Bunuel wrote:
The price of a car was m dollars. It then depreciated by x%. Later, it appreciated by y% to n dollars. If there are no other changes in the price and if \(y = \frac{x}{1 - \frac{x}{100}}\), then which one of the following must n equal?
(A) 3m/4
(B) m
(C) 4m/3
(D) 3m/2
(E) 2m
Here's my approach
Setting up the problem algebraically:
\(m * ( 1- \frac{x}{100})*( 1+ \frac{y}{100}) = n\)
We know:
\(y= \frac {x}{1- \frac {x}{100}}\)
So we can substitute for \(y\):
\(m * ( 1- \frac{x}{100})*( 1+ \frac{\frac {x}{1- \frac {x}{100}}}{100}) = n\)
\(m * ( 1- \frac{x}{100})+ ( 1- \frac{x}{100})(\frac {x}{1- \frac {x}{100}}*\frac {1}{100}) = n\)
\(m * ( 1- \frac{x}{100})+ (x*\frac {1}{100}) = n\)
\(m * 1- \frac{x}{100}+ \frac {x}{100} = n\)
Some maths later:
\(m = n\)