% / word problem GMAT P1

[smallsorrow]

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

1)100% decrease
2)50% decrease
3)40% decrease
4)40% increase
5)50% increase

[scoobydooby]

option 4

let rate be R, or R=(A^2)/B
B increased by 100% indicates B doubled or B2=2B1, rate has to be kept constant

A1^2/B1=A2^2/B2
A1^2/B1=A2^2/2B1, rearranging
A2^2/A1^2=2B1/B1=2
or A2/A1=sq rt 2/1
or A2=sq rt 2*A1
(A2-A1)/A1*100=(sq rt 2*A1-A1)/A1=(1.414-1)/1*100=41.4% (positive)
hence option 4: 40% increase

[raunekk]

imo:D

40% increase..

LEt concentration of A (Ca)= 10 and conc. of B(Cb) = 5

acc. to question rate R = Ca^2/Cb = 100/5 = 20

now B conc. doubled = 10

thus to reach a rate R as close as 20,we need A to be around 200...

so, if we take Ca=14 , R = 196 / 10 = 19.6 = 20 (approxi)

Thus % change = (14 - 10)/ 100 = 40 % increase.

i hope this helps..