This is not a 1 mole this way or other way, you are allowed mole fractions... Calculation of the final concentrations is sometimes difficult, but given initial concentrations of all substances, reaction stoichiometry and K value always possible.
Let's assume we started with equilibrium mixture containing four substnces - A, B, C, and D. let's assume they react
A + 2B <-> C + 2D
(this is your example, I just don't want to use original substances, as values we will use are not correct).
Further let's assume - like you stated - that initially we had 1 mole of each substance, and mixture was at equilibrium. Finally, to make things simple, let's assume it all happens in 1L, and we are dealing with concentrations, not partial pressures of gases.
Initially all concentrations equalled 1, so
K = [A][ B]2 / [C][D]2 = 1
Now, we remove all C. According to LeChatelier's principle A and B reacts, producing C and D. How much reacted? Let's say x A reacted. If so, 2x of B reacted and x C was produced together with 2x of D (that's all from the reaction stoichiometry). So after equilbrium has been reached we have 1-x of A, 1-2x B, x C and 1+2x D. And we know that
K = [A][ B]2 / [C][D]2 = [1-x][1-2x]2 / [ x][1+2x]2 = 1
Solve for x - and you know new concentration of C and you can calculate new concentrations of everything...