Which of the following reaction goes farthest to completion?

A. K = 10^2

B. K = 10^-2

C. K = 10

D. K = 1

higher the equilibrium constant , fastest the rate of reaction to completion. 
for understanding this concept let see one example .
A + B ⇄ C + D 
Equilibrium constant , K = [C][D]/[A][B] 
For fastest completion of reaction numerator of RHS will be higher the denominator . Means higher the numberator , higher will be equilibrium constant and higher will be rate of reaction to completion.

Hence, here option (A) is correct. Because equilibrium constant in case of (A) is higher than other