percent-ratio: chemical properties

[smohsin]

Can anyone please help in solving the following:

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 Chemical 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 unchnaged.

Ans: 100% decrease, 50% decrease, 40% decrease, 40% increase or 50% increase.

[KeyserSoze525]

What's the answer?

[smohsin]

The GMAT prep says - 40% increase

[KeyserSoze525]

I think I figured it out.

If the rate varies by A^2 and 1/B then the rate is equal to:

R = A^2/B or R = A/sqrt(B)

If you increase B by 100% or double it:

R = A^2/2B or R = A/sqrt(2B) or R= A/sqrt(2)*sqrt(B)

In order to maintain the rate, A needs to be multiplied by sqrt(2)

so an increase of sqrt(2) (approx. 1.41) = 40% increase.