It's not necessary to calculate which reaction had a bigger shift since the question is asking to compare the two reactions based on equilibrium constants. Calculating the shift depends on the initial concentrations and using ICE tables, but that's time consuming for the MCAT.
In both reactions, Cl2 is a reactant. Le Chatelier's principle tells us that adding Cl2 to the reaction would shift the reaction in the forward direction (producing more products). However, how much Cl2 is consumed depends on how large the equilibrium constant is.
The equilibrium constant K can be viewed as a ratio of products to reactants with the exponents representing the stoichiometric coefficients in the reaction (
The Equilibrium Constant).
So K = [products] / [reactants].
K > 1 means the equilibrium favors the products while K < 1 means the equilibrium favors the reactants. K being close to 1 means the equilibrium is balanced between reactants and products. You can view balanced equilibrium reactions as something like 50-50 since the reaction doesn't favor strongly to either side.
Reaction 1 has K = 1.95. That's greater than 1 so it favors the products but it's still relatively close to 1. What this means is adding Cl2 to the reaction would favor the products to the extent that slightly more than 50% of Cl2 gets consumed in the process (because the equilibrium is essentially still balanced between reactants and products rather than favoring extremely to one side).
Reaction 2 has K = 2.1*10^4. This is much larger than 1 so the reaction heavily favors the products. This means that adding Cl2 to the reaction will essentially get entirely depleted to favor the products and this reaction is strongly one-sided in the forward direction.
Since Reaction 2 has a much larger equilibrium constant than Reaction 1, adding Cl2 will cause the greatest shift in Reaction 2.
