Dear Manhattan GMAT instructors
I am struggling with the following problem (Source: The Princeton Review, 1,037 practice questions, 2012; quant diagnostic question 11):
The force of gravity between two objects in space is directly proportional to the product of the masses of the objects and indirectly proportional to the square of the distance between them. I fate distance between two objects is doubled, by what percent must the product of the masses increase if the force of gravity is to remain the same?
(A) 50%
(B) 100%
(C) 200%
(D) 300%
(E) 400%
According to the solution key, the correct solution is (D). I get to (E) though.
What am I missing in my attempt? If
G = Force of gravity
M1 = Mass object 1
M2 = Mass object 2
D = Distance
G = M1 * M2 = 1/d^2
if i now double the distance --> 2d --> my new equation is 1/4d^2 = x * M1 * M2 and then I get to x = 4 in order to keep G constant an get back to my original equation
Thanks
BK