. If there is a stronger acid on the reactant side, the reaction goes as written. If the stronger acid exists on the product side, the reaction is disfavored and will not go as written.
I hope this helps.