Data Sufficiency

Please Help! I am having trouble figuring out this problem..


The answer is D.

Let's say X is the rate of the chemical reaction and k is some constant. The relationship described between X, A, and B can be represented by:

X = k * A^2 / B

If we increase B by 100% -- in other words, double B to 2B -- by how much would we need to increase A by in order to keep the chemical reaction rate the same? Let's use n to represent that increase factor on A:

X = k * (nA)^2 / (2B)

Setting these equal to each other, we can cancel a bunch of stuff and solve for n (which is what we're after):

k * A^2 / B = k * (nA)^2 / (2B)
k * A^2 / B = k * n^2 *A^2 / (2B)

1 = n^2 / 2
2 = n^2
n = sqrt(2) ~= 1.4

A must be increased to 1.4 A or, in other words, a 40% increase.

Rey

great, thanks!