# The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A. GMAT Explanation, Video Solution, and Additional Practice!

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 rate unchanged?

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

Almost everyone gets this one wrong or at least struggles the first time around. That said, there’s almost no work to do. It’s all about parsing the given information and understanding the question.

## Define the question

Which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged? Let’s think about what that actually means. Concentration of chemical B is increased and we want to cancel out the resulting change with some change in A. OK, conceptually not so bad.

## Setup

So B is getting doubled. What do we need to do to A to stay in the same place? The chemical reaction increases by the square of A and decreases by B. So we most certainly need an increase in the concentration of A. With that we can cancel any decreases, A, B, and C.

But, of course, we can do better than that.

Let’s set up an equation with the given information:

A^2/2 = 1

Yeah, it’s that basic. If the concentration of chemical B is increased by 100 percent that means that the rate of the certain chemical reaction is halved or divided by 2. Why? Because be is inversely proportional. Chemical A works in the opposite direction but it is squared.

So the question is, what must A be in order to make the fraction equal 1 (reaction rate unchanged)?

## Solve

Let’s go ahead and solve:

A^2 = 2

A = √2

√2 is approximately 1.4. So A in order for the reaction rate to remain unchanged the concentration of A must be multiplied by 1.4 or increased by 40%.

Choose D.

## Additional challenging algebraic translation percent change example questions

This one is similar but different. I think it’s a good one to connect here because GMAT tutoring students tend to get stuck in the same way. It also relies on a very basic equation setup. Once you’ve got the equation, for the most part the follow through is very easy: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is