Bunuel wrote:
The price of a certain property increased by 10% in the first year, decreased by 20% in the second year, and increased by 25% in the third year. What was the amount of the dollar decrease in the property price during the second year?
(1) The price of the property at the end of the third year was $22,000.
(2) The decrease in the property price over the first two years was $2,000 less than the increase in the property price during the third year.
Solution
Step 1: Analyse Question Stem
• Let us assume that originally, the price of the property was $x
o The price of the property in the first year \(= 1.1x\)
o The price of the property in the second year \(= (1.1)*(0.8)*x \)
o The price of the property in the third year \(= (1.1)*(0.8)*(1.25)*x\)
• We need to find the amount of decrease (in dollars) in the property for the second year.
o Or, we need to find the value of \(1.1x -(1.1)*(0.8)*x = 1.1*0.2*x …….Eq.(i)\)
So basically, we need to find the value of x to find the amount of decrease (in dollars) in the property for the second year.
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: The price of the property at the end of the third year was $22,000.
• According to this statement: \((1.1)*(0.8)*(1.25)*x = 22,000\)
o We can find the value of x from the above equation and substitute it in Eq.(i) to find the required amount.
Hence, statement 1 is sufficient and we can eliminate answer Options B, C and E.
Statement 2: The decrease in the property price over the first two years was $2,000 less than the increase in the property price during the third year.
• According to this statement: \(x - (1.1)*(0.8)*x + 2000 = (1.1)*(0.8)*(1.25)*x -(1.1)*(0.8)*x\)
o \(⟹ x [(1.1)*(0.8)*(1.25) – 1] = 2000\)
We can easily solve the above equation to find out the value of x and then we can substitute the value of x into the Eq.(i) to find the required amount.
Hence, statement 2 is also sufficient.
Thus, the correct answer is
Option D. _________________