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The price of a car was m dollars. It then depreciated by x%.
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29 Apr 2019, 01:55
29 Apr 2019, 01:55
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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) \(\frac{3m}{4}\)
(B) \(m\)
(C) \(\frac{4m}{3}\)
(D) \(\frac{3m}{2}\)
(E) \(2m\)
(A) \(\frac{3m}{4}\)
(B) \(m\)
(C) \(\frac{4m}{3}\)
(D) \(\frac{3m}{2}\)
(E) \(2m\)
Re: The price of a car was m dollars. It then depreciated by x%.
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06 May 2019, 07:04
06 May 2019, 07:04
1
1
y=100x/100-x.
by condition,
{(100+(100x/100-x)} m(100-x/100)=100n
By calculation, we get n=m.
So, B
by condition,
{(100+(100x/100-x)} m(100-x/100)=100n
By calculation, we get n=m.
So, B
Re: The price of a car was m dollars. It then depreciated by x%.
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13 Aug 2020, 12:32
13 Aug 2020, 12:32
1
Carcass 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) \(\frac{3m}{4}\)
(B) \(m\)
(C) \(\frac{4m}{3}\)
(D) \(\frac{3m}{2}\)
(E) \(2m\)
(A) \(\frac{3m}{4}\)
(B) \(m\)
(C) \(\frac{4m}{3}\)
(D) \(\frac{3m}{2}\)
(E) \(2m\)
Choose \(m = 100\), \(x = 25\)
\(y =\) \(\frac{25}{(1-25/100)}\)
\(y =\) \(\frac{25}{(3/4)}\)
\(y = 25 * \frac{4}{3}\)
\(y = \frac{100}{3}\)
\(y = 33.3\)
\(y = \frac{1}{3}\)
So \(m\) depreciates by 25%. That means:
\(100(1-\frac{1}{4})\)
\(100(\frac{3}{4})\)
\(100(\frac{3}{4})\) is the price after the depreciation. We're keeping this the way it is, and you'll see why next.
After the depreciation, the new price appreciated by y%. This means that:
\(100(\frac{3}{4})(\frac{4}{3})\) =
\(100\).
So in the end, the price never changed.
The answer is B
