Proportion Question

[fangtray]

The rate of a certain chemical reaction is directly porportional 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%, 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

I used the plugging in method, and i ended up with 50% increase. but that is wrong.

[neelgandham]

The rate of a certain chemical reaction is directly porportional 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%, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?

Rate is directly proportional to ((CA)^2) / (CB), i.e

Rate of Chemical Reaction= K * ((CA)^2) / (CB), where K is a constant and CA, CB are concentration of chemical A and B respectively.

Rate of Chemical Reaction One = K * ((CA)^2) / (CB)
Rate of Chemical Reaction two = K * ((p*CA)^2)/(2CB), where p = Percentage of CA
Since Rate of Chemical Reaction One = Rate of Chemical Reaction two
K * ((CA)^2) / (CB) = K * ((p*CA)^2)/(2CB)
Implies, p^2 = 2
p = 1.414.

So it is a 41.4% Increase ~ 40% Increase

p.s: In a hurry hence the crappy notes, let me know if you need any further help!

[GMATGuruNY]

I posted a solution here:

https://www.beatthegmat.com/the-rate-of- ... 60321.html

[Anurag@Gurome]

The rate of a certain chemical reaction is directly porportional 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%, 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

I used the plugging in method, and i ended up with 50% increase. but that is wrong.

Rate of a certain chemical reaction, R, is directly proportional A²/B
When the concentration of chemical B is increased by 100 percent, then concentration of chemical A also increases by, say, a%.
Then, R = A²/B = (aA)²/2B
A²/B = a²A²/2B
1 = a²/2
a² = 2
a = 1.4, which means there is [spoiler]40% increase[/spoiler] in the concentration of chemical A.

The correct answer is D.