问一道PREP的数学题

暗绯莎

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 persent, 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

其实我连题目都没怎么看懂，答案是D。。。

感觉PREP的数学比GWD的难很多啊。。。大家是不是那么觉得的？

切尔西

我搜索了个解释，你可以看下，一下来自www.urch.com
This question really isn't as nasty as it looks. Let's work it out together.

GMAT Prep Tells Us that a certain chemical reaction rate is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present.

This can be written as rate of chemical reaction = A^2/B.

A^2/B is simply the ratio of chemical A to chemical B that must be maintained to keep this reaction rate unchanged.

So the question asks:

"If the concentration of chemical B is increased by 100%, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?"

This means we are now going to have two rates: R1 and R2

R1 = the original ratio of the chemical reaction = A^2/B
R2 = a variation of this ratio in which B is doubled = A1^2/B(2)

So now we have two distinct linear equation:

Where A^2/ B = A1^2/B(2). Remember we need to solve for A.

So step by step:

A^2 * 2B/ B = A1^2 (Multiply 2 B by both sides)

A^2 * 2 = A1^2 (Cancel the two "B"s)

A * sqrt 2 = A (Take the square root of both sides of the equation.)

So the question asks us: "which of the following is closest to the percent change in the concentration"

sqrt 2 is approximatiely 1.4. Therefore 1.4 * A = the percent change in A.

This equals a 40 percent increase.