8. An office building was sold in 2018 for P dollars, resold in 2019 for 20% more, then decreased by x% in 2020 and sold for P again. What is x?
Answer: C
x is 25%
The percentage decrease, x, in 2020 that led the office building to be sold for the original price P again is 25%. This is derived from the sequence of price changes over the years.
A) 10
If x were 10%, the sale price in 2020 would be calculated as follows: starting with the 2019 sale price of P multiplied by 1.2 (for the 20% increase), then decreasing that by 10%. This would result in a final price of P * 1.2 * 0.9 = P.08, which is not equal to P. Thus, 10% is incorrect.
B) 20
If x were 20%, the final sale price in 2020 would be calculated as follows: taking the 2019 sale price of P multiplied by 1.2 and then reducing it by 20%, leading to a final price of P * 1.2 * 0.8 = P.96. This does not equal P, making 20% incorrect.
C) 25
When x is 25%, the calculation would proceed with the 2019 sale price of P multiplied by 1.2, and then decreased by 25%. The final price would be P * 1.2 * 0.75 = P, confirming that a 25% decrease brings the price back to the original amount P, thus making this option correct.
D) 30
If x were 30%, the final sale price would be computed by taking the 2019 price of P multiplied by 1.2 and reducing it by 30%. This leads to a calculation of P * 1.2 * 0.7 = P.84, which is not equal to P. Therefore, 30% is incorrect.
Conclusion
The correct answer is 25% because it successfully adjusts the inflated sale price back to the original amount P after a series of increases and decreases. The other options fail to revert the sale price to P, demonstrating that they do not satisfy the conditions of the problem.