You can do this problem very quickly without doing any math. If you look closely at the problem, you'll see that the equation is simply a weighted average of 10 and 20.
x/(x+y) + y/(x+y) will equal 1 --> x/(x+y) + y/(x+y) = (x+y)/(x+y) = 1
So we can simplify this equation by saying x/(x+y) = X and y/(x+y) = Y where X + Y = 1. This now writes 10X + 20Y = k. This is the weighted average equation above. Since X + Y = 1 and X and Y are both positive, they will both be percentages and k will be between 10 and 20.
Since we know that x < y, we know that Y has to be greater than 50%. This also means that k has to be between 15 and 20. The only answer that fits that description is D.
Taking the GMAT Again...PhD this time!
October 2008 Score: GMAT - 750 (50 Q, 41 V)
Manhattan GMAT 1 - 11/20/11 - 750 (50 Q, 42 V)
Manhattan GMAT 2 - 12/3/11 - 780 (51 Q, 45 V)
