The price of a certain house went down 40 percent. By what percent does the new price have to be increased in order to bring it back up to the original price?
A. \(20\%\)
B. \(33 \frac{1}{3} \%\)
C. \(40\%\)
D. \(60\%\)
E. \(66 \frac{2}{3} \%\)
The OA is E
Source: Manhattan Prep
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Solution:
We can let the original price of the house be $100, and the new price is $60 after the price decrease of 40%. To bring $60 back to $100, we can create the following equation, where x is the percent change:
60(1 + x/100) = 100
1 + x/100 = 100/60
x/100 = 5/3 - 1
x/100 = 2/3
x = 2/3 * 100 = 66 ⅔
Answer: E
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