GMAT Prep - Directly proportional

[crackgmat007]

The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of B present. If the concentration of chemical B is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?

A) 100% decrease
B) 50% decrease
C) 40% decrease
D) 40% increase
E) 50% increase

OA - D

This question was already discussed, but I want to confirm if there is something wrong with my approach. Please let me know if I am missing something? This is how I solved.

Given,

The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present

R/A^2 = c

proportional to the concentration of B present.

R * B = C

If the concentration of chemical B is increased by 100 percent

2B --> to maintain the constant, we need to divide R by 2, hence

R/2 * 2B = C

which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?

(R/2)/A^2 must be equal to c. Can someone explain next steps? Tx much.

[ghacker]

Ur taking the direct proportionality as an indirect one

Rate = K [A]^2

and Rate = K'/

Or Rate = R[A]^2/

So this means

R[A']^2 /[2B] = R[A]^2/

or [A'] = root2*[A]

[A'] = 1.41[A]



so its a 40% increase