GMAT Question 13

The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 100%, which one of the following is the closest to the percentage 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

Solution:
Let the rate of the reaction be R
 Let concentration of chemical A be A
 Let concentration of chemical B be B 
Then R is proportional to A²
R is also proportional to 1/B
Hence, R is proportional to A²/B
If C is a constant, R=C*(A²/B)
 If the concentration of B is increased 100% B becomes 2B ( B+(100/100)*B = 2B)
 Let A2 be the new concentration of chemical A for the rate to be constant
Then R=C*(A²/B) = C*(A2²/(2*B))
Hence, A² = A2²/(2) So A = A2/√2
 A2 = √2 * A = 1.41 * A
Hence A becomes 1.41 * A
If the concentration of B is increased 100% 
So, there is a 41% increase in A.
 Answer is D